Comptonization models and spectroscopy of X-ray and gamma-ray sources

Abstract

We compare the analytical Generalized Comptonization model which takes into account the relativistic effects /1/, and Monte Carlo calculations for photon Comptonization by relativistic plasma clouds. We show that the new analytical model extends the previous work to a much wider range of plasma temperatures and optical depths. In general, the emergent spectra from a hot plasma cloud depend upon the spectral and spatial distributions of source photons as well as the plasma temperature and geometry. Based on the comparison between the theoretical and Monte Carlo calculations, we determine quantitatively a range of plasma geometry parameters and temperatures for which the emergent upscattering spectra are insensitive to the spectral and spatial distribution of source photons. Within this parameter range, we show that the shape of the emergent spectrum depends on two parameters only, namely the plasma temperature and β, the parameter which characterizes the photon distribution over the number of scatterings which the soft photons undergo in the plasma cloud in order to become the hard ones. We find the exact solution of the Kompaneets equation in the case of subrelativistic energies and plasma temperatures, in the optically thick regime. The solution recovers the low and high energy asymptotic forms studied in /1/. Also, we modify the Sunyaev & Titarchuk formula /2/ in order to obtain a fairly good subrealtivistic analytical approximation. This new formula, verified by Monte-Carlo calculations, contains as partial cases the Titarchuk's analytical results /1/, for optically thick and thin cases respectively. The analytical models, examined by the present Monte Carlo calculations, make possible a more efficient spectral analysis of data obtained from X-ray and gamma-ray sources.