Analytic forms for Hard X-ray Spectra with Compton Reflection

Astronomy and Astrophysics – Astronomy

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Scientific paper

Compton reflection of hard X-rays seems to be a common process in AGN. It is potentially significant both as a diagnostic of individual AGN, and because the emission of all AGN likely make up the diffuse X-ray background. We follow the classical, "multi-stream" method as presented by Chandrasekhar, to develop an approximate solution for the Compton reflection of a power law X-ray spectrum incident on a semi-infinite, plane parallel slab. The set of particular solutions of the transfer equations can be combined to solve a variety of boundary conditions; e.g., an isotropic or 1/cos law for the incident spectrum, or even to consider a finite optical depth for the slab. For pure Thomson scattering, (applicable in the 20 to 100 keV range), a third order polynomial in the energy adequately fits the albedo. The coefficients of the polynomial are particular numerical values depending on the boundary conditions and the exiting angle, and depending on integer powers of the incident photon index. These expressions are therefore very time efficient for fitting to actual X-ray spectral data.

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