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Astron. Astrophys. 324, 344-356 (1997)

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1. Introduction

A window to a previously unexplored parameter domain has been opened with the availability of an imaging polarimeter system, ZIMPOL (Z urich Im aging Stokes Pol arimeter) (Povel et al.  1991 ; Keller et al.  1992 ; Stenflo et al.  1992 ; Stenflo 1994 ; Povel 1995 ), which reaches an accuracy of [FORMULA] in the degree of polarization. At this level of precision the whole solar spectrum is full of polarized spectral structures that are present even in the absence of any magnetic fields, since both the line and continuous spectrum are partly formed by scattering processes. As the illumination of the scattering particles in the solar atmosphere is not entirely isotropic, the incident radiation induces an atomic alignment of the excited states, with the result that the emitted light is partially polarized.

An anisotropy of the incident radiation field is always present even for a spherically symmetric sun due to the limb darkening of the solar disk, but small-scale inhomogeneities, like granulation and magnetic flux tubes, cause local fluctuations. The scattering polarization that is due to the limb-darkening anisotropy is zero at disk center for symmetry reasons and increases monotonically as one approaches the solar limb.

Since the resulting linearly polarized spectrum is very different in appearance and information contents as compared with the ordinary intensity spectrum, it has been found convenient to refer to it as "the second solar spectrum" (Stenflo 1996 ; Stenflo & Keller 1996a , b).

The prime objective of the present paper is to develop a theoretical framework that can be used to interpret the multitude of spectral structures seen in "the second solar spectrum", since previous theories have been too incomplete, only address certain aspects of the general problem, or do not have a suitable form for practical applications. Although the pioneering work by Landi Degl'Innocenti (1983 ), extended by Landi Degl'Innocenti et al. (1991a ,b), has provided a general theory for Rayleigh scattering in terms of a density matrix formalism, and Bommier (1996 ) has formulated the partial frequency redistribution problem for Rayleigh scattering in weak magnetic fields to 4th order and higher in quantum perturbation theory, these formulations do not easily lend themselves to practical, exploratory applications. Furthermore the observed polarization is generally not only due to Rayleigh scattering but is in a large number of cases produced by Raman scattering involving many atomic levels with quantum interferences between them. A suitable theoretical framework is needed to address such common cases in a convenient way.

The theory of the present paper is formulated for the general case of Raman scattering (that has Rayleigh scattering as a special case) with atomic coherences in a magnetic field of arbitrary strength and direction, taking into account all the fluorescent contributions within or between the atomic multiplets considered (including hyperfine multiplets). Explicit expressions are however only given for the case of zero magnetic field. Although the theory may be incorporated in a radiative transfer formalism, we bypass in the present paper the radiative transfer problem for exploratory purposes by introducing a parametrized model that is useful for identifying the physical effects and for obtaining model fits to the shapes of the polarized line profiles.

With these tools the underlying physics behind a number of observed spectral structures can then be identified in terms of Raman and fluorescent scattering within multiplets, quantum interferences between excited states of different total angular momenta, hyperfine structure and isotope effects.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998