Iteration Profiles in Radiative Transfer Problems. I. From Vectorial to Scalar Coupling
Abstract
We have recently introduced a new algorithm, the implicit integral method (IIM), for solving radiative transfer problems in which the specific source functions (for each frequency and direction) depend linearly on the radiation field via a single quantity which is independent of both frequency and direction. We define this kind of relationship as scalar coupling. The fact that our method turned out to be fast, robust, and highly reliable leads us to seek its extension to include those problems where the above, necessary condition is not fulfilled. In these problems, the specific source functions depend on the radiation field through a nonfactorable redistribution operator. In our definition, these are cases of vectorial coupling.
In this paper we present the successful application of the IIM, through an iterative procedure, to two specific instances of vectorial coupling. The first is the determination of the temperature distribution, selfconsistent with the energy conservation constraint, within a LTE stellar atmosphere model. Here the physical processes other than radiative transfer require an iterative procedure for the global solution of the problem. Thus we take advantage of this circumstance to solve iteratively the radiative transfer part as well.
The second is the case of the nonLTE twolevelatom line formation problem in which partial redistribution is taken into account in the presence of a background continuum. This problem allows a direct solution, but at the cost of using algorithms that necessarily require the storage and inversion of very high order matrices. On the contrary, we show that a solution based on the iterative application of the IIM, thanks to the outstanding features of the latter, is not only fast, but above all much more reliable in numerical terms.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 1995
 DOI:
 10.1086/176222
 Bibcode:
 1995ApJ...451..328C
 Keywords:

 LINE: FORMATION;
 METHODS: NUMERICAL;
 RADIATIVE TRANSFER;
 STARS: ATMOSPHERES