The diffusion of radiation in moving media

IV. Flux vector, effective opacity, and expansion opacity

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 September 2002
Accepted: 10 December 2002

Abstract

For a given velocity and temperature field in a differentially moving 3D medium, the vector of the radiative flux is derived in the diffusion approximation. Due to the dependence of the velocity gradient on the direction, the associated effective opacity in general is a tensor. In the limit of small velocity gradients analytical expression are obtained which allow us to discuss the cases when the direction of the flux vector deviates from that of the temperature gradient. Furthermore the radiative flux is calculated for infinitely sharp, Poisson distributed spectral lines resulting in simple expressions that provide basic insight into the effect of the motions. In particular, it is shown how incomplete line lists affect the radiative flux as a function of the velocity gradient. Finally, the connection between our formalism and the concept of the expansion opacity introduced by Karp et al. ([CITE]) is discussed.