Spectral and temporal properties of Compton scattering by mildly relativistic thermal electrons

TL;DR

This paper introduces new solutions and methods for thermal Comptonization in mildly relativistic electrons, improving spectral fitting and providing detailed timing properties for astrophysical X-ray sources.

Contribution

It extends the kinetic equation solution to mildly relativistic regimes and develops an accurate Monte Carlo method for spectral and timing analysis.

Findings

Validated kinetic-equation solution against Monte Carlo results.

Provided detailed photon emission time distributions.

Compared results with existing methods, demonstrating improved accuracy.

Abstract

We have obtained new solutions and methods for the process of thermal Comptonization. We modify the solution to the kinetic equation of Sunyaev \& Titarchuk to allow its application up to mildly relativistic electron temperatures and optical depths $\gtrsim{1}$. The solution can be used for spectral fitting of X-ray spectra from astrophysical sources. We also have developed an accurate Monte Carlo method for calculating spectra and timing properties of thermal-Comptonization sources. The accuracy of our kinetic-equation solution is verified by comparison with the Monte Carlo results. We also compare our results with those of other publicly available methods. Furthermore, based on our Monte Carlo code, we present distributions of the photon emission times and the evolution of the average photon energy for both up and down-scattering.