Radiative transfer in one-dimensional inhomogeneous atmospheres

Abstract

Abstract.We use Ambartsumian's method of addition of layers to show that various problems, including the standard ones, of radiation transfer in a plane-parallel inhomogeneous atmosphere may be reduced to the solution of the Cauchy problems for linear differential equations. This allows avoiding the known difficulties arising in solving the boundary-value problems to which the classical approach leads. For the purpose of exposition, the paper deals with the simplest one-dimensional problem of multiple scattering for an atmosphere of finite optical thickness. The idea of the approach is that we start with determining the reflection and transmission coefficients of an atmosphere by solving the initial-value problem for a set of linear differential equations of the first order. After that the internal radiation field is found immediately without solving any new equation. The approach is applied to several classical problems of astrophysical interest. In particular, we evaluate the mean number of scatterings undergone by different types of photons. The transfer of radiation in an atmosphere with arbitrarily distributed internal sources is considered. Analytical solutions for these problems are obtained. Simple recursion formulas are derived to find the radiation intensity emitted by a multicomponent atmosphere. The problem of multiple scattering of radiation with partial redistribution over frequencies is discussed to demonstrate the generalization of the approach to the matrix case. The results of numerical calculations are given.

Group-theoretical description of radiative transfer in one-dimensional media

“…At the same time, it has been shown [1,2] that an inhomogeneous atmosphere has a polarity property, i.e., its optical properties are described by three parameters:…”

“…Our earlier papers [1][2][3][4] deal with radiative transfer in one-dimensional inhomogeneous atmospheres where the scattering coefficient (or the probability of re-emission of a photon in an elementary scattering event) λ is a function of optical depth. They dealt with different problems encountered most often in applications, as well as the typical difficulties which arise when inhomogeneities are taken into account.…”

“…It is based on generalized (to the case of an inhomogeneous atmosphere) addition laws for the reflection and transmission coefficients derived previously [1,2]. Laws of this type for a homogeneous atmosphere were first obtained by Ambartsumyan [5,6].…”

Ambartsumian’s invariance principle and some nonlinear relations in radiative transfer theory

“…For example, Eqs. (9)-(12) remain in force even when the media are inhomogeneous, with, of course, their polarity taken into account [11].…”

Solution of linear radiative transport problems in plane-parallel atmospheres. I.

“…The idea behind this method has been developed previously by the author [18][19][20][21][22] in papers on radiative transfer problems in inhomogeneous media and, for solving a given linear radiative transfer problem, involves a preliminary determination of the global optical properties of an atmospherethe reflection and transmission coefficients, as well as some other related quantities, for a family of atmospheres with different optical thicknesses. This makes it possible to determine the radiation field inside the medium without solving any new equations.…”