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Astron. Astrophys. 333, 1130-1142 (1998)

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1. Introduction

One can describe spicules as cylindrical structures appearing at the boundaries of the supergranules of the solar atmosphere. Their diameters are about 700 km, and the spicules mount in the corona conducted by the magnetic field. One can observe matter up to a height of [FORMULA] km with a mean inclination of [FORMULA] relative to the normal to the solar surface. This paper deals with the theory of the density matrix of photons resonantly scattered by atoms having an ensemble velocity. The theory of the multilevel atom scattering the incident photospheric radiation is outlined by a quantum formalism (Bommier 1977 ; Bommier & Sahal-Bréchot 1978 ). We apply the theory to neutral H atoms in spicules. We illustrate our method by calculating the Stokes parameters I, Q, U of H [FORMULA], one of the lines mostly used to observe spicules. We obtain a non negligible degree of polarization and rotation of the polarization direction due only to the effect of the velocity field, that is, neglecting the effect of any magnetic field on polarization.

The method of calculation described hereafter is derived from the theoretical method that has been developed for a two-level atom by Sahal-Bréchot et al. (1998 ), as outlined in Sahal-Bréchot et al. (1992 ) and in Sahal-Bréchot & Choucq-Bruston (1994 ). The present paper is concerned by the adaptation of the method to the particular multi-level case of the H [FORMULA] line of hydrogen.

In Sects. 2and 2.1we define the photospheric profile of the H [FORMULA] line used for our theoretical model, and also the density matrices of the incident and scattered radiation allowing for correlations due to the Doppler effect. In Sect. 2.1and 7, we give the equations of statistical equilibrium in tensorial notation. We solve these equations and find an analytical approximation for the tensors (Sects. 3, 3.1and 3.2). This enables us to calculate the density matrix of the scattered photons opening the way to the expression of the Stokes parameters I, Q, U of the line (3.3). Sect. 3.4is devoted to the integration over the velocity distribution accounting for the ensemble velocity of the matter in spicules. From the Stokes parameters one obtains the polarization degree and the rotation of the polarization plane. We summarize our results in Sects. 4, 4.1and 4.2. Finally we consider the effect of collisions with protons and electrons on the atomic radiator (Sect. 5).

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© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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