An implicit integral method to solve selected radiative transfer problems. 3: Factorization versus linearization

Crivellan, L.; Simonneau, E.
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The Astrophysical Journal, vol. 428, no. 2, pt. 1, p. 753-759

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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 equilibrium. This is a necessary step in the iterative temperature correction when computing stellar atmosphere models. Our method consists of a proper factorization of the Planck function through a normalized frequency profile bnu=bnu(T), computed from a trial temperature, and B(T), the integral over frequencies of the Planck function itself. It holds that B(sun nu)(T) = bnu B(T); integral bnu d nu=1. The quantity B(T) is proportional to the fourth power of the temperature required. Such an approach, which works exactly as the customary linearization method, can easily be applied also to correcting a trial radiation field, within a class of more general radiative transfer problems.