Green's matrix for Compton reflection of polarized radiation from cold matter

The Compton-reflected spectrum from cold matter for incident X-rays and gamma-rays with arbitrary angular, spectral and polarization properties can be determined by a simple folding of Green's matrix with the incident spectrum. We calculate Green's matrix by numerically solving the polarized radiative transfer equation for an optically thick planar slab of neutral matter using a method based on discrete space theory. We account for both angular and polarization properties of the fully relativistic Compton scattering cross-section as well as photoelectric absorption and the generation of a fluorescent Fe line. We describe through simple models the basic characteristics of polarized spectra produced by Rayleigh and Compton scattering. The emphasis is on exact computations of Compton-reflected spectra. For the first time, the Fe line equivalent width can be calculated self-consistently for an arbitrary angular distribution of the incident spectrum using Green's matrix formalism.