Solution of the Comoving-Frame Equation of Transfer in Spherically Symmetric Flows. III. Effect of Aberration and Advection Terms

Abstract

We investigate the importance of the advection and aberration terms, which are of order V/c, in the comoving-frame transfer equation in spherical geometry. Characteristic trajectories are found which reduce the spatial derivatives to a perfect differential, and a generalization of the numerical procedure developed in the earlier papers of this series that permits the integration of the transfer equation on these characteristics is presented. For cases in which V/c 1, a perturbation solution is developed which reduces the problem to that solved in the first paper in this series. For velocities of the form V(r) r (n = 0, 1, 2), it is shown that the magnitude of the effects arising from the advection and aberration terms is about 5 V/c relative to the solution with these terms omitted. In stellar winds V/c <% 0.01; hence we conclude that aberration and advection terms may safely be ignored, and that consideration of the Doppler-shift term alone is adequate in the computation of spectra from such expanding atmospheres. Subject headings: radiative transfer - stars: atmospheres