The effect of multiple Compton scattering on the temperature and emission spectra of accreting black holes
Spherical accretion onto a black hole with magnetic field dissipation is treated. For an optical depth close to 1, multiple Compton scattering is the predominant cooling mechanism near the hole. The effect is introduced in the energy balance equation using at each shell the spectral index of the Comptonized emission (derived from Monte Carlo calculations and analytic solutions of the Kompaneets equation) for homogeneous spheres having optical depths equivalent to that of the shell. In the inner region of the flow, the temperature obtained with this procedure differs appreciably from that computed without taking into account Comptonization losses.