Comptonization of X-rays by low-temperature electrons

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Astronomical Spectroscopy, Compton Effect, Electron Scattering, X Ray Sources, Boundary Value Problems, Electron Energy, Fokker-Planck Equation, Green'S Functions, Photons, Radiative Transfer, Relativistic Effects, Thomson Scattering

Scientific paper

A method is described for calculating the spectrum that results from the Compton scattering of a monochromatic source of X-rays by low-temperature electrons, both for initial-value relaxation problems and for steady-state spatial diffusion problems. The method gives an exact solution of the inital-value problem for evolution of the spectrum in an infinite homogeneous medium if Klein-Nishina corrections to the Thomson cross section are neglected. This, together with approximate solutions for problems in which Klein-Nishina corrections are significant and/or spatial diffusion occurs, shows spectral structure near the original photon wavelength that may be used to infer physical conditions in cosmic X-ray sources. Explicit results, shown for examples of time relaxation in an infinite medium and spatial diffusion through a uniform sphere, are compared with results obtained by Monte Carlo calculations and by solving the appropriate Fokker-Planck equation.

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