A numerical solution of the line transfer equation in a spherically symmetric atmosphere.

Abstract

A numerical solution based on finite differences is proposed for solving the line transfer equation in a spherically symmetric atmosphere. The author discretizes the curvature term in the equation by the backward difference scheme for the outward-going ray from the atmosphere and by the forward difference scheme for the backward-going ray. As the radiation field is highly anisotropic in the far-wings of the line, the accuracy of the method is improved by computing the source function first using the numerical scheme for a limited set of rays. The intensity in the line is then computed with the known source function using the formal solution of the transfer equation with a large grid of rays. The solution is compared with the published results using different representation of the transfer equation and is found to be quite accurate. Another salient feature of the method is that one can enforce the non-negativity of the solution quite easily.