Comptonization Models and Spectroscopy of X-Ray and Gamma-Ray Sources: A Combined Study by Monte Carlo and Analytical Methods

We compare the analytical generalized Comptonization models, which take into account the relativistic effects, with Monte Carlo calculations for photon Comptonization by relativistic plasma clouds. We show that the new analytical models extend 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 numb...