An Analytic Approximation for Plane‐parallel Compton Scattering near Accretion Disks

Compton scattering by a locally plane parallel atmosphere is analyzed withinthe Kompaneets approximation. In contrast to almost all previous analyticcalculations of inverse Compton scattering, we assume neither homogeneity norisotropy of the photon distribution. However, we do adopt an assumed angulardistribution of the photons. For any specified energy dependence of the fluxentering the base of the atmosphere, an analytic expression is obtained for theflux at any optical depth. Only integrals over the input flux are involved. Ifthe thickness of the atmosphere is much less than its radial position on anaccretion disk, the contribution from all radii may be summed. The initialmotivation (addressed in a subsequent paper) is the computation of the energyspectrum of (possibly modulated) photons originating from a specified radialregion of an accretion disk, relative to the total energy spectrum.Comment: Accepted for publication by The Astrophysical Journal. 15 pages, no figure