Towards the Modelling of the Second Solar Spectrum

This paper addresses the modelling issue of the second solar spectrum. This is the name given to the linearly polarized spectrum which can be observed close to the solar limb using spectro-polarimeters of high polarimetric sensitivity (Stenflo and Keller, 1997). The second solar spectrum is due to scattering processes and offers a rich diagnostic potential for exploring solar magnetic fields via the Hanle effect. However, it is full of mysterious spectral features that cannot be understood with simplified polarization transfer theories, thus suggesting that the underlying scattering physics is more complex than previously thought. In this paper we argue that understanding the second solar spectrum requires the consideration of scattering processes in multilevel atomic models, taking fully into account the transfer of atomic polarization among all the levels involved. To give support to this statement, we begin by pointing out the drastically different predictions, given by the standard resonance line polarization theory, with respect to the emergent polarization in three different line transitions. This standard theory neglects the atomic polarization of the lower level of the line transition under consideration, i.e. it assumes that there are no population imbalances among the lower-level sublevels. The density matrix polarization transfer theory is then applied to formulate the scattering polarization problem taking properly into account atomic polarization in both the upper and the lower line levels. The consideration of lower-level atomic polarization leads to coupled non-linear and non-local sets of equations, even for the two-level model atom case considered in this paper. The unknowns of these equations are the irreducible tensor components of the atomic density matrix whose self-consistent values have first to be obtained to be able to calculate the emergent Stokes profiles. To solve this non-LTE problem of the 2 kind we present some iterative methods that are very suitable for developing a general multilevel scattering polarization code. With these numerical methods some model calculations are performed in order to demonstrate that the inclusion of lower-level atomic polarization leads to similar emergent linear polarization signals in such three different line transitions, as some observations show. After pointing out that the “Na solar paradox” (Landi Degl’Innocenti, 1998) might admit, in principle, a multilevel solution, the paper ends establishing a new solar paradox: “the Mg solar paradox”, for which no multilevel solution seems to be possible. This new result demonstrates that there indeed exists ground and metastable-level atomic polarization in the solar chromosphere and it suggests that the solution to these “solar paradoxes” is to be found by carefully revising our current ideas about the chromospheric magnetic field. Published in 1999 in the book Solar Polarization, edited by K.N. Nagendra & J.O. Stenflo. Kluwer Academic Publishers, 1999. (Astrophysics and Space Science Library ; Vol. 243), p. 73-96 2 JAVIER TRUJILLO BUENO