The Sobolev approximation for line formation with partial frequency redistribution

Abstract

Attention is given to the formation of a spectral line in a uniformly expanding infinite medium in the Sobolev approximation, with emphasis on the various mechanisms for frequency redistribution. Numerical and analytic solutions of the transfer equation are presented of a number of redistribution functions and their approximations, including type I and type II partial redistribution, coherent scattering and complete redistribution, and the Fokker-Planck and uncorrelated approximation to the R sub II function. The solutions for the mean intensity are shown to depend very much on the type of redistribution mechanism, while for the frequency-weighted mean intensity, which enters the rate equations, this dependence is weak. It is inferred that use of Sobolev escape probabilities based on complete redistribution can be an adequate approximation for many calculations for which only the radiative excitation rates are needed.