The computation of Comptonization — A comparison between generalized Kompaneets equation and Monte Carlo method

The down-Comptonization, which occurs during the passage of hard X-rays through “cold” plasmas, is an important process of radiative transfer in X-ray astronomy and radiation physics. This paper presents a brief introduction to the the generalized Kompaneets equation, which may be widely valid under rather loose conditions of by hν ⪡ mec2 and kTe ⪡ mec2. It can be used for both the up- Comptonization (hν ⪡ mec2) and down-Comptonization (hν, ⪢ mec2). The latter is exceedingly important for X-ray and γ-ray astronomy, which are developing rapidly these days. On the basis of this equation, the spectral evolution is numerically investigated for four common radiation spectra in astrophysics (namely, the Gaussian-type emission line, the blackbody spectrum, the powerlaw spectrum and the thermal bremsstrahlung radiation spectrum) in the case of down-Comptonization. We compare the results with the results of Monte Carlo simulation, and the correctness and effectiveness of the generalized Kompaneets equation are confirmed. Finally, the important significance and potential applications of this equation in X-ray and γ-ray astronomy are pointed out.