The diffusion of radiation in moving media

III. Stochastic representation of spectral lines

¹ Institut für Theoretische Astrophysik, Tiergartenstrasse 15, 69121 Heidelberg, Germany
² Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany
³ Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany

Corresponding author: R. Wehrse, wehrse@ita.uni-heidelberg.de

Received: 11 January 2002
Accepted: 15 May 2002

Abstract

In this paper we present analytical expressions for the radiative flux, the effective extinction coefficient, and the radiative acceleration deep inside a differentially moving, very optically thick medium with many spectral lines. It is shown that the line contribution is essentially given by the characteristic function of wavelength averages of the extinction coefficient. It can be calculated either by means of the generalized opacity distribution function or by means of a Poisson point process model. Several examples are given to demonstrate the basic consequences of line densities, widths, and strengths, as well as velocity gradients on the diffusive flux. We demonstrate that for Poisson distributed lines the diffusive flux decreases with increasing absolute values of the velocity gradient (i.e. that the flux has a maximum for static media), and that such lines have hardly a direct influence on the radiative acceleration.