Solutions to radiative transfer problems using approximate lambda operators

Abstract

An approximate analytical method and an exact numerical method for solving non-LTE problems are presented. The analytical method relies on concepts of radiative transfer theory such as the core-saturation approximation, the Eddington-Barbier relation, and the upper boundary condition, to derive a simple first-order differential equation for the line source function. The more efficient technique is developed using a linear test function and a one-point quadrature relation between the specific intensity and the source function. A 1% accuracy in the line source function can be obtained after four iterations, with a very rapid convergence and no evidence of numerical instabilities.