Abstract
A three-dimensional (3D) $Ly{\alpha}$ radiative transfer code is developed to study the Wouthuysen-Field effect, which couples the 21 cm spin temperature of neutral hydrogen and the $Ly{\alpha}$ radiation field, and the escape fraction of $Ly{\alpha}$ from galaxies. The Monte Carlo code is capable of treating arbitrary 3D distributions of $Ly{\alpha}$ source, neutral hydrogen and dust densities, gas temperature, and velocity field. It is demonstrated that the resonance-line profile at the center approaches to the Boltzmann distribution with the gas temperature. A plane-parallel ISM model, which is appropriate for the neutral ISM of our Galaxy, is used to calculate the $Ly{\alpha}$ radiation field strength as a function of height above the galactic plane. We also use a two-phase, clumpy medium model which is composed of the cold and warm neutral media (WNM). It is found that the $Ly{\alpha}$ radiation field is strong enough to thermalize the 21 cm spin temperature in the WNM to the gas kinetic temperature. The escape fraction of $Ly{\alpha}$ is found to be a few percent, which is consistent with the $Ly{\alpha}$ observations of our Galaxy and external galaxies.