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Astron. Astrophys. 328, 726-751 (1997)

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Master equation theory applied to the redistribution of polarized radiation, in the weak radiation field limit

II. Arbitrary magnetic field case

V. Bommier

1 Laboratoire 'Atomes et Molécules en Astrophysique', CNRS URA 812 - DAMAp, Observatoire de Paris, Section de Meudon, F-92195 Meudon, France (Veronique.Bommier@obspm.fr)

Received 11 February 1997 / Accepted 4 August 1997

Abstract

This paper addresses the problem of partial redistribution of polarized radiation in the presence of a magnetic field of arbitrary strength. It is the continuation of a previous paper (Paper I) devoted to the same problem, treated in the simpler case of vanishing magnetic field. In the present paper, we give the results of the derivation of the master equation for the atomic density matrix, and of the coefficients of the radiative transfer equation, following the method described in Paper I(which makes use of the summation of the perturbation series development for the atom-radiation interaction), now applied to the case of a non-zero magnetic field of arbitrary strength. The other hypotheses underlying the derivation of Paper Iare maintained in the present paper, namely: (a) weak radiation field (stimulated emission is neglected with respect to spontaneous emission); (b) 2-level atom; (c) unpolarized lower level. The redistribution matrix, that relates the frequency, polarization and direction of the incident photon to those of the scattered photon, is derived in the presence of a magnetic field of arbitrary strength. 3 successive levels of approximation are proposed, in the case of a weak magnetic field, in order to derive simpler expressions for the redistribution matrix that might conveniently be used in radiative transfer calculations.

Key words: atomic processes – line: formation – line: profiles – magnetic fields – polarization – radiative transfer

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© European Southern Observatory (ESO) 1997

Online publication: March 26, 1998

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