Optically thick X-ray transfer - The shell game

This paper investigates the radiative transfer of X-rays through a shell that is optically thick to Compton scattering, surrounding a point source of continuum X-rays. The emission and absorption of X-rays due to K-shell transitions of iron are included. The calculations are done in two entirely independent ways: by Monte Carlo simulation and by solving a Fokker-Planck diffusion equation. The emergent spectra agree very well for Thomson depths of at least about 2. The validity is confirmed of the modification to the Fokker-Planck equation of Kompaneets (1957) that is required when the photon energy is large compared with the average thermal energy of the electrons. A procedure is also developed for treating models of compact X-ray sources consisting of incomplete shells.