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 radiative 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 } \gg 1 , \tau \gg 1 , and \tau \gg \tau _ { a } , the effective absorption optical depth in a random walk scenario would be equal to \sqrt { \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 .