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.
Abstract. The paper aims at revealing the role of the Compton effect when considering the W-L scattering of the solar photospheric radiation by coronal supra-thermal streams. We first document several examples of well observed cases of linear W-L coronal threads extending above flaring active regions which are good candidates to give the signature known from the interpretation of radio type III bursts. The height-dependent model problem of Compton scattering on the beam of fast electrons gyrating around the lines of force of the magnetic field is considered. The resulting change in frequency averaged over the beam and the solid angle, within which the photospheric radiation falls, is computed for both sunward and antisunward directed streams. The dependence of the effect on the height above the solar surface, the speed of electrons and the slope angle is discussed. For illustration, we consider the case, in which the frequency distribution of the incident radiation is Planckian. The effective value of the cross-section of interaction is compared with that for the Thomson scattering. In particular, we conclude that, depending on the angle between the directions of the initial outburst and the magnetic field, the streams moving away from the Sun may produce drifts in frequency to the shortwave, as well as to the longwave domains of the spectrum. The effect may become essential even for moderate energies of fast electrons, and it should be measurable using precise photometric color index determination, if only the fractional density of fast electrons is not too small.
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