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Astron. Astrophys. 342, 201-211 (1999)

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Integration of the radiative transfer equation for polarized light: the exponential solution

M. Semel and A. López Ariste

DASOP, URA 326, Observatoire de Paris, Section de Meudon, France

Received 18 March 1998 / Accepted 6 November 1998


The radiative transfer equation (RTE) for polarized light accepts a convenient exponential solution when the absorption matrix commutes with its integral. We characterize some of the matrix depth variations which are compatible with the commutation condition. Eventually the vector solution may be diagonalized and one may obtain four independent scalar solutions with four optical depths, complex in general. When the commutation condition is not satisfied, one must resort to a determination of an appropriate evolution operator, which is shown to be well determined mathematically, but whose explicit form is, in general, not easy to apply in a numerical code. However, we propose here an approach to solve a general case not satisfying the commutation condition.

Key words: polarization – radiative transfer – methods: numerical – Sun: magnetic fields – stars: magnetic fields

Send offprint requests to: M. Semel

Correspondence to: Meir.Semel@obspm.fr

© European Southern Observatory (ESO) 1999

Online publication: December 22, 1998