AN IMPLICIT INTEGRAL METHOD TO SOLVE SELECTED RADIATIVE-TRANSFER PROBLEMS .3. FACTORIZATION VERSUS LINEARIZATION

In view of more general applications, we have developed a new approach to render explicit the temperature both in the source function of the radiative transfer equation and in the constraint of radiative equili brium. This is a necessary step in the iterative temperature correctio n when computing stellar atmosphere models. Our method consists of a p roper factorization of the Planck function through a normalized freque ncy profile b(nu) = b(nu)(T), computed from a trial temperature, and B (T), the integral over frequencies of the Planck function itself. It h olds that B(nu)(T) = b(nu)B(T); integral b(nu) dnu = 1. The quantity B (T) is proportional to the fourth power of the temperature required. S uch an approach, which works exactly as the customary linearization me thod, can easily be applied also to correcting a trial radiation field , within a class of more general radiative transfer problems.