A Generalization of the Sobolev Method for Radiation Transport with Local and Nonlocal Line Overlap

Abstract

We have generalized the Sobolev or large velocity gradient method forsolving radiative transfer problems in moving media to treat spectrallines that overlap locally or nonlocally. When the rest frequencies oftwo spectral lines differ by less than their thermal Doppler width,then the lines overlap locally and photons from one line can influencethe populations of the levels of the other line. Similarly, in amedium with velocity gradients and velocity differences enough toDoppler shift one line onto the other, the lines overlap nonlocallyand one line can affect the level populations of the other. We havederived expressions for both the intensity and the mean intensity whenthere is local or nonlocal line overlap. These expressions are generaland can be used for any temperature as long as the large velocitygradient approximation is satisfied. The mean intensity is essentialfor the radiative rates that enter into the statistical equilibriumequations, and the accurate inclusion of the effects of line overlapis crucial.