text:
\section{Introduction}
White dwarf (hereafter WD) is the end point of the stellar evolution of a progenitor with
a mass of $M\leq8M_{\odot}$,  and  for over 97\% of all stars.
There are WDs with a  strong magnetic field in the range of $B_s\sim 10^{3}-10^9$G, which has been determined by the polarization and/or Zeeman splitting, and the WD belonging to this
class is called  a {\it magnetic WD} (Ferrario et al. 2015). The first magnetic WD, Grw+$70^{\circ}$8247 with
$B_s=100-300$MG, was reported in the 1970s (Kemp et al. 1970; Angel et l. 1985),
and it  is located about ~13{\rm pc} (43 lt-yr)  away. The number of the
magnetic WDs is rapidly increased by the Sloan Digital Sky Survey (SDSS; York et al.
2000; Kepler et al. 2013). The WD catalog
based on  the SDSS DR7 (c.f. Kleinman et al. 2013)
includes $19713$ WDs, in which  $\sim  12831$ is the
hydrogen atmosphere WD (called DAs). Among the DAs listed in SDSS-DR7,
Kepler et al. (2013) measured  the Zeeman splitting from $\sim 4\%$ (521) of
all  DAs observed and estimated
the surface magnetic field at  $B_s=1\sim 700$MG. In the SDSS DR10, Kepler
et al. (2015) discovered 9089 new WDs, including 206 magnetic WDs.
  Although the volume density of magnetic WDs  is still unknown, these observations would suggest that $5-10$\% of the WDs are magnetic
  WDs (Sion et al. 2014; Kepler et al 2015). The space density of the WDs  estimated as $5\times 10^{-3}{\rm pc^{-3}}$ by the
  direct measurement of local WDs (Holberg 2002 and references therein)
  suggests that a large number of the magnetic WDs are existing in the galaxy.

  A magnetic WD is observed as an isolated system or a binary system, and the highly magnetic WD is
  found in the binary system, which is known as
cataclysmic variable (hereafter CV). The CVs usually accrete matter on the WDs
 from the late-type  main-sequence companion through Roche lobe overflow, and
the magnetic CVs comprose $\sim 20$\% of all CVs
($\sim 1100$ CVs; Ritter \& Kolb 2010).  The magnetic CV is mainly
 divided into two groups, that is, polar and intermediate polar system (IP).
The WD of the polar has a surface magnetic field of $B_s>10$MG, which is
sufficiently large to lock the two stars into synchronous rotation with the orbital period ($P_{obs}\sim 100-500$minutes, Ferrario et al. 2015).
 The WD in the IP has a  smaller surface magnetic field
$B_s\sim 0.1-10$MG than that in the polar. The magnetic field of WDs
is not sufficient to lock the companion into the synchronous rotation, and the
spin of the WD is observed with a shorter period than the orbital period.
Both polars  and IPs emit X-rays owing  to accretion
of the matter from the companion on the WD's surface.

Since the synchronous rotation of two stars in polar, there is no angular momentum
of the accreting matter relative  to the WD, and the formation of the accretion disk is prevented.
For the IPs, the accretion disk can present, and the angular momentum
 transfer by the disk matter will spin up the magnetic WD.
The accretion process on the  compact object is discussed with  the so-called co-rotation radius, $r_{co}=(GM_{WD}P_{WD}^2/4\pi^2)^{1/3}$,  where the WD's spin frequency is  equal to the disk rotation frequency
(Keplerian frequency), and the Alfven radius, $r_M=3\times 10^{10}\dot{M}_{16}^{-2/7}M_{WD,1}^{-1/4}\mu_{WD,33}^{4/7}$cm (Frank et al. 2002),
 where the magnetic pressure of the WD is equal
to the dynamic pressure of the accretion disk.  Here $M_{WD}$ is
the mass of the WD,
 $M_{WD,1}=M_{WD}/M_{\odot}$, $\dot{M}_{16}$ is the accretion rate in units of
 $10^{16}{\rm g~s^{-1}}$ and $\mu_{WD,33}$
is the dipole moment of the WD in units of  $10^{33}{\rm G~cm^{3}}$.
When $r_{M}<r_{co}$, the inner edge of the accretion disk can enter
inside the co-rotation radius and the disk matter can accrete
onto  the compact object. Then, the condition of the accretion through the disk
may be written down as $\dot{M}_{16}\ge P_{WD,h}^{-7/3}\mu_{WD,33}^2M_{WD,1}^{-49/24}$, where  $P_{WD,h}=P_{WD}/1{\rm hour}$.

Some  WDs in the IPs are rapidly rotating with a period
$P_{WD}<100$s (Ferrario et al. 2015, and reference therein): $P_{WD}=33.1$s
 for AE~Aquarii (AE~Aqr), 70.8s  for DQ~Her, and  67.6s for V455~And.
For those magnetic WDs, an accretion rate close to the  Eddington rate
$\dot{M}_{E}\sim 10^{20}{\rm g/s}$ is necessary to satisfy the condition ($r_M<r_c$)
 for  the formation of the accretion disk.
However, the  time-averaged rate of the  mass transfer from the companion
 is observed with $\dot{M}_{16}=1-100$ (Patterson 1994) for those systems,
suggesting  that these systems  will not contain the disk,  and probably
the matter from Roche lobe directly streams  toward the WD surface, or most of the matter from the companion
is centrifugally ejected (propeller phase).  In fact,
the Doppler tomography profile of the AE~Aqr
(e.g. Wynn et al. 1997) indicates that the AE~Aqr
is in the propeller phase (Ikhsanov et al. 2004).  Moreover,
the pulse timing study of the AE~Aqr revealed that the WD is spinning down at a
rate of $\dot{P}_{WD}\sim 5.64\times10^{-14}$ (de Jager et al. 1994),
 corresponding to a spin-down luminosity of
 $L_{sd}=I(2\pi)^2\dot{P}_{WD}/P_{WD}^3\sim 6\times 10^{33}I_{50}{\rm erg/s}$, where
 $I_{50}$ is the WD's moment of inertia in units of $10^{50}{\rm g~cm^2}$. Because of the low
mass accretion rate with the high spin-down rate, the AE~Aqr has been considered
as the first WD pulsar candidate that operates the mechanisms of the neutron star (NS)
pulsar-like particle acceleration and the non-thermal radiation process in the magnetosphere.

The mechanism of the  NS pulsar-like particle acceleration
in the magnetosphere of  the magnetic WD has been discussed
 by several authors (Usov 1988; Ikhsanov  1998; Kashiyama et al. 2011).
 In the model, an electron (or a positron) that  emerged from the polar cap region is accelerated by an
 electric field parallel to the open magnetic field lines. The electric potential difference
across the open field lines is estimated by
\begin{equation}
V_{a}=(2\pi)^2\frac{\mu_{WD}}{2c^2P^2_{WD}}\sim 6\times 10^{13}
\left(\frac{\mu_{WD}}{10^{34}{\rm Gcm^3}}\right)\left(\frac{P_{WD}}{33{\rm s}}\right)^{-2}
{\rm static Volt},
\end{equation}
which can accelerate the electron up to
$\gamma_{max}\sim eV_{a}/m_ec^2\sim 10^8\mu_{WD,34}(P_{WD}/33{\rm s})^{-2}$. This relativistic electron emits the nonthermal photon via the curvature radiation process with a  characteristic energy of
\begin{equation}
E_{\gamma}=\frac{3}{4\pi}\frac{hc\gamma^3}{R_c}
\sim 200{\rm MeV}\left(\frac{\gamma}{10^8}\right)^3
\left(\frac{P}{33{\rm s}}\right)^{-1}
\left(\frac{R_c}{\varpi_{lc}}\right)^{-1},
\end{equation}
where $R_c$ is the curvature radius of the magnetic field line and $\varpi_{lc}=cP_{WD}/2\pi$
is the light-cylinder radius. Kashiyama et al. (2010) discussed
 the mechanism of the NS pulsar-like pair-creation process in the magnetic WD magnetosphere
as the possible  source of the cosmic-ray electrons and positrons. Although very high energy emission (de Jager 1994) and nonthermal X-ray emission (Terada et al. 2008) from
AE Aqr were reported, the observational  view on the  WD pulsar has  not been
firmly established.  In section~\ref{discuss}, we will discuss the NS pulsar-like high-energy emission process
of the magnetic WD.

New discovery of the pulsed radio/optical/UV emission from AR Scorpii (hereafter AR~Sco) sheds light on the nonthermal nature of the magnetic  WD  (Marsh et al. 2016).
AR~Sco is the IP with an orbital period of  $P_{o}\sim 3.56$hr, and it  is composed of
an M star ($M_2\sim 0.3M_{\odot}$ and $R_2\sim 0.3R_{\odot}$)  and a magnetic WD.
The interesting properties of the emission from AR~Sco
are the nonthermal,  pulsed, and highly linearly polarized emission.
The radio/optical/UV emission modulates periodically on a period of
$P\sim 1.97$minutes, which is thought to be  the spin period of the magnetic WD. The double-peak structure of the pulse profile and the morphology of the linear
polarization (Buckely et al. 2017) in the optical bands are
resemble to those of the Crab pulsar, which is the isolated young NS pulsar and emits the electromagnetic waves in radio to high-energy TeV bands (Kuiper et al. 2001; Kanbach et al. 2005; Takata et al. 2007). Moreover, the optical emission also modulates on the orbital period (3.56hr), which will reflect the heating of the
dayside of the companion star by the interaction of the magnetic field/radiation
by the WD. The modulation of the optical emission from the companion
star with the orbital motion is also similar to that of the millisecond
NS pulsar/low-mass star binary system (Fruchter et al. 1988; Kong et al. 2012).

AR~Sco's broadband electromagnetic spectrum in radio to X-ray bands is characterized by the synchrotron radiation from the
relativistic electrons, indicating
the acceleration process in the magnetosphere of the WD. As pointed out by Geng et al. (2016), on the other hand, the number of
the particles that emit the observed
nonthermal optical emission of AR~Sco is significantly larger than the number that can be supplied by the WD itself. This
suggests that the synchrotron-emitting electrons are supplied from the companion star's surface, and the acceleration process is different from that of the NS pulsar. Geng et al. (2016) suggested an electron/position beam from
the WD's polar cap sweeping the stellar wind from the companion star, and a bow shock propagating into stellar wind accelerates the electrons in the wind.

Geng et al. (2016) discussed the emission due to the interaction between the companion star
and the WD's open magnetic
field lines that extend beyond the light cylinder ($\varpi_{lc}=5.6\times 10^{11}$cm),  and hence
assumed that the WD is a nearly perpendicular rotator. In this paper,
we investigate another possibility that the electrons accelerated around the
companion stellar surface are trapped by the close magnetic field lines of
the WD.  The injected electrons  from the stellar surface are accelerated at the vicinity  of the companion star and  initially
travel toward the WD's surface along the magnetic field line.
We will solve  the evolution
of the pitch angle of such electrons  under the effects of the
synchrotron radiation energy-loss and the first adiabatic invariance. In section~2, we will describe our model and the basic equation for the motion
of the trapped electrons. We also discuss
the direction of the emission by the
relativistic electrons to calculate the light curve.  In section~3, we will
show our results  and discuss the mirror effect of the electron's motion.
We al show the model  pulse profile in optical and X-ray bands.
In section~4, we discuss the particle acceleration and the high-energy emission
from the outer gap accelerator of the WD in AR~Sco and will calculate
the expected fluxes of the curvature radiation process and
the inverse-Compton scattering (hereafter IC) process.

\section{Theoretical Model}
\subsection{Energy injection}
In this section, we will discuss the emission model for the observed radio/optical/X-ray emission from AR~Sco.  The WD's magnetic field lines sweep periodically across the surface of the companion star. The strength of the magnetic field of the WD at the surface of the companion star will be of the order of
\begin{equation}
B_{WD}\sim 195\left(\frac{\mu_{WD}}{10^{35}{\rm G cm^3}}\right)\left(\frac{a}{8\cdot 10^{10}{\rm cm}}\right)^{-3}{\rm G}.
\end{equation}
The modulation of the optical emission with the orbital period ($\sim 3.56$hr) indicates that the spinning  of the secondary star is synchronized with the
orbital motion. With such a rapidly spinning M star, the stellar dynamo
 process can generate a polar magnetic field of several kG (Reiners et al. 2009). A magnetic interaction between the WD and M star will cause the magnetic reconnection or ohmic dissipation, and the dissipated  magnetic energy will be used for
 (1) the heating  of the M star surface, (2) acceleration of the electrons, and (3) outflow  from the M star.

The magnetic interaction will produce an azimuthal component
($\delta B_{\phi}$) of the magnetic field  of the WD, and its pitch
$\eta=\delta B_{\phi}/B$ may increase  at $\eta\rightarrow 1$
before the magnetic field becomes unstable against  the magnetic
dissipation process. In this model, we estimate the power of the magnetic
dissipation as (Lai 2012; Buckley et al. 2017 and references therein)
\begin{eqnarray}
L_{B}&=&\frac{\eta B^2}{8\pi}(4\pi R_2^3\delta)\Omega_{WD} \nonumber
\sim 2.8\times 10^{32} {\rm erg/s} \nonumber \\
&\times &\left(\frac{\mu_{WD}}{10^{35}{\rm G~cm^3}}\right)^{2}
\eta \left(\frac{\delta }{0.01}\right)\left(\frac{R_2}{3\cdot 10^{10}{\rm cm}}\right)^3 \left(\frac{a}{8\cdot 10^{18}{\rm cm}}\right)^{-6}
\left(\frac{P_{WD}}{117{\rm s}}\right),
\label{injection}
\end{eqnarray}
where $\Omega_{WD}=2\pi/P_{WD}$,  $R_2$ is the radius of the  M star, and $\delta\sim 0.01$ is the skin depth (see  Buckley et al. 2017).

The magnetic interaction on the companion surface  may eventually cause an ablation of
the matter from the M star surface and  an acceleration of the electrons to the relativistic energy. The ablation of the companion star
 by the WD magnetic field could occur  if the binary is close enough so that
an energy deposition on the envelope of the stellar surface is high.
The ablation of the companion star by the deposition of the  electromagnetic
 energy is a common process for the millisecond NS  pulsar and low-mass
companion star binary, which is  called as  black widow/redback pulsars (Roberts 2013). In the black widow/redback systems, it has been observed that most of
the deposited energy on the stellar surface is converted into the  heating of
the companion star surface and/or the nonthermal radiation process, and
a tiny  fraction (0.1-1\%) of
 it is used for the ablation of the matter from the companion star
 (van den Heuvel \& Paradijs 1988; Cheng 1989).
 Since the mass loss  driven by the irradiation from the compact star has not been well understood,
 we introduce the efficiency factor $\chi$ for converting the dissipated energy
into the kinetic energy of the wind,
\begin{equation}
\chi=\frac{\dot{M}v^2_{esc}/2}{L_{B}}.
\label{chi}
\end{equation}
For the black widow/redback system, the efficiency factor has been estimated as $\chi\sim 0.01-0.001$.

In terms of the efficiency factor, we estimate the rate of the particles leaving from
the companion star surface as
\begin{eqnarray}
\dot{N}_p&\sim&\frac{\dot{M}}{m_p}=
\frac{\chi L_{B}}{\frac{1}{2}m_pv_{esc}^2} \nonumber \\
&\sim &5\times 10^{40}\chi\left(\frac{L_{B}}{10^{32}{\rm erg/s}}\right)
\left(\frac{v_{esc}}{5\cdot 10^{7}{\rm cm/s}}\right)^{-2}{\rm /s},
\label{dotn}
\end{eqnarray}
where $v_{esc}=\sqrt{2GM_2/R_2}$ is the escape velocity,  with
$M_2(\sim 0.3M_{\odot})$ being the mass of the companion star. Because of the charge conservation, we assume  that  the number of the electrons that leave from
the stellar surface  and that are accelerated by the magnetic dissipation process is of
the order of  $\dot{N}_e=\dot{N}_p$.

In this model, we assume that most of the dissipated magnetic
energy is  used  for the acceleration of the electrons and/or the heating of the companion surface.
Hence, the typical Lorentz factor of the accelerated
electrons may be  estimated  to be
\begin{eqnarray}
  \gamma_0 &\sim& \frac{L_B}{\dot{N_e}m_ec^2}=\frac{m_pv_{esc}^2}{2\chi m_ec^2 }\nonumber \\
  &\sim& 50\left(\frac{\chi}{5\cdot 10^{-5}}\right)^{-1}
\left(\frac{v_{esc}}{5\cdot 10^{7}{\rm cm/s}}\right),
\label{lorentz}
\end{eqnarray}
where $\chi\sim 10^{-5}$ will be  chosen to fit the observed luminosity and SED  of AR~Sco.

\subsection{Motion of  trapped electron }
In AR~Sco, the light cylinder of the WD is $\varpi_{lc}\sim 5.6\times 10^{11}$cm, which is larger than the separation ($a\sim 8\times 10^{10}$cm) between two stars. Hence, the companion star
will interact with the close magnetic field lines of the WD, unless the WD is a nearly perpendicular rotator. As we discuss above, the magnetic interaction between the closed magnetic field of the WD and
the companion star will produce the pitch  $\delta B_{\phi}/B\sim 1$ for
the WD and will cause the magnetic reconnection/dissipation, which accelerates the electrons. After
sweeping across the companion star surface, the magnetic field line
of the WD will remain to  be closed, and the injected electrons may be trapped at the closed magnetic
field lines by the magnetic mirror effect. Since the radius of the gyration motion  of an electron
is much smaller than the size of the magnetosphere, $r_{gy}\sim 440{\rm cm}(\mu_{WD}/10^{35}{\rm G~cm^{3}})^{-1}(\gamma_0/50)$, we  ignore any drift
motion crossing the magnetic field lines in the {\it co-rotating frame} of the  WD, that is, in the laboratory frame,
the  trapped electron is co-rotating with the WD by the $\vec{E}\times \vec{B}$ drift,  and
it moves only  along the magnetic field line.

 We expect that the observed optical emission from AR~Sco is produced by the
electron with the typical Lorentz factor $\gamma_0\sim 50$ of equation~(\ref{lorentz}). With the typical Lorentz factor
$\gamma_0\sim 50$, on the other hand,  the time scale of the synchrotron  loss around the companion star is estimated as
\[
\tau_{syn}\sim 400{\rm s}\left(\frac{\mu_{WD}}{10^{35}{\rm G cm^3}}\right)^{-2}
\left(\frac{a}{8\cdot 10^{10}{\rm cm}}\right)^{6}\left(\frac{\gamma_0}{50}\right)^{-1},
\]
which is longer than the crossing time scale of $a/c\sim 2.5{\rm s}$. This
indicates that the injected electrons do not lose their energy around the
companion star, and  they  migrate into the
inner magnetosphere before the synchrotron energy-loss.
For the electrons moving toward the WD surface,
 the increase in the perpendicular momentum due to the first adiabatic
invariance competes with the decrease in it due to the synchrotron loss.

 The evolution of the Lorentz factor and the pitch angle
 along the magnetic field line under the synchrotron energy-loss and the first adiabatic invariance
 may be described by (Harding et al. 2005)
\begin{equation}
\frac{d\gamma}{dt}=-\frac{P_{\perp}^2}{t_{s}},
\label{gamma}
\end{equation}
and
\begin{equation}
  \frac{d}{dt}\left(\frac{P_{\perp}^2}{B}\right)=-2\frac{B}{t_s\gamma}
  \left(\frac{P_{\perp}^2}{B}\right)^2,
\label{perp}
\end{equation}
where $B$ is the local magnetic field strength, $t_s=3m_e^3c^5/(2e^4B^2)$,
and $P_{\perp}=\gamma \beta\sin \theta_p$ with $\beta=v/c$ and $\theta_p$  the
pitch angle. To solve above equations, we apply the pure dipole magnetic field of
\begin{equation}
\vec{B}=\frac{3\vec{n}_p(\vec{n}_p\cdot\vec{\mu}_{WD})-\vec{\mu}_{WD}}
{r^3},
\end{equation}
where $\vec{n}_p$ is the unit vector of the position. In this paper, $\alpha$ denotes the angle between the spin axis and the magnetic axis of the WD.

When  the synchrotron loss time scale is much longer than the crossing time scale, the perpendicular momentum of the electrons moving toward the WD surface from the companion star increases as
\begin{equation}
P_{\perp}(r)=\left(\frac{a}{r}\right)^{3/2}P_{\perp,0},
\end{equation}
where $P_{\perp,0}$ is the initial perpendicular momentum.
The magnetic mirror could  occur  at the point
\begin{equation}
r_m\sim a\sin^{2/3}\theta_{p,0}
\end{equation}
where $\theta_{p,0}$ is the initial pitch angle, provided that the crossing
time scale $\tau_{m,c}=r_m/c$ is shorter than  the synchrotron loss time scale
at $r_m$, $\tau_{m, syn}=3m_e^3c^5a^6\sin^2\theta_{p,0}/(2e^4\mu_{WD}^2\gamma_0)$.  From the inequality  $\tau_{m,syn}>\tau_{m,c}$, the critical
 initial pitch angle, above which
 the electron is subject to the magnetic mirroring,
 may be written as
\begin{eqnarray}
\sin\theta_{p,0}&>&\left(\frac{2e^4\mu_{WD}^2\gamma}{3m_e^3c^6a^5}\right)^{3/4} \\
\nonumber
&\sim&0.03\left(\frac{\mu_{WD}}{10^{35}{\rm G cm^3}}\right)^{3/2}
\left(\frac{\gamma_0}{50}\right)^{3/4}
\left(\frac{a}{8\cdot 10^{10}{\rm cm}}\right)^{-15/4}.
\end{eqnarray}

\subsection{Radiation Process}
\label{radiation}
Besides the IR/optical/UV emission, the AR~Sco is also observed in the X-ray
bands, and this will indicate that the   electrons with a Lorentz factor
 larger  than $\gamma_0\sim 50$ exist in the magnetosphere of the WD.
To explain the X-ray emission,  we assume that a process related to
 the magnetic dissipation on the companion star
 surface accelerates the electrons to the relativistic speed and  forms
 a power-law distribution of the electrons over  several decays in energy:
 \begin{equation}
f(\gamma)=K_0\gamma^{-p},~~\gamma_{min}\le\gamma\le\gamma_{max},
\label{distri}
\end{equation}
where we use $\gamma_{min}=\gamma_0$ of  equation~(\ref{lorentz}).
For the maximum Lorentz factor of the accelerated particle
is determined as the Lorentz factor at  which the synchrotron cooling timescale $\tau_s\sim 9m^3_ec^5/(4e^4B^2\gamma)$ is
 equal to the acceleration timescale  $t_a\sim \gamma m_ec/(\xi eB)$,
 yielding $\gamma_{max}\sim 8\times 10^6 \xi^{1/2}(\mu_{WD}/10^{35}{\rm Gcm^3})^{-1/2} (a/8\cdot 10^{10}{\rm cm})^{1/2}$, where $\xi<1$ represents the efficiency of the acceleration.  By assuming the power-law index of $p\sim 2.5$, which is a fitting parameter, we calculate the normalization ($K_0$) and the
  minimum Lorentz factor by solving  the conditions that
  $\int f(\gamma)d\gamma=\dot{N}_e$
  and $\int \gamma m_ec^2f(\gamma)d\gamma=L_{B}$.
 The spectrum of the synchrotron radiation at the photon energy $E_s$
is calculated from
\begin{equation}
P_{syn}(E_s)=\frac{\sqrt{3}e^2B\sin\theta_p}{hm_ec^2}F_{sy}\left(\frac{E_s}{E_{syn}}\right),
\end{equation}
where $h$ is the Plank constant, $E_{syn}=3he\gamma^2 B\sin\theta_p/(4\pi m_ec)$ is the typical photon energy, and $F_{sy}(x)=x\int_0^{\infty}K_{5/3}(y)dy$ with $K_{5/3}$ being the modified Bessel function of the order $5/3$.

\subsection{Radiation direction}
\begin{figure}[h]
  \centering
  \epsscale{1.0}
  \plotone{fig1}
  \caption{Schematic view of the AR~Sco system and the coordinate in the study. The observer is located
    within the plane made by the spin-axis (z-axis) and x-axis. The spin phase zero $\Phi_0$ is defined as when the magnetic axis points toward the observer. In the figure, the M star is assumed to be located
    at the plan by the spin axis and x-axis. The electrons are injected from the companion star by the
    magnetic field interaction.
    The star symbols represent position of the first magnetic mirror point of the electrons injected
    into the southern hemisphere.  The travel time to the first magnetic mirror point is shorter
    for the electron injected at $\Phi_0=0.5$ than those injected at $\Phi_0=0$ (see section~\ref{pulse}). }
  \label{wd}
\end{figure}
To investigate the expected modulation of the observed emission  with the WD's spin, we calculate the propagation  direction and the time of arrival (TOA)
of each emitted photon. For the coordinate system, we introduce the $z$-axis at the spin axis of the WD and also assume that the spin axis of the WD and orbital axis are aligned for
 simplicity. The $x$-axis is chosen  so that the observer is located at the
 first quadrant in the ($x,~z$) coordinate (Figure~\ref{wd}).
 The direction of the magnetic momentum $\vec{\mu}_{WD}$ (the magnetic axis)
 is inclined by $\alpha$ from the $z$-axis, and it is rotating around the $z$-axis.

For a high Lorentz factor, we can anticipate that the emission direction of the particles coincides with the direction of the particle's velocity. In the laboratory frame, the
unit vector of the electron motion that is co-rotating with the WD may be described by (Takata et al. 2007)
\begin{equation}
\vec{n}_e=\beta_0\cos\theta_p\vec{b}+\beta_0\sin\theta_p\vec{b}_{\perp}+\beta_{co}
\vec{e}_{\phi},
\label{emidi}
\end{equation}
where the first, second, and third terms on  the right-hand side represent
the motion along the magnetic field line, the gyration motion, and the co-rotation motion,
respectively. The value of the parallel speed $\beta_0$ in equation~(\ref{emidi})
at each point is calculated from the conditions that $|\vec{n}_e|=1$ and $\beta_{co}=\varpi/\varpi_{lc}$,
where $\varpi$ is the axial distance from the spin axis of the WD.
In addition, the vectors $\vec{b}=\vec{B}/B$, $\vec{b}_{\perp}$,
 and $\vec{e}_{\phi}$
are the unit vectors along the magnetic field line, perpendicular to the magnetic field line,
and in the azimuthal direction, respectively. The unit vector $b_{\perp}$ is defined by
\begin{equation}
\vec{b}_{\perp}=\cos\delta\phi_g\vec{k}+\sin\delta\phi_g\vec{b}\times \vec{k},
\label{gyration}
\end{equation}
where $\vec{k}$ is  any unit vector perpendicular to the magnetic field line
and $\delta\phi_g$  refers to the phase of the gyration motion.

The emission direction of equation~(\ref{emidi}) is interpreted
as  the  angle measured from the rotation axis, $\zeta=\cos^{-1}n_{e,z}$,
where $n_{e,z}$ is the component of the emission direction  along the
rotation axis and the  azimuthal angle $\phi$ measured from the $x$-axis.
 Since the observer is laid on the first quadrant of the plane made by the $x$-axis
and $z$-axis (Figure~\ref{wd}),  we
 pick up the photon traveling in the direction  $\phi=0$ to calculate the pulse profile.

The TOA  of the emitted photon measured on the Earth
may be expressed by
\[
{\rm TOA}=t_{\Phi_{0}}+\delta t_{emi}+\frac{D-\vec{r}\cdot\vec{n}_e}{c},
\]
where $D$ is the distance to the source.
The first, second,  and  third terms on the right-hand side represent
the time of the injection of the relativistic electron
into the WD magnetosphere, the travel time  of the electron to the emission
point after the injection, and the flight time of the emitted photon
from the emission point ($\vec{r})$ to the Earth, respectively. We can safely ignore the effect of the flight time due to the
orbital motion of the WD, since it will be  $\delta t \ll  a/c\sim 2{\rm s}$, which is much smaller than the
spin period. The TOA can be translated into
the spin phase of WD as
\begin{equation}
\Phi=\Phi_0+2\pi\frac{\delta t_{emi}}{P_{WD}}
-\frac{\vec{r}\cdot\vec{n}_e}{\varpi_{lc}},
\label{phase}
\end{equation}
where $\Phi$ is the spin phase at the detection of photon and $\Phi_0$ is
the spin phase at the injection of electrons. In this paper, we define $\Phi_0=0$ as the time when
the WD's magnetic axis is oriented in the plane made by WD's  rotation axis and the observer (Figure~\ref{wd}).  We note that the second term on the
right-hand side does not appear if the high-energy electrons are continuously injected on the
same magnetic field line with time, such as the high-energy emission from
the NS pulsar (Takata et al 2007). Moreover, since the main emission region
is  located at the position $r\ll a=8\times 10^{10}$cm, the third term on the right-hand side, $\sim r/\varpi_{lc}\ll a/\varpi_{lc}\sim 0.14$, is negligible, while  it is important
to produce the sharp pulse in the light curve of the high-energy emission from
the NS pulsar.

\section{Results}
\begin{figure}
\centering
\epsscale{1.0}
\plotone{fig2}
\caption{Trajectory of the electron calculated from  equations (\ref{gamma}) and (\ref{perp}).
 Top panel: evolution of Lorentz factor along the radial distance. Bottom
panel: evolution of Lorentz factor and perpendicular momentum ($P_{\perp}$)
as a function of time. The magnetic field of the WD
is assumed to be the pure dipole field with $\mu_{WD}=6.5\times 10^{34}{\rm G~cm^3}$,  and the magnetic axis is aligned with the spinning axis ($\alpha=0^{\circ}$). The electron with the pitch angle  $\sin\theta_{p,0}=0.1$ and the Lorentz factor $\gamma_0=50$ is injected
from $r/a=1$ ($t/P_{WD}=0$) and the equator.
The electron is trapped at the close magnetic field line
by the magnetic mirror.}
\label{traj}
 \end{figure}
\begin{figure}
\centering
\epsscale{1.0}
\plotone{fig3}
\caption{Same as Figure~\ref{traj}, but $\sin\theta_{p,0}=0.05$.
  The electron is not  trapped by the magnetic mirror. }
\label{traj005}
 \end{figure}

We treat the companion star as the point object located at
$r=a=8\times 10^{10}$cm and on the equator of the WD, for simplicity.
This  may be a rough treatment for this system,
 since the size of the companion star is not negligible
compared to the size of the orbital  separation.  However, we expect
that the main results discussed in this paper will not be modified even if
we take into account the size of the companion star. Under this assumption,
we evaluate the magnetic energy dissipation and the
injection of the electrons at the companion star.

 \subsection{Magnetic mirror effect}
 \label{mirror}
Figures~\ref{traj} and~\ref{traj005} represent the evolution
of the Lorentz factor and the perpendicular momentum ($P_{\perp}$)
calculated from  equations~(\ref{gamma}) and~(\ref{perp}).
 In the calculations, the electron with the initial Lorentz factor $\gamma_0=50$ and
the sine of the pitch angle $\sin\theta_0=0.1$ for Figure~\ref{traj} or $\sin\theta_0=0.05$
for  Figure~\ref{traj005} is injected toward the WD surface from $r=a=8\times 10^{10}$cm. We  assume
the magnetic dipole field with $\mu_{WD}=6.5\times 10^{34}{\rm G~cm^3}$ and the inclination angle of $\alpha=0^{\circ}$.

The top panel of Figure~\ref{traj} shows the evolution of the Lorentz factor as a function
of the radial distance and indicates that the injected electron is trapped at
$\sim 0.25<r/a<1$ by the magnetic mirror effect. At around $r\sim a$, the synchrotron cooling time scale is longer than the dynamical time scale $\sim a/c$, and the electron migrates toward
the WD with an almost constant Lorentz factor. As the dotted line in the bottom panel of Figure~\ref{traj} shows,
the perpendicular momentum $P_{\perp}$ increases with a time owing
to  the first  adiabatic invariance. Around the magnetic mirror point, where the pitch angle becomes
$\sin\theta_p\sim 1$, the synchrotron energy-loss increases, and it rapidly decreases  the Lorentz factor.
After the magnetic mirror,
the electron moves toward the outer magnetosphere
 with the synchrotron loss time scale longer than the dynamical time scale,
and hence the Lorentz factor is almost constant.
 Since the electron travels on the closed magnetic field lines,
it eventually moves toward WD's surface  in another hemisphere and is reflected back again by the magnetic mirror.
As Figure~\ref{traj} indicates, most of the initial energy
of the electron injected
 with  $\sin\theta_{p,0}=0.1$ is lost by the synchrotron radiation at the first magnetic mirror point.

For the smaller initial pitch angle of $\sin\theta_{p,0}=0.05$ in Figure~\ref{traj005},
the electrons can enter the  inner magnetosphere, and
the stronger synchrotron energy-loss prevents  the magnetic mirror.
The top left panel of Figure~\ref{skymap} represents the evolution of the
Lorentz factor as a function
of the time from the injection. The figure indicates that the electron injected
with the  small pitch angle of $\sin\theta_{p,0}=0.1$  (solid line)
radiates away all the initial energy within
a  timescale less than the  spin period, while for the electron
with a larger pitch angle
$\sin\theta_{p,0}=0.2$ (dashed line) and 0.5 (dotted line), the energy-loss time scale is longer
than the spin period of the WD.
\begin{figure}
\centering
\epsscale{1.0}
\plotone{fig4}
\caption{Sky map of observing  angle ($\zeta$) and spin phase ($\Phi$) for the
electron injected with the Lorentz factor $\gamma_0=50$ and
 the pitch angle $\sin\theta_{p,0}=0.1$ for the top right panel,
0.2  for the bottom left panel, and 0.5 for the bottom right panel.
 The brightness of the color represents the intensity of the
observed emission. The electrons are injected from $r=a$ and the equator at $\Phi_0=0$.
The top left panel shows the evolution of the Lorentz factor as a function of time. The dipole magnetic
field with  $\alpha=0^{\circ}$  is used for the calculation.
The effect of the gyration motion is taken into account in the calculation. }
\label{skymap}
 \end{figure}
\subsection{Formation of the pulse}
\label{pulse}
\begin{figure}[h]
  \centering
  \epsscale{1.0}
  \begin{tabular}{@{}cc@{}}
    \includegraphics[width=0.5\textwidth]{fig5-1} &
    \includegraphics[width=0.5\textwidth]{fig5-2} \\
  \end{tabular}
  \caption{Main panel: The relation between the phase of the injection
    of the electron ($\Phi_0$)
    and the spin phase of  the observed  emission from the first mirror point.
    The initial Lorentz factor
    and the pitch angle are given by $\gamma_0=50$ and $\sin\theta_{p,0}=0.1$, respectively.
    In addition, emission  from a specific gyration phase is calculated.
    Inset: sky map of $(\zeta,~\Phi)$. Emission from all gyration phases
    is included.}
  \label{phaser}
\end{figure}

Figure~\ref{skymap} shows  the sky map of the angle ($\zeta$) and the spin phase
 ($\Phi$)  for the emission from the electron injected at $\Phi_0=0$ with the Lorentz factor $\gamma_0=50$ and
the  pitch angle  $\sin\theta_{p,0}=0.1$ (top right),  0.2 (bottom left), and 0.5 (bottom right); the brightness of the color in the figure refers the observed intensity. With $\gamma_0=50$,
the electrons injected with $\sin\theta_{p,0}\ge 0.1$ are subjected  to the magnetic mirror,  as the top left panel of  Figure~\ref{skymap} indicates, and the synchrotron  energy-loss mainly occurs at the magnetic mirror point. Around the magnetic mirror point, the pitch angle of the electron is increased to  90 degree, and the gyration motion produces  the synchrotron beam that
covers the large region  in the angle $\zeta$, as we can see in Figure~\ref{skymap}.

As we can also see in Figure~\ref{skymap}, the sky map of the observed emission from one electron depends on the initial pitch angle.  For the injected
electron with
 $\sin\theta_{p,0}=0.1$ (see top right panel),
 since the most of the electron's energy  is radiated
away  at the first magnetic mirror point, and the synchrotron emission  at
subsequent magnetic mirror points is negligible. As a result, the emission from this electron can be mainly observed at narrow spin phase width.  For $\sin\theta_{p,0}=0.2$ (bottom left panel),
  the magnetic mirror point is located outside of that for $\sin\theta_{p,0}=0.1$, and hence  the synchrotron energy-loss at the first magnetic mirror is less than that for $\sin\theta_{p,0}=0.1$. As we can
  see, however, the emissivity at the first magnetic mirror point is still much  higher than
the emissivity at subsequent mirror points. In our model, therefore, the emission at the
first mirror point provides the  most contribution on the observed emission from the AR~Sco.

For the larger pitch angle with $\sin\theta_{p,0}=0.5$ (bottom right panel),
the electron is  trapped at $r\sim a$ and the time scale  of synchrotron
energy-loss is much longer than the spin period, as the dotted line in the
top left panel shows. The emission from this electron covers  almost the
whole sky,  and it may  be observed as a nonpulsed emission. Moreover,  such an
electron whose
cooling time scale is longer than the spin period will be absorbed by the companion star after one rotation of the WD and will not contribute much to the observed emission.

Since the WD is spinning,  the electrons will be injected on the different magnetic field lines
 at the different spin phases, that is,  $\Phi_0$ in equation (\ref{phase}).  We integrate the emission from all magnetic field lines
to compare with the observations.  As we discussed above,
the emission from the first magnetic mirror point of the injected electron mainly
contributes to the observation.  In such a situation,  we find that the structure of the
pulse profile   mainly depends on how the spin phase of the detected photon  ($\Phi$ in equation (\ref{phase}))
is related to the injected  phase $\Phi_0$.  If the  phase of the detection
$\Phi$  monotonically shifts with the phase of injection $\Phi_0$,
 the predicted pulse profile does not significantly modulate with the spin period.
 For example, the left panel in Figure~\ref{phaser} shows such a relation
 calculated with the magnetic inclination $\alpha=0^{\circ}$ and the  magnetic gyration phase $\delta\phi_g$ in equation~(\ref{gyration}); the small window in the figure shows the sky map of $\Phi$ and $\zeta$ with
 the contribution from the whole gyration phase.
 Because of the rotation  axisymmetric geometry
 of the magnetic field lines for  $\alpha=0^{\circ}$, the observed phase $\Phi$  monotonically
shifts with the injected phase $\Phi_0$, as the figure shows. As a result, the observed intensity  for $\alpha=0^{\circ}$ is the constant with the time for any viewing  angle $\zeta$.

For a large inclined rotator ($\alpha=60^{\circ}$), the phase $\Phi$ of the detected photon
from  the first mirror point does not monotonically shift with the phase of the injection
$\Phi_0$, as the line in  the right panel of Figure~\ref{phaser} indicates. We can
see in the figure that the photons emitted at
the first mirror point by  the electrons injected at $0<\Phi_0<0.2$ are  observed at a narrower width in the spin phase around $\Phi\sim 0.2$. In the sky map of $\Phi-\zeta$, therefore,
 the intensity at $\Phi\sim 0.2$ is  higher than the intensity at other phases,
 as the inset in Figure~\ref{phaser} shows. As a result, the observer with
 an appropriate  viewing angle $\zeta$ will  measure a significant
 modulation of the emission with the spin period of the WD.

The concentration of the detected photons at the narrower spin phase for the larger  inclination angle
can be understood as follows. In the present calculation for Figure~\ref{phaser},
 we inject the electron into the  southern  hemisphere of the WD's magnetosphere (Figure~\ref{wd}). At
 the companion star, the radial direction of the magnetic field of the WD
 depends on the spin phase.  For example, the radial direction at $\Phi_0=0$ (the magnetic axis points toward the companion)
 points to the outer  magnetosphere, while  at $\Phi_0=0.5$ it is directed
 toward the inner  magnetosphere (Figure~\ref{wd}). For the electron
injected at $\Phi_0\sim 0$, it initially moves toward the light cylinder and returns to the inner  magnetosphere along the closed magnetic field line, and therefore it takes a longer time, after
the injection,  to reach  the first magnetic mirror point than the electron that is injected at a  later time ($\Phi_0>0$).
This difference in the travel time to the first magnetic mirror point
causes an enhancement of the observed emission at the specific spin phase.
As we can see in the Figure~\ref{phaser}, the emission from the half-hemisphere makes
one high-intensity region in the sky map. As we expect, therefore,
the contribution from the  opposite  hemisphere creates another high-intensity region, which
separates $\sim 0.5$ spin phase. The observer  whose line of sight cuts through two bright
regions in the sky map will measure the double-peak structure in the light curve.

\subsection{Application to AR Scorpii}
\begin{figure*}
\centering
\plotone{fig6}
\caption{Light curve in 0.1-1eV energy bands as a function of the inclination angle ($\alpha$) and the viewing angle ($\zeta$). The companion star is located
  between the WD and the  observer (inferior conjunction), and
  the phase zero in each panel
  corresponds to the time when the magnetic axis points toward the observer.
  The light curve of two  rotations of the WD is represented in each panel. }
\label{light}
 \end{figure*}
\begin{figure*}
\centering
\epsscale{1.0}
\plotone{fig7}
\caption{Same as Figure~\ref{light}, but with 1-10keV energy bands.}
\label{lightx}
\end{figure*}
\subsubsection{Parameters and assumptions}
To apply the model to AR~Sco, we assume that  the magnetic interaction at the companion star injects the same number of the electrons  at the  northern
and southern hemispheres from the equator of the WD.
We represent the results with $\mu_{WD}=6.5\times 10^{34}{\rm G~cm^3}$, $\eta=1$, and  $\delta=0.01$ in equation~(\ref{injection})
and the efficiency $\chi=10^{-5}$ defined in equation (\ref{chi}).
 We fit the SED of the AR~Sco with $p=2.5$.
With these parameters, the minimum and maximum Lorentz factors are estimated
as $\gamma_{min}\sim 50$ and $\gamma_{max}\sim 5\times 10^6$, respectively.
Other important parameters are the inclination angle $\alpha$ and
the viewing angle $\zeta$ that affect the predicted pulse profile. As we have assumed,
the spin axis of the WD is perpendicular to the orbital plane, and the WD is rotating in the same sense
as the binary orbit of the companion.

 As we discussed in section~\ref{mirror}, the evolution of the Lorentz factor and the perpendicular momentum of the injected electrons depend on the initial pitch angle. The  distribution
 of the pitch angle of the particles for different  acceleration processes
 has been
investigated by
the previous authors (Achterberg et al. 2001;  Kartavykh et al. 2016), but it is still
under investigation with a more realistic situation.
In this study, therefore, we assume an isotropic distribution in the
initial pitch angle $\theta_{p,0}$, that is,
\[
\frac{d\dot{N}_e}{d\theta_{p,0}}={\rm constant}.
\]
We note that, in  our  model, the electrons that are
trapped at the close magnetic field line by the magnetic mirror are eventually
absorbed by the companion stellar surface after one rotation   of the WD.
In the calculation, we do not take into account the synchrotron self-absorption, which may be important for
the radio band (Geng et al. 2016).

\subsubsection{Pulse profile}
Figures~\ref{light} and~\ref{lightx} summarize the predicted pulse profiles in
optical (0.3-1eV) and X-ray (1keV-10keV) energy bands, respectively, at the inferior conjunction of the companion orbit, where the companion star is between the WD and the observer;
each panel  shows the pulse profile as a function of the magnetic inclination $\alpha$
and the Earth viewing angle $\zeta$. In addition, the each panel shows the
pulse profile in the two spin phases of the WD  with normalized intensity, and the  phase zero
 (and unity) corresponds to the time when the magnetic axis points toward the
observer (Figure~\ref{wd}).

We find that the model with a  smaller viewing angle predicts
a single pulse profile in the optical emission,
as Figure~\ref{light} indicates.
For the smaller inclination angle, the observer misses  the emission from
the half-hemisphere.
The optical/UV emission from AR~Sco has been observed as the pulsed emission
with the sharp double-peak structure in the light curve.
In the current model, the double-peak structure can be produced for  a larger magnetic inclination and a larger Earth viewing angle.
We note that  a larger viewing angle of the AR~Sco is  expected by the observed
orbital modulation of the optical emission from the companion star and by  a large amplitude of the modulation.

By comparing between Figures \ref{light} and~\ref{lightx}, we find that
 the  predicted X-ray pulse
 is broader and the light-curve structure
 is more complicate in comparison with
  the optical light curve.  In the current model,
  the X-rays are produced by the Lorentz factor of
$\gamma>10^4$, for which the synchrotron cooling time scale is comparable to or shorter
than the crossing time scale. Unlike the optical emission, therefore,
the emission region is not restricted at the first magnetic mirror, but it spreads to
a wide space in the WD's magnetosphere.

\subsubsection{Orbital evolution of the pulse profile}
\begin{figure*}
  \centering
  \epsscale{1.0}
  \plotone{fig8}
  \caption{Orbital evolution of the pulse profile in the optical bands. The black,
    blue, red, and green histograms show the pulse profiles at the inferior conjunction,
    descending note, superior conjunction and ascending node, respectively, of
    the companion orbit. The phase zero corresponds to the time when the magnetic
    axis points toward the Earth. The inclination angle and the viewing angle
  are $\alpha=50^{\circ}$ and $\zeta=65^{\circ}$, respectively.}
  \label{lighto}
\end{figure*}

\begin{figure*}
  \centering
  \epsscale{1.0}
  \plotone{fig9}
  \caption{Power spectrum of the Fourier analysis for the model light curve calculated with the time of
    the three orbits. Tot left: global power spectrum. Top right: local power spectrum at the fundamental frequency.
    Bottom left: local spectrum at around the first harmonic frequency. Bottom right: local spectrum at around
    the second harmonic frequency. The locations for the fundamental, first harmonic, and second harmonic
  for the spin and beat frequencies are indicated with the dashed lines in the panels.}
  \label{powerspe}
  \end{figure*}
As we discussed in section~\ref{pulse}, the pulse peaks are mainly made
by the emission of  the electrons injected when the magnetic axis of the WD
is laid within the plane made by the WD's spin axis and the companion star. Because
of the orbital motion of the companion, therefore, the spin phase of the pulse shifts
with the orbital phase.  The pulse profile
presented in Figures~\ref{light} and~\ref{lightx} assumes the geometry
in which  the companion star is located at the inferior conjunction of the companion orbit, where the companion  is between the WD and the observer. Figure~\ref{lighto} compares the pulse profiles of the optical emission  at the inferior conjunction, descending node, superior conjunction, and ascending node, respectively, of the companion orbit. The phase zero in all panels corresponds to the time when the magnetic axis points toward the observer. We can see the shift of the pulse peaks and the evolution of the peak intensity with the orbital motion of the companion. We can also see the evolution
of the pulse profile along the orbit.

By assuming that  the WD is rotating in the same sense as the binary orbit of the companion, we make  the time sequence of the calculated intensity for about one orbit and perform the Fourier analysis of it.
Figure~\ref{powerspe} shows the power spectrum for the global frequency
(top left), around the fundamental frequency (top right), around
the second  harmonic frequency (bottom left), and around the third harmonic frequency (bottom right).
In the figure, we can see the peak of the power spectrum around the beat frequency $\nu_B=(1/117{\rm s}-1/3.56{\rm hours})\sim 0.0085$Hz and its harmonics,
reflecting that the pulse peak monotonically shifts along the orbit.
In the figure, we also see that the first harmonic frequency has a stronger power, since the pulse profile has
a  double-peak structure.
These results are consistent with the power spectrum of the optical observations (Marsh et al.2016).

Marsh et al. (2016) reported no significant detection of the
pulsed emission in the X-ray bands. It could be due to the shift of the
pulse peak with the orbital phase, since the current X-ray instruments
cannot resolve the individual pulses of the AR~Sco. The time-averaged light
curve will be no pulsation or a modulation with a small pulse fraction. We may need a detailed analysis
for the timing of arrival of each X-ray photon to detect the pulsation.

\subsubsection{Spectrum}
Finally, Figure~\ref{spectrum} compares  the observed   SED (Marsh et al. 2016) and model
calculations for the different inclination angles:
$\alpha=20^{\circ}$ (solid), $40^{\circ}$ (dashed),
$60^{\circ}$ (dot-dashed) and $80^{\circ}$ (dotted), respectively. In addition, we assume a power-law index of  $p=2.5$ of the injected electrons to
explain the broadband spectrum.  We take into
account the emission of each  injected electron up to $t=P$ (one rotation),
since the injected electron may be absorbed by
the companion star after one rotation of the WD.  We can see that the model interprets
the global features of the observed SED with the  spectral peak at $\sim 0.01$eV.
For $0.1-1$eV, the model flux is smaller than the observed flux. This is because the emission from
the companion star contributes to the observed flux in this energy band. In the figure, we can see that the different inclination angle predicts a slightly different model spectrum;
the SED of the larger  inclination angle has
a  spectral peak  at higher energy. This is because the magnitude of the magnetic field at the first magnetic mirror point tends to be
higher for larger inclination angle.  We note that the model SED
is insensitive to  the viewing  angle $\zeta$, because the radiation beam
from each electron at the mirror point covers a large region in the angle $\zeta$,
as Figure~\ref{skymap} shows.

\begin{figure}
  \centering
  \epsscale{1.0}
  \plotone{fig10}
  \caption{Spectrum of ARScorpii. The observational data
    (filled circles and thick dashed lines) without error bars are taken from
    Marsh et al. (2016). The different lines show the model calculations
    for the different inclination angles; $\alpha=20^{\circ}$ (solid), $40^{\circ}$ (thin-dashed),
    $60^{\circ}$ (dashed-dotted) and $80^{\circ}$ (dotted), respectively. In each model calculation,
   the emission from each electron is taken into account up to the time $t=P$ after the injection.
   The results are for $\mu_{WD}=6.5\times 10^{34}{\rm G~cm^3}$, $\chi=10^{-5}$,
   $\gamma_{max}=5\times 10^{6}$ and $p=2.5$.}
  \label{spectrum}
\end{figure}

\section{Discussion}
\label{discuss}
No concrete evidence  of the accretion onto the WD in AR~Sco has been found, and it is considered that
the system is now in  the propeller phase (Beskrovnaya \& Ikhsanov 2017). Hence,
if there is no flow of accretion matter from the companion star on the
open magnetic  field line region, the WD could  operate the mechanisms of the neutron star (NS)
pulsar-like particle acceleration and the  nonthermal radiation process in the magnetosphere. In this section,
we estimate the flux and typical photon energy of the emission  with a simple outer gap model.
The outer gap accelerator assumes the particle acceleration around the light cylinder (Cheng et al. 1986),
and it has been considered as the origin of the observed GeV gamma-ray emission from the NS pulsars (Abdo et al. 2013).

With the dipole magnetic field, the polar cap radius of the WD in AR~Sco is of the
order of
\[
R_{p}=R_{WD}\sqrt{\frac{R_{WD}}{\varpi_{lc}}}\sim 2.5\times 10^{7}\left(\frac{R_{WD}}{7\cdot 10^8{\rm cm}
}\right)^{3/2} {\rm cm}.
\]
For the pulsar electrodynamics, the electric current emerges from the polar cap and is circulating in  the open field region.
The magnitude of the total electric
current will be given by the Goldreich-Julian value,
$I_{GJ}\sim \Omega_{WD} \mu_{WD}/2\varpi_{lc}$, (Goldreich \& Julian 1969).
The electric current running  through the outer gap is of the order of
\[
I_{gap}\sim f_{gap} I_{GJ},
\]
where $f_{gap} (<1)$ is the fractional gap thickness, which is defined by
the ratio of the angular size of the gap thickness measured on the
stellar surface to the angular size of the polar cap $\theta_p=\sqrt{R_{WD}/\varpi_{lc}}$.

Using the fractional gap width $f_{gap}$, the available electric potential drop in the outer gap
is of the order of
\[
V_{gap}=f^2_{gap}V_{a}
\]
where $V_{a}=\mu_{WD}/(2\varpi^2_{lc})$ is the electric potential difference  between the magnetic axis and  the rim of the polar cap.  The current  carrier is accelerated in the
outer gap by the electric field parallel to the magnetic field
line. For the outer gap region,  the typical magnitude of the electric field can be estimated as
\begin{equation}
E_{||}\sim \frac{V_{gap}}{\varpi_{lc}/2}\sim f_{gap}^2\frac{\mu_{WD}}{\varpi_{lc}^3}.
\end{equation}
For the outer gap accelerator, the accelerated particles lose their energy via the curvature radiation process and the IC process.  The evolution
of the Lorentz factor ($\Gamma$) of an electron
along the magnetic field line   may be written as
\begin{equation}
  m_ec^2\frac{d\Gamma}{dt}=eE_{||}c-P_{curv}-P_{IC},
  \label{outtraj}
\end{equation}
where $P_{curv}$ and $P_{IC}$ are the energy-loss rate of the curvature
radiation and the IC process, respectively.
The loss rate of the curvature radiation is  given
by $P_{curv}=2e^2c\Gamma^4/(3R_c^2)$ with $R_c$ being the curvature radius of the
magnetic field line.  For an isotropic soft-photon field,
the energy-loss rate of
the IC process is calculated from
\[
P_{IC}=\int\int(E_{\gamma}-E_s)\frac{\sigma_{IC}c}{E_s}\frac{dN_s}{dE_s}dE_sdE_{\gamma},
\]
where $E_{\gamma}$ and $E_{s}$ are the energies of the scattered and seed photons, respectively, and $dN_s/dE_s$ is the soft-photon field distribution. The cross
section is described by
\[
\sigma_{IC}=\frac{3\sigma_T}{4\Gamma^2}
\left[2q{\rm ln}q + (1+2q)(1-q)
  +\frac{(\Gamma_qq)^2(1-q)}{2(1+\Gamma_qq)}\right],
\]
where $\Gamma_q=4\Gamma E_s/m_ec^2$, $q=E_0/[\Gamma_q(1-E_0)]$ with
$E_0=E_{\gamma}/\Gamma m_ec^2$ and $1/(4\Gamma^2)<q<1$ (Blumenthal \& Gould 1970).

For the NS pulsar, the IC loss in the outer gap is negligible, and
the electric force is immediately  balanced with the radiation
drag force of the curvature radiation.
The saturated Lorentz factor is defined by equating between the acceleration term and the decelerating term
on  the right-hand side of  equation~(\ref{outtraj}),
\begin{equation}
  \Gamma_{sat}=\left(\frac{3R_c^2}{2e}E_{||}\right)^{1/4}
  \sim5\times 10^7f^{1/2}\left(\frac{\varpi_{lc}}{3\cdot 10^{8}{\rm cm}}\right)^{-1/4}
  \left(\frac{\mu_{NS}}{10^{30}{\rm G\cdot cm^3}}\right)^{1/4},
  \end{equation}
where $\mu_{NS}$ is the magnetic moment of the NS and we assume $R_c\sim\varpi_{lc}\sim 3\times 10^{8}$cm.
In the case of the saturated motion, the luminosity of the emission from the outer
gap is of the order of
\[
L_{\gamma}\sim I_{gap}\times \delta \Phi_{gap}\sim f^3L_{sd},
\]
where $L_{sd}$ is the spin-down power of the NS.

For AR~Sco, we can see that the IC energy-loss can be  comparable to or stronger
than the curvature radiation energy-loss. In the Thomson limit of the IC process, the energy-loss ratio
of the two radiation processes of AR~Sco becomes
\begin{equation}
  \frac{P_{IC}}{P_{curv}}=\frac{4\sigma_Tc\Gamma^2 U_{ph}/3}{2e^2c\Gamma^4/(3R_c^2)}\sim 1\left(\frac{R_c}{\varpi_{lc}}\right)^2\left(\frac{U_{ph}}{5\cdot 10^{-4}{\rm erg~cm^{-3}}}\right)\left(\frac{\Gamma}{3\cdot 10^7}\right)^{-2},
  \end{equation}
where $U_{ph}$ is the energy density of 0.01-1eV photons around the light cylinder
of the  WD.

The saturated motion of the Lorentz factor is  achieved    when
the maximum Lorentz factor accelerated by the electric potential drop $V_{gap}$ is
larger than the saturated Lorentz factor, that is, $eV_{gap}/m_ec^2>\Gamma_{sat}$.
For the AR~Sco, the saturation of the Lorentz factor will be achieved  when the fractional gap thickness satisfies the condition  that
\begin{equation}
  f_{gap}>1.4\left(\frac{\mu_{WD}}{10^{35}{\rm G~cm^3}}\right)^{-1/2}
  \left(\frac{\varpi_{lc}}{5.6\cdot 10^{11}{\rm cm} }\right)^{5/6},
\end{equation}
when the curvature radiation  is the  main energy-loss and
\begin{equation}
  f_{gap}>12\left(\frac{\mu_{WD}}{10^{35}{\rm G~cm^3}}\right)^{-1/2}
  \left(\frac{\varpi_{lc}}{5.6\cdot 10^{11}{\rm cm} }\right)^{1/2}
  \left(\frac{U_{ph}}{5\cdot 10^{-4}{\rm erg~cm^{-3}} }\right)^{1/2},
  \end{equation}
when the IC process is the main energy-loss. Since $f_{gap}$ should be less
than unity,   no saturation motion in the our gap accelerator will be realized for the WD in the AR~Sco.

For the NS pulsar, the fractional gap thickness will be determined by the pair-creation process between
the gamma rays from the curvature radiation process
and the background X-ray from the stellar surface (Takata et al. 2012). For the WD pulsar, on other hand,
the fractional gap thickness could be determined by the photon-photon pair creation process of the TeV photon from
the IC process. The optical depth of the TeV photon is estimated as $\tau_{p}\sim \sigma_{\gamma\gamma}n_{opt}\varpi_{lc}
\sim 10^{-3}(n_{opt}/10^{10}{\rm cm^{-3}})$, where $\sigma_{\gamma\gamma}\sim \sigma_T/3$ is the cross section
of the pair-creation and $n_{opt}$ is the number density of the  $\sim 1$eV photon around the light cylinder. For the WD in AR~Sco,
the fractional gap thickness $f_{gap}\sim 1$ is required to produce TeV photons in the outer
gap (Figure~\ref{tev}).  If a part of the open field line region is occupied by the matter from the companion star, the possible
fractional gap thickness is  less than unity. Because of the theoretical uncertainties,
we parameterize the fractional gap thickness in this section.

Figure~\ref{outgap} summarizes the integrated flux (left panel) measured on the Earth
and the peak photon energy (right panel) of the curvature radiation process in the outer gap of AR~Sco
as a function of the gap fraction $f_{gap}$; in the figure, the solid and dashed lines show the results
for the magnetic moment of $\mu_{WD}=3\times 10^{34}{\rm G~cm^3}$ and $10^{35}{\rm G~cm^3}$, respectively, and
the solid angle of $4\pi$ rad is assumed. The figure indicates that if the gap fraction is larger than
$f_{gap}\sim 0.7$, the future hard X-ray/soft gamma-ray missions
would  measure the curvature  radiation from the AR~Sco. With a  magnetic moment $\mu_{WD}\sim 10^{35}{\rm G~cm^3}$, for example, the flux measured on the Earth will be  $10^{-12}~{\rm erg/cm^2}$ and the
peak photon energy of the spectrum is in $E=0.1-10$MeV for $f_{gap}>0.7$. This sensitivity could be achieved by
the future hard X-ray/soft gamma-ray missions.

The soft X-ray emission from AR~Sco is observed with a flux $F\sim 5\times 10^{-12}{\rm erg~cm^{-2}~s^{-1}}$ (Marsh et al. 2016), and it will not be the origin of  the outer gap. The current model predicts the gap fraction $f_{gap}\sim 0.3$
to produce the soft X-ray with the curvature radiation process. With $f_{gap}\sim 0.3$, however, the
predicted flux is much smaller than the observation. If the fractional gap width is $f_{gap}<0.2$, the peak
photon energy of the outer gap emission is located in the optical band. In such a case, however, the outer gap
emission is buried under the emission from the trapped electrons/stellar emission discussed in the previous
sections.

Figure~\ref{tev} shows the predicted flux measured on the Earth and the peak photon
energy of the IC process of the outer gap. As we can see in Figure~\ref{tev},
the IC process produces $>0.1$TeV photons if the gap fraction is $f_{gap}>0.3$.
Moreover, for $f_{gap}>0.5$,
the expected flux is $>10^{-13}{\rm erg~cm^{-2}~s^{-1}}$, which would be measurable
by the future CTA observation.

In summary, we discussed the radio/optical/X-ray emission from AR~Sco. In our model,
the magnetic dissipation process  on the M star surface produces
(i) an outflow from the companion star, (ii) heating of the
companion star surface, and (iii) acceleration of the electron to relativistic energy.  The accelerated electrons, whose typical Lorentz factor is
$\gamma_0\sim 50$, are trapped in the close
magnetic field lines. We solved the motion of the trapped electrons along  the magnetic field under the effects of
the synchrotron loss and the first adiabatic invariance. We found
that the electron injected toward the WD's surface
with a pitch angle of $\sin\theta_{p,0}\ge 0.05$ is trapped at the
closed  magnetic field lines by the magnetic mirror effect.  For such an electron,
most of the  initial energy is released at the first mirror point by the synchrotron  radiation process. We
demonstrated that for the inclined rotator with the dipole
magnetic field, the synchrotron emission from the trapped electrons injected at the different spin phase
can  create the light curve with a double-peak structure, which is consistent with the observations.
The model expects that the pulse profile is linearly shifts with the orbital phase, and this shift is observed as
the beat frequency in the spectral power of the Fourier analysis. The model interprets
the global features of the observed SED in radio to X-ray energy bands. We discussed
the curvature radiation and the IC process in the outer gap
accelerator of the WD in AR~Sco.  The curvature radiation from the outer gap could be
measured by the future hard X-ray and soft gamma-ray missions, if the gap fraction
is $f_{gap}>0.7$. The TeV emission via the IC process from AR~Sco
may be also detected  by the future CTA project.

We express our appreciation to an anonymous referee
for useful comments and  suggestions.
We thank to Drs. Lin, L.Chen-Che and Hu, Chin-Ping for useful discussion on the timing analysis.
J.T. and H.Y. are supported by NSFC grants of Chinese Government under 11573010, U1631103, and 11661161010. K.S.C. is supported by GRF grant under 17302315.

\begin{figure*}
  \centering
  \epsscale{1.0}
  \begin{tabular}{@{}cc@{}}
    \includegraphics[width=0.5\textwidth]{fig11-1} &
    \includegraphics[width=0.5\textwidth]{fig11-2} \\
  \end{tabular}
  \caption{Predicted integrated flux (left) and peak photon energy in SED (right)
    of the curvature radiation process in the outer gap of AR~Sco's WD. The
  dashed and solid lines are the magnetic moment of $\mu_{WD}=3\times 10^{34}{\rm G~cm^{3}}$ and $10^{35}{\rm G~cm^{-3}}$, respectively.}
  \label{outgap}
  \end{figure*}

\begin{figure}
  \centering
  \epsscale{1.0}
  \plotone{fig12}
  \caption{Predicted integrated flux (black) and peak photon energy in SED (red)
    of the IC process in the outer gap of AR~Sco's WD. The
    magnetic moment is assumed to be $\mu_{WD}=5\times 10^{34}{\rm G~cm^3}$. }
  \label{tev}
\end{figure}

redpajama_set_name: RedPajamaArXiv


September 16th commemorates Mexico's 205th anniversary of independence from Spanish rule in 1810. Mexicans all over the world celebrate Mexico's independence from Spanish rule every 15th of September with El Grito (The cry of independence).
Cafe Coyote is celebrating with El Grito Reenactment on September 15th at 8:45pm as well as offering Taco Tuesday specials, $2 & $3 Tacos ALL DAY LONG!
And Don Fulano Tequila 1/2 Price ALL NIGHT LONG!


text:
McCarter, Lloyd G.
Rank and organization: Private, U.S. Army, 503d Parachute Infantry Regiment. Place and date: Corregidor, Philippine Islands, 16 19 February 1945. Entered service at: Tacoma, Wash. Born: 11 May 1917, St. Maries, Idaho. G.O. No.: 77, 10 September 1945.
Citation... He was a scout with the regiment which seized the fortress of Corregidor, Philippine Islands. Shortly after the initial parachute assault on 16 February 1945, he crossed 30 yards of open ground under intense enemy fire, and at pointblank range silenced a machinegun with hand grenades. On the afternoon of 18 February he killed 6 snipers. That evening, when a large force attempted to bypass his company, he voluntarily moved to an exposed area and opened fire. The enemy attacked his position repeatedly throughout the night and was each time repulsed.
By 2 o'clock in the morning, all the men about him had been wounded; but shouting encouragement to his comrades and defiance at the enemy, he continued to bear the brunt of the attack, fearlessly exposing himself to locate enemy soldiers and then pouring heavy fire on them. He repeatedly crawled back to the American line to secure more ammunition. When his submachine gun would no longer operate, he seized an automatic rifle and continued to inflict heavy casualties. This weapon, in turn, became too hot to use and, discarding it, he continued with an M-l rifle. At dawn the enemy attacked with renewed intensity. Completely exposing himself to hostile fire, he stood erect to locate the most dangerous enemy positions. He was seriously wounded; but, though he had already killed more than 30 of the enemy, he refused to evacuate until he had pointed out immediate objectives for attack. Through his sustained and outstanding heroism in the face of grave and obvious danger, Pvt. McCarter made outstanding contributions to the success of his company and to the recapture of Corregidor.

redpajama_set_name: RedPajamaCommonCrawl


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Any discussion of the influence of Chinese architecture upon the design of Japanese temples must acknowledge that the relationship between the two design aesthetics is not simply one of Japanese acquisition of foreign styles and forms. Rather, this essay will argue that this influence may best be described as a dialectic or a "conversation" taking place in Japanese culture over centuries. In the course of this "conversation" Chinese Buddhist architectural styles - themselves influenced by earlier Indian models - influenced the design of native Japanese Shinto shrines. However, the more direct transplantation of Chinese Buddhist temple architecture in Japan was likewise often influenced by older Japanese architectural principles - as most famously embodied in the Shinto shrines - to finally evolve into a architectural style that - in Zen Buddhist temples - may best be described as an amalgam of the two forms.
This essay will argue that a key point of disagreement, and eventual harmonization, in this "conversation" revolved around the role of nature in the architecture of Japanese temples. While earlier Shinto models reflected a Japanese aesthetic of harmonization with nature, the Buddhist temple architecture imported directly from the Asian mainland emphasized a more abstract and monumental disregard for the natural environment. Through an analysis of the similarities and the differences of Japanese Shinto shrine and Buddhist temple design, this essay will outline the parameters of this conversation between native and 2 foreign forms in Japanese architecture.
Given the fact that most early Japanese architecture consisted of wood structures, and so were particularly vulnerable to the ravages of time, very little is known of their design style. What we know of native Japanese, pre-Buddhist architectural styles consists, to a large degree, of what may be learned from Shinto shrines. The architecture and design of these shrines dates back to around the 6th or 7th centuries B.C., and their forms have been preserved over time as a result of intense religious conservatism causing them to "have been rebuilt, time after time, in a ritually scrupulous imitation of the past" (Soper, 5). However, the examples of Shinto shrines, as they exist today, also show signs of the influence of Buddhist temple architectural forms imported from China. In order to better illustrate the nature of this influence, it would be useful to first comprehend the architecture of Shinto shrines.
The typical Shinto shrine reflects, in both form and function, the religious aesthetics of the Shinto belief system. The most striking feature of the Shinto shrine - in Japanese jinja or "place of deities" (Earhart, 18) - is the minimal amount of decoration and a deliberate plainness of design, with straight lines and earth colours predominating. This is in accordance with the Shinto ideals of purity and simplicity (Anesaki, 13, 15). Even the great shrines of Ise are, in comparison with Buddhist 3 counterparts, not very large and purposely simple in construction (Aston, 223, 226). Over time, however, Shinto shrines have assumed a wide diversity of forms, to the point that today a Shinto shrine may be anything from a tiny shrine by the roadside to a sectioned off corner of a factory (Anesaki, 12). Critics consider that this diversity of forms is representative of the diversity of influences - and amalgamation of conservative native traditions and foreign traditions such as Buddhism, upon the development of Shintoism over the centuries (Anesaki, 7, 13).
In general, however, Shinto shrines share many characteristics in their design. The most common of these is the torii, or traditional Shinto gateway; one of the most familiar sights in the Japanese landscape (Reader, 138). Usually made of wood, but sometimes of stone or even metal, the torii consists of one or two unadorned long cylinders - often tree trunks - mounted horizontally upon two upright posts set on the either side of the approach to the shrine (Holtom, 22). The word torii means "birdperch", which is indicative of its physical form but gives no hint of its symbolic significance within both the design of the Shinto shrine, and within the faith itself (Aston 231-32; Holtom, 22).
A Shinto shrine most often occupies a rectangular area of land defined as sacred by the use of a surrounding sacred fence or wall. The opening in this fence, at the front and placed in the exact middle between left and right sides, is guarded by the torii. Thus the torii functions, in religious terms, to protect the opening in the shrine fence against the contamination of the 4 outside world (Holtom, 22). While a singular torii is most common, there may even be a succession of torii of diminishing size, each one smaller than the one previous, lining the avenue to the shrine. In this configuration they serve to gradually prepare and purify the worshipper on the path from the secular world to the sacred ground of the shrine itself (Anesaki, 14).
This importance, within Shintoism, of the ideal of purification may also be seen in the next characteristic feature of a Shinto shrine encountered by worshippers once they pass through the torii gateway (Earhart, 6). Water, a predominant feature in Shinto rites, plays an equally important symbolic role in the landscape design of the traditional Shinto shrine. Worshippers must cross a bridge, a sori-bashi or taiko-bashi representing the floating Bridge of Heaven (the rainbow), over a stream whose waters symbolically wash away the impurities of those who pass over it, preparing them to greet the kami, or deities, in a state of spiritual cleanliness (Aston, 232; Reader, 140). The ideal of purification by water is also represented in Shinto shrines by the ever-present fountains of running water, the temizuya, which often flow out of the mouths of bronze dragons. At these the worshippers may wash their hands or rinse out their mouths to further cleanse and purify themselves (Reader, 140).
However, while the path to the shrine is dominated by features which possess a spiritual function or symbolic significance, aesthetics also play a role in the design of the shrine. This may be seen in the stone lanterns which often line 5 the path to the shrine, sometimes in great number, and decorate the gardens of the enclosure. When lit at night, these lanterns function practically as a light source; but their "gentle illumination" also serves to convey a sense of peacefulness and serenity of the shrine, thus marking the sacred ground off from the disorder of the secular world (Anesaki, 14).
Finally, after making their way through the usually wooded landscape of the shrine's enclosure, the worshipper comes to the shrine buildings themselves. There is the haiden or "worshipsanctuary" - open on all sides between supporting pillars - before which worshippers may ring a suspended bell to get the attention of the gods, and kneel or pause briefly in prayer. The haiden and honden, as well as the secondary shrines often located about the grounds (massha), sometimes show Buddhist or Chinese influences, but most often they reflect the Shinto emphasis on simplicity; often built on ancient models, raised on poles above the ground, and with thatched roofs (Anesaki, 13; Earhart, 18). The deliberate lack of decoration in these buildings, and their noted cleanliness, are representative of the design of the shrine as a whole in reflecting the ideal of purity at the heart of Shinto (Anesaki, 13).
The arrival of Buddhism in Japan in the 6th century A.D. can be considered the architectural antithesis to the thesis of native architecture as represented by Shinto shrines. As will be seen, 6 out of the combination of these a synthesis in Japanese architecture was to develop.
While the European architectural vision of man's interaction with the natural world has famously consisted of concrete examples of physical conquest, the Chinese architectural approach has generally been to represent this opposition symbolically. The Chinese philosophical vision of the cosmos was focused on a celestial ideal, with the role of man being to extend the Heavenly order to the natural chaos of the world (Soper, 15).
This being said, the Chinese architectural focus on order was largely in agreement with the Japanese emphasis upon order, rhythm and predictability (Kidder, 20). Thus, the earliest Buddhist temples carefully ordered design fitted comfortably within Japanese architectural perspectives. Indeed, for a century or two after the initial arrival of Buddhism from China, the Buddhist temples complexes constructed in Japan were almost entirely adopted forms; the ease of the adoption being facilitated by the similarities between the two cultures preoccupation with structural principles of order (Kidder, 15).
Note, for example, how the above-noted symbolic function of 8 the fence and torii of Shinto shrines - to demarcate the contamination of the secular world from the purity within the shrine - echoes the architectural form of Chinese temples and cloisters that isolate their occupants from the outside world and is thus "symbolic of its inmates' renunciation of the world and separation from it" (Kidder, 15). Even the symmetrical designs of early Chinese Buddhist temples in Japan presented united fronts against the evil forces of the outside that may come from any direction (Alex, 18).
However, while the Japanese clearly had not issue with Chinese architectural preoccupations with order, the typical Chinese emphasis on symmetry and artificial forms were alien to the Japanese mindset. The architectural evolution of temples in Japan thus reflects the gradual adaptation of foreign forms within Japanese culture.
It is interesting to note, however, that when these early temples - such as the Horyuji Temple near Nara - burned down or required repair as early as the 7th century, the principle of axial balance was abandoned in preference for the native Japanese taste for asymmetry (Alex, 20-21). As well, the natural thatched roof and structural simplicity of Shinto shrines were adopted to replace the artificiality of the tile roof and painted adornment of the original structures (Kidder, 37). However, it should also be noted that Shinto shrines were themselves influenced by Chinese Buddhist temple architecture, with more paint and structural adornments being used. The overall effect of this exchange of architectural design ideas of native Japanese and imported Chinese forms was to render Shinto shrines respectable for urban sites, and Buddhist architecture more suitable for rural or forested sites (Kidder, 37).
Perhaps nothing so well illustrates this Japanese synthesis of architectural forms as does the architecture of Japanese Zen Buddhist temples. Zen Buddhism, which arrived in Japan in the 13th century, differed dramatically from the Buddhism that had arrived in the 6th century. Its fundamental tenets of simplicity and restraint were reflected in the design of its temples; which was more in keeping with the Japanese character than the monumental 10 structures accompanying the earlier wave of Buddhism teaching (Alex, 40).
From this perspective, Zen Buddhist temples in Japan may be seen to be a characteristically Japanese amalgam of native forms and foreign influences. Their simplicity and disciplined aesthetic, and emphasis upon harmony as opposed to opposition to Nature, were in keeping with traditional Japanese attitudes; a fact that may serve to explain the rapid growth of Zen Buddhism in Japanese society.
As has been seen, the influence of Chinese architecture upon Japanese temples has been a complex story of aesthetic crosspollination. In a sense, we may see the thesis of native tradition combining with the antithesis of foreign ideas, to culminate in the eventual synthesis of styles in later Buddhist and Shinto architecture. Thus, this influence is not simply a one-way process. Rather, it involves a "conversation" or exchange of cultural ideas between Japanese and Chinese civilizations that was physically represented in the Japanese landscape by the evolutionary narrative of Japanese temple design.
Alex, William. Japanese Architecture. New York: George Braziller, 1963.
Anesaki, Masaharu. Religious Life of the Japanese People. Tokyo: Kokusai Bunka Shinkokai (Japanese Cultural Society), 1970.
Aston, William. Shinto: The Way of the Gods. New York: Longmans, Green, 1905.
Earhart, H. Byron. Japanese Religion: Unity and Diversity. Belmont, California: Dickenson, 1969.
Holtom, D.C. "Shinto Shrines" Religion in the Japanese Experience: Sources and interpretations. Ed. H. Byron Earhart. Belmont, California: Dickenson, 1974. 19-23.
Kidder, J. Edward. Japanese Temples: Sculpture, Paintings, Gardens, and Architecture. Tokyo: Bijutsu Shuppan-Sha, 1964.
Reader, Ian. Religion in Contemporary Japan. London: MacMillan, 1991.
Soper, Alexander Coburn. The Evolution of Buddhist Architecture 13 in Japan. New York: Hacker, 1978.


text:
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Relayer is the third in a series of remixed and expanded Yes albums.
Presented in a mini vinyl replica gatefold card sleeve (with protective inner sleeves) with booklet featuring new sleeve notes by Sid Smith along with rare photos and archive material, the album has been mixed for 5.1 Surround Sound from the original studio masters by Steven Wilson and is fully approved by Yes.
The CD features a new stereo album mix by Steven Wilson.
The blu-ray features:
- 5.1 DTS-HD Master Audio Surround (24bit/96khz) mixed from the original multi-channel recordings.
- the new stereo album mix in DTS-HD Master Audio (24bit/96khz).
- the original album mix in a DTS-HD Master Audio flat transfers from the original master tape source. (24bit/192khz)
- exclusive needle-drop of an original UK vinyl A1/B1 pressing transferred in 24bit/96khz audio.
- exclusive instrumental versions of all new mixes in DTS-HD Master Audio stereo (24bit/96khz).
- numerous audio extras appear in high-resolution stereo including demos and studio run-throughs of album tracks making for an alternative version of Relayer.
- blu-ray exclusive features include additional demo/studio run-throughs, full album instrumental mixes, a full album needle-drop of an original UK A1/B1 vinyl pressing, singles edits, a live tracks & needle-drops of the banded tracks from the original US vinyl promo album.
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"…we had so much happening musically and sonically, we needed surround sound to realise the concept."– Jon Anderson (interviewed for the sleeve-notes to this release)
The ultimate way to enjoy one of the most challenging and brilliant albums by this venerable Progressive institution.
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CD - New Stereo Mixes:
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text:
Unter der Adresse 67–69 South Street in der schottischen Stadt St Andrews in der Council Area Fife befindet sich ein Wohngebäude. 1959 wurde das Bauwerk als Einzeldenkmal in die schottischen Denkmallisten in der höchsten Denkmalkategorie A aufgenommen.

Beschreibung
Das Wohngebäude stammt aus dem 16. Jahrhundert. Im Laufe der Jahrhunderte wurde es überarbeitet und zuletzt im Jahre 1974 restauriert.

Das vierstöckige Wohngebäude steht an der Nordseite der South Street (A918) im historischen Zentrum St Andrews'. Links schließt sich das St John's House an. Seine südexponierte Bruchsteinfassade ist drei Achsen weit. Die beiden oberen Geschosse wurden zu einem späteren Zeitpunkt aufgestockt. Rechts führt ein Durchgang auf den Hinterhof. Bei dem schließenden Metallgittertor handelt es sich um ein Replikat. Im Erdgeschoss sind Geschäftsräume untergebracht. Die Decken der rückwärtig abgehenden Flügel sind teils als Gewölbe gearbeitet. Die abschließenden Dächer sind mit Schiefer eingedeckt.

Einzelnachweise

Weblinks

Wohngebäude in Fife
Kategorie-A-Bauwerk in Fife
Erbaut im 16. Jahrhundert
St Andrews

redpajama_set_name: RedPajamaWikipedia


"GETTING A HANDLE ON HANDEL!"
To the modern musical ear and indeed to the modern music-listening audience, Handel is certainly no longer a stranger. The Early and Baroque Music revival is long established; the Oratorios and, in more recent years, the Operas by George Frederick Handel have become not only more popular, but are now even part of a staple diet in the concert halls and stages of the modern music lover's world.
Yet for many singers - and sadly many singing teachers, too - Handel's music is still often considered to be something that takes second or third place to the more accepted conventional concert & operatic repertoire of Mozart, Rossini, Donizetti, Verdi, Puccini, Strauss, even Schubert & Schumann, etc. The idea of singing Handel often seems to imply a professional step backwards in the minds of many young artists, as if it is not particularly relevant to their modern artistic development and personal artistic expression.
That way of thinking is of course plainly misguided. Handel's music, particularly his music for voices, is actually a wonderful step forward in the pure Belcanto tradition that started with Caccini, Monteverdi and Cavalli, culminating in the great romantic Belcanto tradition of the 19th & early 20th centuries. Handel's study & love of Italian music of the late 17th and early 18th centuries is plainly evident; and it is clear that he, more than any of his contemporaries, developed the art of Dramma per Musica to such a sophisticated extent that it laid the foundations for the operas of Mozart and the oratorios of Mendelssohn (to name just two of the many later composers who greatly admired Handel's music).
Stylistically, there are many things to explore in Handel's vocal music. The ground rules for singing Baroque music in general are not so hard to grasp. Singers are often needlessly frightened at the prospect of improvised decorations & cadenzas, unsure how much they should decorate a line, whether to use less or no vibrato, or ambivalent about where and when to insert appoggiaturas, etc. There are also questions of phrasing, articulation and line that need to be taken into account; and of course, all the frustrations and dramatic questions thrown up by that most dreaded of musical forms, the great Da Capo Aria!
Interestingly enough, when singers begins to understand where Handel is coming from stylistically and where he is going as a musical dramatist, then suddenly Gluck, Haydn, Mozart and their successors all begin to sit in a new, perhaps better, perspective.
Many singers, musicians and music lovers also forget that Handel's Oratorios are rooted in his theatrical & operatic expression and tradition, (unlike the Germanic oratorio tradition of Bach or Telemann). The switch to writing oratorio was one of financial necessity when Handel's operatic entrepreneurship collapsed, forcing him to find other outlets for his dramatic expression. Unsurprisingly, many of Handel's religious and secular oratorios readily lend themselves to staging; some are by their nature more difficult to stage than others, as allegory and commentary begin to replace genuine stage action. But what is common to all Handel oratorios (as well as the operas) is the fact that the story telling is full of dramatic expression; whether it is expression of love, lust, greed, fear, grief, religious fervour or joy, they are full of real life and humanity. It is for this very reason that I am enthused to explore the arias & scenes of the oratorio repertoire as well as those of the operas.
Although the fashions of his time may still dictate certain elements of musical performance and dramatic expression, it is true to say that some understanding of Handel's style helps to enable performers to adapt their modern sensibilities (their 21st century thinking and understanding of the world we live in today) in such a way as to find a true personal expression of Handel's writing. Indeed such an approach also works the other way round, bringing Handel into our own time dramatically, intellectually, philosophically, musically. Without the input & exploration of a modern performer's personal expressive skills, sensibilities and experience, music in whatever form and from whatever period has little or no chance of coming to life. The modern world that we as artists live in now (and all that implies) cannot and must not be denied, especially when it comes to trying to understand the past; this applies equally to the exploration of all music and the world it comes from.
Ultimately our three day course will try to give the singers a chance to explore not only the niceties and rigours of baroque arias & scenes in a sense of "Handelian Style", but also to grip the handle and push open the door to the world and rewards of Handel's musical dramatic expression. Despite having roots going back 400 years, Handel's vocal music remains somehow timeless and, without any doubt, renewably contemporary.


Most of us have at some time or another acted like klutzes when a friend or relative has had a life-threatening illness like cancer, particularly if that person is going through fairly grueling treatment for the condition. It's difficult to know how to react and what to say. My advice is to try to put yourself into the cancer patient's shoes and imagine how you would want to be treated if you were in his or her situation.
I've had breast cancer twice, undergoing the memorable experience of chemo and radiation. I found many people, even total strangers, would bend over backwards to help me once they knew I was dealing with cancer.
Some examples: I got my passport rushed through even though the photos I provided weren't quite right. I'd shot them before doing chemo, so I was grateful not to have to get new ones showing my bald head. Then a booked-up plumber came over right away to fix a leaking toilet, giving me a discount on his fee. Later on, a phone company rep took it upon herself to give me a credit instead of a penalty when I blamed chemo brain fog for being late paying the bill.
Nevertheless, I came across some stunningly dim responses from certain folks, most of whom were well-meaning.
A now ex-friend of mine was one of only a small group of people whom I told about my second cancer diagnosis when I had just found out about it. Instead of offering me any help or sending words of encouragement, he blabbed about my condition to all our mutual acquaintances. The thoughtless fellow then began besieging me with emails about all kinds of things that supposedly might cause cancer. Why did he think I wanted to read those messages? That horse had already bolted—I already had cancer. Finally I had to tell him to stop sending me all that stuff. He and other clueless dolts, who will remain anonymous, inspired me to compile a long list of cancer etiquette do's and don'ts to help friends, family and caregivers avoid inept behavior.
The biggest no-no: Telling the cancer patient that whatever treatment plan she or her doctors have chosen is completely wrong.
Do not bombard a breast cancer patient with alternative cancer cures and/or therapists, emphasizing that your suggestions are the only way she'll avoid a recurrence. Everybody and their mother's uncle seem to have their own personal foolproof method for getting rid of the disease which they reckon that the poor, suffering cancer victim ignores at her peril. Don't insist she's making herself ill because she's not thinking enough positive thoughts. Equally, do not ridicule her for any alternative treatment she chooses. If a Voodoo Witch Doctor is able to mitigate her pain, nausea and depression, do not make her feel bad about it, so long as the guy is not draining all her finances or getting himself written in as the beneficiary of her estate.
For caregivers: Try to anticipate her needs rather than waiting for her to tell you.
If you're with her for long intervals, ask if you can bring over a meal or make one at her home. Offer to make her some tea or run a bath for her.
For friends: Instead of saying, "Is there anything I can do?" offer tangible suggestions.
Here are a few ideas on questions you could ask: Can I pick up your kids from school today? Can I do some babysitting? What shopping can I get for you? Would you like me to take your dog for a walk? Can I tidy your house? Can I do some gardening for you?
Don't be unnaturally cheerful and/or patronizingly pitying.
She doesn't want to hear you telling her at length how sorry you feel for her, especially if she hardly knows you.
And finally…bring her European chocolates.
I have to admit that, as a lifelong chocoholic from Britain, I'm biased about that. Just make sure you know if she prefers dark or milk. Dark is my favorite. During chemo, however, the 70% cacao chocolate I normally liked seemed too bitter but I still enjoyed the stuff that was 50%. Yes, I know sugar is said to be bad for cancer, but chocolate is good for the soul!
CJ Grace was a BBC staff journalist in Britain and then worked for China Radio International in Beijing. The author of "Adulterer's Wife: How to Thrive Whether You Stay or Not," she is currently completing "Hotel Chemo: Learning to Laugh through Breast Cancer and Infidelity." When CJ discovered her husband's infidelity and then got breast cancer - for the second time - she refused to be a victim and kept her wicked sense of humor. After receiving a copy of "Adulterer's Wife," Arianna Huffington invited CJ to write for HuffPost. CJ has an infidelity advice column on her website in association with DivorceForce.com. Her mantra: The best revenge is to get past the need for it. Visit adultererswife.com to find out more. Showcasing her BBC-trained British accent, CJ also has a voiceover business, rentabrit.com.