Extend the Kompaneets Equation to Down-Comptonization Process in a Novel Way

TL;DR

This paper introduces a novel relativistic correction to the Kompaneets equation, enabling accurate modeling of both up- and down-Comptonization processes in astrophysics, especially in high-energy regimes.

Contribution

A new relativistic extension of the Kompaneets equation is proposed, valid across nonrelativistic and relativistic energy regimes, improving modeling of Comptonization processes.

Findings

Excellent agreement between the new equation and numerical simulations.

The extended equation accurately models down-Comptonization in high-energy astrophysics.

The correction broadens the applicability of the Kompaneets equation.

Abstract

Comptonization is a very important phenomenon in astrophysics. Kompaneets equation describes up-Comptonization process in nonrelativistic astrophysics, while it fails for down-Comptonization Scattering which is the most important radiative transfer process in hard X-rays and $\gamma$-rays astronomy. In this study, we explore both up-Comptonization and down-Comptonization processes. A new relativistic corrections is introduced to the Kompaneets equation which is valid in both nonrelativistic energy regime with the photon energy $h\nu << m_ec^2$ and the electron temperature $KT_e << m_ec^2$. Numerical comparisons are presented which show excellent agreement between the Kompaneets equation and the new equation.