On thermalization of radiation in hydrostatic atmospheres

TL;DR

This paper investigates how radiation thermalizes in a hydrogen atmosphere with a hydrostatic density profile, using probabilistic methods and solving radiative transfer equations to determine the optical depth for thermalization.

Contribution

It introduces a probabilistic approach to define thermalization depth and provides analytical and numerical solutions for radiation in hydrostatic atmospheres.

Findings

Quantitative estimates of optical depth for thermalization.

Frequency-dependent probabilities of free-free absorption.

Validation of results through analytical and numerical solutions.

Abstract

The problem of thermalization of radiation within a self-emitting hydrogen isothermal atmosphere is considered for the case of a hydrostatic profile of the plasma density. The probabilistic approach to define the thermalization depth for the photon of a given frequency is used. Quantitative conclusions are made on the value of the optical depth at which the radiation can be viewed as thermalized up to a given frequency. The analytical and numerical solutions of the radiative transfer equation confirm the obtained results. The frequency dependencies of the probability of free-free absorption of a photon due to single interaction in a cold nonmagnetized and magnetized plasma are calculated.