binary black hole mergers, had they occurred, would destroy such a spike (see [15], [16], [17]). 

However an alternative and more conservative scenario is cusp regeneration. This cannot occur directly in the dark mat- ter because its relaxation time is extremely long. However, this is not the case for the central stars, and once a cusp forms in the stars, scattering of dark matter particles o ff of stars can redistribute the dark matter in phase space on a time scale of order the relatively short star-star relaxation time [18], result- ing in a ρ ∝ r − 3 / 2 density cusp in the central parsec of the dark matter [19]. 

Sterile neutrinos would form such a dark matter cusp, al- though the spike density is limited by phase space considera- tions for non-degenerate neutrinos (see, [20]). Using the val- ues of the velocity dispersion for the Milky Way of 100 km / s [21] and a sterile neutrino mass of 17.4 keV, we find a limit on the density ρ$_{cr}$ < 1 . 4 × 10$^{9}$M$_{⊙}$ / (pc$^{3}$). This would guarantee a point-like source if there is indeed a cusp. 

We have found that there is an excess in the intensity in the 8.7 keV line observed from the Galactic center over the the- oretical value expected for the intensity in the FeXXVI Ly γ line. This intensity excess equals (1 . 1 ± 0 . 6) × 10 − 5 ph / (cm 2 s), where the errors are at the 90% confidence level. We show that this excess cannot be explained by means of standard ioniza- tion and recombination processes, since the ratio of the fully stripped (FeXXVII) to FeXXVI ion fractions becomes (un- physically) negative in the temperature range of (5 keV, 15 keV), when the observed ratio of FeXXVI Ly γ to FeXXVI Ly α iron lines is applied. 

We suggest that a physically acceptable explanation of the intensity excess in the 8.7 keV line is due to decays of ster- ile neutrinos that that are in a halo of dark matter around the Milky Way. The dark matter density profile we adopt is obtained by numerical simulations [9]. The dark matter mass from the Milky Way dark matter halo within the field of view of the Suzaku observation is small compared with 

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## IV. CONCLUSIONS 

the total mass of the dark halo ≃ 10$^{12}$M$_{⊙}$, however it su ffi ces ≃ 2 . 5 × 10$^{6}$M$_{⊙}$ to produce a significant flux (1 . 1 ± 0 . 6) × 10 − 5 ph / (cm 2 s) via decays of sterile neutrinos. 

Nearby low surface brightness dwarf galaxies have a central dark matter density as high as 〈 ρ 〉 ∼ 5M$_{⊙}$ / pc$^{3}$(200GeV / cm$^{3}$) and are consistent with a common mass scale of ∼ 10$^{7}$M$_{⊙}$ [22] and even a universal dark matter profile with a limiting central dark matter surface density of log(r$_{0}$ ρ$_{0}$ ) = 2 . 15 ± 0 . 2 , in units of log(M$_{⊙}$ / pc$^{2}$) . [23]. The corresponding density is well within the phase space constraints for 17 keV sterile neutrinos. 

One explanation of the common mass scale is that dark mat- ter haloes do not exist at lower masses. Warm dark matter particles have large enough free streaming lengths to erase all density fluctuations that might have formed lower mass halos if the mass of the warm dark matter particle is approximately 5 keV for a minimum halo mass of 10$^{7}$M$_{⊙}$. In the present case, the mass of such sterile neutrinos is 2 × 8 . 7 = 17 . 4 keV. The minimum halo mass scale is approximately 10$^{5}$M$_{⊙}$. Note that the actual dwarf masses could extend to lower values than evaluated at the 300 pc scale by [22]. 

We estimated the mixing angle of sin$^{2}$(2 θ ) = (4 . 1 ± 2 . 2) × 10 − 12 from the excess in the intensity and the decay rate is found to be decay rate: Γ = (9 . 0 ± 4 . 8) × 10 − $^{28}$s − $^{1}$. These values lie in the allowed region of the mixing angle and decay rate parameter space for a dark matter sterile neutrino with a mass of 17-18 keV (see [12]). Sterile neutrinos in this region of mass, decay rate and mixing angle parameter space can contribute significantly to dark matter. Such neutrinos wou ld be virtually indistinguishable from cold dark matter except in the lowest mass dwarf galaxies where cores would be formed. High resolution x-ray observations should reveal a point-like line source of comparable strength to the Suzaku line excess if a cusp is present around the central black hole. 

We are grateful to Kwang-il Seon and Vladimir Dogiel for valuable discussions. 

arXiv:0906.1788 

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## ACKNOWLEDGMENTS 

