ITERATION PROFILES IN RADIATIVE-TRANSFER PROBLEMS .1. FROM VECTORIAL TO SCALAR COUPLING

We have recently introduced a new algorithm, the implicit integral met hod (IIM), for solving radiative transfer problems in which the specif ic 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 s calar 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 the se problems, the specific source functions depend on the radiation fie ld through a nonfactorable redistribution operator. In our definition, these are cases of vectorial coupling. In this paper we present the s uccessful application of the IIM, through an iterative procedure, to t wo specific instances of vectorial coupling. The first is the determin ation of the temperature distribution, self-consistent with the energy conservation constraint, within a LTE stellar atmosphere model. Here the physical processes other than radiative transfer require an iterat ive procedure for the global solution of the problem. Thus we take adv antage of this circumstance to solve iteratively the radiative transfe r part as well. The second is the case of the non-LTE two-level-atom l ine formation problem in which partial redistribution is taken into ac count 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 o nly fast, but above all much more reliable in numerical terms.