Covariant Compton Scattering Kernel in General Relativistic Radiative Transfer

TL;DR

This paper derives a closed-form, covariant Compton scattering kernel applicable in general relativistic radiative transfer, enabling efficient and accurate modeling of scattering in complex astrophysical environments.

Contribution

We present the first explicit closed-form covariant Compton scattering kernel valid across arbitrary energy ranges, expressed via hypergeometric functions, improving computational efficiency and accuracy.

Findings

Kernel and moments evaluated numerically with various techniques.

Results match previous numerical methods in restrictive settings.

Provides a foundation for advanced relativistic radiative transfer simulations.

Abstract

A covariant scattering kernel is a core component in any self-consistent general relativistic radiative transfer formulation in scattering media. An explicit closed-form expression for a covariant Compton scattering kernel with a good dynamical energy range has unfortunately not been available thus far. Such an expression is essential to obtain numerical solutions to the general relativistic radiative transfer equations in complicated astrophysical settings where strong scattering effects are coupled with highly relativistic flows and steep gravitational gradients. Moreover, this must be performed in an efficient manner. With a self-consistent covariant approach, we have derived a closed-form expression for the Compton scattering kernel for arbitrary energy range. The scattering kernel and its angular moments are expressed in terms of hypergeometric functions, and their derivations are shown explicitly in this paper. We also evaluate the kernel and its moments numerically, assessing various techniques for their calculation. Finally, we demonstrate that our closed-form expression produces the same results as previous calculations, which employ fully numerical computation methods and are applicable only in more restrictive settings.