On the accuracy of the ALI method for solving the radiative transfer equation

¹ Centre de Recherche Astronomique de Lyon, UMR 5574 du CNRS, Observatoire de Lyon, 9 avenue Charles André, 69561 Saint-Genis-Laval Cedex, France e-mail: rutily@obs.univ-lyon1.fr
² Observatoire de la Côte d'Azur, Département G. D. Cassini, UMR 6529 du CNRS, BP 4229, 06304 Nice Cedex 4, France e-mail: fpaletou@mail.ast.obs-mip.fr

Corresponding author: L. Chevallier, loic.chevallier@obs.univ-lyon1.fr

Received: 25 April 2003
Accepted: 30 July 2003

Abstract

We solve the integral equation describing the propagation of light in an isothermal plane-parallel atmosphere of optical thickness , adopting a uniform thermalization parameter ϵ. The solution given by the ALI method, widely used in the field of stellar atmosphere modelling, is compared to the exact solution. Graphs are given that illustrate the accuracy of the ALI solution as a function of the parameters ϵ, and optical depth variable τ.