Effect of Dust on Lyman-alpha Photon Transfer in Optically Thick Halo
  We investigate the effects of dust on Ly{\alpha} photons emergent from an
optically thick medium by solving the integro-differential equation of the
radiative transfer of resonant photons. To solve the differential equations
numerically we use the Weighted Essentially Non-oscillatory method (WENO).
Although the effects of dust on radia-tive transfer is well known, the resonant
scattering of Ly{\alpha} photons makes the problem non-trivial. For instance,
if the medium has the optical depth of dust absorption and scattering to be
{\tau}a>>1, {\tau}>>1, and {\tau}>>{\tau}a, the effective absorption optical
depth in a random walk scenario would be equal to \surd
{\tau}a({\tau}a+{\tau}). We show, however, that for a resonant scattering at
frequency {\nu}0, the effective absorption optical depth would be even larger
than {\tau}({\nu}0). If the cross section of dust scattering and absorption is
frequency-independent, the double-peaked structure of the frequency profile
given by the resonant scattering is basically dust-independent. That is, dust
causes neither narrowing nor widening of the width of the double peaked
profile. One more result is that the time scales of the Ly{\alpha} photon
transfer in the optically thick halo are also basically independent of the dust
scattering, even when the scattering is anisotropic. This is because those time
scales are mainly determined by the transfer in the frequency space, while dust
scattering, either isotropic or anisotropic, does not affect the behavior of
the transfer in the frequency space when the cross section of scattering is
wavelength-independent. This result does not support the speculation that dust
will lead to the smoothing of the brightness distribution of Ly{\alpha} photon
source with optical thick halo.
