The Diiusion of Radiation in Moving Media Iv. Flux Vector, Eeective Opacity, and Expansion Opacity

For a given velocity and temperature eld in a diierentially moving 3D medium, the vector of the radiative ux is derived in the diiusion approximation. Due to the dependence of the velocity gradient on the direction, the associated eeective 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 ux vector deviates from that of the temperature gradient. Furthermore the radiative ux is calculated for innnitely sharp, Poisson distributed spectral lines resulting in simple expressions that provide basic insight into the eeect of the motions. In particular, it is shown how incomplete line lists aaect the radiative ux 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. (1977) is discussed.