Rosseland and flux mean opacities for Compton scattering

TL;DR

This paper accurately computes Rosseland and flux mean opacities for Compton scattering across various temperatures and degeneracy levels, highlighting differences from previous models especially at low temperatures and high degeneracy.

Contribution

It provides exact calculations of Rosseland mean opacity using relativistic kinetic equations, including analytical approximations and methods for degenerate electrons.

Findings

Significant differences from previous models at low temperatures and high degeneracy.

Nearly identical Rosseland and flux mean opacities in diffusion approximation.

Provides analytical expressions and methods for true absorption correction.

Abstract

Rosseland mean opacity plays an important role in theories of stellar evolution and X-ray burst models. In the high-temperature regime, when most of the gas is completely ionized, the opacity is dominated by Compton scattering. Our aim here is to critically evaluate previous works on this subject and to compute exact Rosseland mean opacity for Compton scattering in a broad range of temperatures and electron degeneracy parameter. We use relativistic kinetic equations for Compton scattering and compute the photon mean free path as a function of photon energy by solving the corresponding integral equation in the diffusion limit. As a byproduct we also demonstrate the way to compute photon redistribution functions in case of degenerate electrons. We then compute the Rosseland mean opacity as a function of temperature and electron degeneracy. We compare our results to the previous calculations and find a significant difference in the low-temperature regime and strong degeneracy. We find useful analytical expressions that approximate well the numerical results. We then proceed to compute the flux mean opacity and show that in diffusion approximation it is nearly identical to the Rosseland mean opacity. We also provide a simple way for accounting for the true absorption in evaluation of the Rosseland and flux mean opacities.