Polarized Radiative Transfer in Solar Atmosphere

The observations indicate the existence of linear polarization in the hydrogen Hα spectral line observed during the solar flare events. This emission of polarized radiation is of the order of 5% and is usually explained as a consequence of collisions of hydrogen atoms with the beam of fast protons coming from coronal regions. This article presents a brief overview of the recent solar flare polarization studies and explains the importance of the line polarization for understanding physics of anisotropical processes. A short introduction to polarized formalisms is presented and a formalism of density matrix is introduced. The coupling of polarized radiation and matter is expressed in the form of radiative transfer equations and equations of statistical equilibrium and the basics of non-LTE modelling in the one-dimensional plane-parallel atmosphere, non-magnetic regime is illustrated. A method of Λ-operator splitting applied to polarized radiative transfer task is presented, in which the importance of the finite width of overlapping absorption profiles for frequency discretization is highlighted, as well as the effect of a convergence acceleration by use of ALI (accelerated lambda-iteration) method for a multilevel problem. Hydrogen line polarization in solar flares The observations of solar flares indicate linear polarization in the line center and near wings of the hydrogen line Hα [e.g. Vogt & Hénoux, 1999]. The direction of polarization vector is mainly close to the radial (flare to disk center) direction and the maximum polarization degree is about 5%. This polarization is often interpreted as due to anisotropic collisional excitation of the n = 3 level by the vertical proton beams with energy of the order of few keV (or neutral electron-proton beams with the same velocity). These particles could come from the coronal region as a result of magnetic– field reconnection event and interact with the chromospheric flaring region. The detailed computation of proton–hydrogen collisional cross-sections shows the significant effect of anisotropical collisions on atomic polarization, so called impact polarization [Balança & Feautrier, 1998]. The opposite effect caused by isotropic velocity distribution of background charged particles may induce a depolarization of atomic states [e.g. Sahal-Bréchot et. al., 1996]. Because of this, the detection of polarization in spectral lines is an important diagnostic tool for studying conditions of flaring regions. Recent works showed that the effect of impact polarization under conditions of formation region of the Hα line in solar flares may locally cause an emission of the radiation with polarization degree comparable with the observations [Vogt et. al., 1997, 2001]. However, the effect of radiative transfer including propagation of the polarization state was yet not included and this text will show how to extend these models by including the radiative transfer effects. Polarization of light From the classical electromagnetic-theory point of view, the monochromatic electromagnetic wave is described by evolution of the electric and magnetic vectors in the plane perpendicular to the direction of propagation. We will not consider the magnetic component of the light because of its negligible effects on atomic states under the conditions of the solar atmosphere. In the orthogonal coordinate system, having the axis z in the direction of propagation (Ω) and the axes x, y in the perpendicular plane, the electric vector of the wave is described by the two components Eλ(t) = Eλe, λ = x, y, (1) where Eλ = Eλeλ , Eλ real, is their amplitude and phase shift factor. To describe light in measurable quantities it is convenient to define the bilinear products Iγδ(t) = WDS'05 Proceedings of Contributed Papers, Part III, 469–474, 2005. ISBN 80-86732-59-2 © MATFYZPRESS