# The generalized Milne problem in gas-dusty atmosphere

## TL;DR

This paper investigates the generalized Milne problem in a non-conservative, gas-dusty atmosphere, analyzing how radiation distribution and polarization depend on key parameters like dust properties and absorption.

## Contribution

It extends the classical Milne problem to include non-conservative atmospheres with dust and electrons, providing new insights into radiation behavior with varying dust and absorption parameters.

## Key findings

- Angular distribution of emerging radiation varies with dust parameters.
- Degree of polarization depends on dust anisotropy and absorption.
- Radiation flux changes within the atmosphere, unlike in the classical Milne problem.

## Abstract

We consider the generalized Milne problem in non-conservative plane-parallel optically thick atmosphere consisting of two components - the free electrons and small dust particles. Recall, that the traditional Milne problem describes the propagation of radiation through the conservative (without absorption) optically thick atmosphere when the source of thermal radiation located far below the surface. In such case, the flux of propagating light is the same at every distance in an atmosphere. In the generalized Milne problem, the flux changes inside the atmosphere. The solutions of the both Milne problems give the angular distribution and polarization degree of emerging radiation. The considered problem depends on two dimensionless parameters W and (a+b), which depend on three parameters: $\eta$ - the ratio of optical depth due to free electrons to optical depth due to small dust grains; the absorption factor $\varepsilon$ of dust grains and two coefficients - $\bar b_1$ and $\bar b_2$, describing the averaged anisotropic dust grains. These coefficients obey the relation $\bar b_1+3\bar b_2=1$. The goal of the paper is to study the dependence of the radiation angular distribution and degree of polarization of emerging light on these parameters. Here we consider only continuum radiation.