Anisotropic Comptonization in thermal plasmas - Spectral distribution in plane-parallel geometry

We present a semi-analytical formulation of the problem of inverse Compton scattering of low-frequency radiation in a hot thermal plasma. The scattering medium is assumed to have a plan-parallel geometry, and an input radiation field is localized on one side of the slab. The angular and energy distributions of the emitted radiation are computed taking into account the effects due to the anisotropy of the input photons. We show how the Comptonized spectrum depends on three parameters, namely the optical depth of the medium, the temperature of thermal electrons, and the viewing angle. The spectral shape is approximately, but not exactly, a broken power law. Our method allows to compute angle-dependent Compton spectra for a broad range of input parameters with a modest computational effort.