Transfer of Lyman Alpha in Diffuse Nebulae

The Monte Carlo method is applied to the solution of the transfer equation for Ly-a radiation in nebulae with optical thicknesses up to 1O~. Plane-parallel geometry, two-level atoms, and constant tem- perature are assumed. The correlation between the direction of scattering and the frequency redistribu- tion is taken into account exactly. A method is developed for accelerating the solution by treating the line core analytically and using the Monte Carlo method only in the wings. It is found that for Doppler broadening the assumption of complete redistribution is a reasonably satisfactory approximation. The mean number of scatterings before escape is on the order of ro. For lines with finite natural width, the presence of Lorentz wings, where scattering tends to be coherent, reduces the mean number of scatterings from the case with zero natural width. This effect is seen only after the optical depth at line center has become great enough that the nebula is opaque at all frequencies in the core. The emergent flux has a double-humped frequency distribution. When the ratio of the natural width to the Doppler width is increased, the width of the emergent line is also increased. For density-bounded H xi regions with optical thickness at the line center of 1O~, illuminated by an incident Lyman-continuum flux, the energy density in Ly-a does not rise to more than twenty-five times the energy density of the incident continuum radia- tion. Radiation pressure from Ly-a does not become large enough to have dynamical effects. Two- photon emission is negligible, but if the grain density within the H ii region is as high as it is in inter- stellar space, almost all Ly-c& photons will be absorbed before they can escape