AN IMPLICIT INTEGRAL METHOD TO SOLVE SELECTED RADIATIVE-TRANSFER PROBLEMS .4. THE CASE OF SPHERICAL GEOMETRY

In the previous papers of this series, we introduced the implicit inte gral method (IIM) to solve those radiative transfer (RT) problems in w hich the source function depends on an integral of the specific intens ity of the radiation field over directions and frequencies. The IIM re sts upon a forward-elimination, back-substitution scheme naturally bas ed on the physics of the RT process, and does not require any matricia l algorithm. Customary methods to solve RT problems, in which the sour ce function depends on the aforesaid integral, rest upon matrix algori thms. In spherical geometry, due to the strong anisotropy of the radia tion field brought about by the limb curvature, the so-called peaking effect, the number of directions necessary to describe this anisotropy is exceedingly high, and consequently the relevant matrices are hard to handle. The present paper deals with the application of the IIM to RT problems in spherical geometry, where the distinctive nonmatricial character of the method can be fully exploited, given the intrinsic hi gh dimensionality of the problem.