# Radiation intensity and polarization in atmosphere with chaotic magnetic field

## TL;DR

This paper studies how chaotic magnetic fields affect the intensity and polarization of scattered radiation in atmospheres, showing that magnetic fluctuations significantly reduce polarization without changing the scattering complexity.

## Contribution

It provides a detailed analysis of Faraday rotation effects in chaotic magnetic fields on radiation polarization, extending the Milne problem to magnetized atmospheres without mean magnetic fields.

## Key findings

- Chaotic magnetic fields do not increase the number of H-functions in the Milne problem.
- Polarization decreases significantly with increased magnetic fluctuations.
- Results can help estimate inclination angles of accretion disks and magnetic fluctuation levels.

## Abstract

We consider the influence of Faraday rotation in chaotic magnetic field on the intensity and linear polarization of multiple scattered radiation. All fluctuations are assumed as Gaussian type and isotropic. The values of magnetic field are less than $10^5$Gauss. In this case the parameter $ \omega_B/\omega=(eB/m_ec)/\omega\simeq 0.93\cdot 10^{-8}\lambda$($\mu$m)$B($G$)$ is small and the radiation scatterings are the usual scatterings on free electrons. Only the Faraday rotation influences on the intensity and polarization of radiation. We consider the Milne problem in the electron magnetized atmosphere without the mean magnetic field. We found that chaotic magnetic field does not increase the number of H-functions, describing the Milne problem. There are four H-functions as in the Milne problem for non-magnetized case. The calculations demonstrate that the polarization of outgoing radiation diminishes strongly with the increasing of the level of magnetic fluctuations. The calculations can be used for estimations of inclination angle $i$ of accretion discs and the level of magnetic fluctuations.