Analytical solution of the radiative transfer equation in the two-stream approximation

¹ Institut f. Theoretische Astrophysik, Universität Heidelberg, Tiergartenstr. 15, 69121 Heidelberg, Germany
² Interdisziplinäres Zentrum f. Wissenschaftliches Rechnen, Universität Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany
³ Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia

Corresponding author: N. V. Kryzhevoi, kolya@ita.uni-heidelberg.de

Received: 15 November 2000
Accepted: 27 February 2001

Abstract

The analytical solution of the plane-parallel radiative transfer equation is obtained in the two-stream approximation for a large class of continuous distributions of the de-excitation coefficient ε (constant, linear, parabolic, with spikes etc.). We present also the method of the discrete space theory for obtaining solutions of the transfer equation in the media with strong density inhomogeneities. These sets of the analytical solutions can be used for the solution of the inverse problem. The deduction of the internal distribution of ε from observational data is facilitated in the case of isothermal media, since the characteristic behavior of the solution refers to the certain behavior of ε. As an example, we find the corresponding parameters of the constant and linear distributions of ε precisely.