## 4. Concluding remarksWe have seen how the physical processes that shape the second solar
spectrum () are quite different in nature from
those of the ordinary intensity (Stokes In spite of these quite drastic idealizations it has been possible
to obtain surprisingly good fits to some of the more prominent
observed polarization features and to identify the underlying physics.
Thus the sign reversals of the polarization curve around the
Na I D At the same time we have identified observed polarization features
that we are not yet able to explain within the framework of the
present theory. While we believe that the triplet polarization peak
around the core of the Na I D The reality of the polarization peak in the Na I
D One aspect that we have left out of the present treatment is the
frequency redistribution problem, which needs to be dealt with before
one can incorporate the present theory (which here only has been given
in frequency-coherent form) in a radiative-transfer formalism with
full physical realism for quantitative modelling of solar structures.
Well-defined formulations of partial frequency redistribution of
polarized radiation exist for single-transition Rayleigh scattering,
but the generalization to multiple excited levels with quantum
interferences is far from straightforward. It is for instance not
clear how collisional redistribution works in the case of a mixed
quantum state, like the and
coherent superposition of the excited states
of the Na I D A major simplification of the theory has been achieved by ignoring
any atomic polarization of the Although our theory for polarized Raman scattering with contributions from entire multiplets in principle allows for the presence of magnetic fields of arbitrary strength and direction, we have only expressed it in explicit form for the case of zero magnetic field. A major future task will be to extend the theory to provide an explicit framework that is suited for calculations that include the Hanle and Zeeman effects as well as the mixed regime of intermediately strong fields. We need to be able to handle arbitrary fields for the interpretation of the next generation of vector polarimetric observations, which will be produced by ZIMPOL II, the second generation of our imaging Stokes polarimeter. Then it will be possible to explore the local spatial fluctuations of the scattering polarization due to magnetic fields and the spectral signatures of the mixed Zeeman-Hanle regime in active regions. The inclusion of magnetic fields in the theory leads to great technical complications because of the complex geometries (which involve the four spatial directions of the incident and scattered radiation, the magnetic field vector, and the local vertical), so certain idealized regimes will first be dealt with, like microturbulent magnetic fields (Stenflo 1982 ; Faurobert-Scholl 1993 ; Faurobert-Scholl et al. 1995 ). Another theoretical challenge will be to develop a sufficiently fast computer code for general multi-level polarized radiative transfer, which is flexible enough to incorporate our Raman scattering theory with magnetic fields. Since we with good reason may disregard the initial-state atomic polarization it is sufficient to treat the statistical equilibrium part of the multi-level problem with standard techniques that ignore the polarization, and then use the resulting level populations to solve the vector radiative transfer equation with the polarized scattering matrix and the absorption Mueller matrix, both of which contain the Zeeman effect. When such a tool for the solution of general polarized radiative transfer problems will become available, we will be in a position to begin to more systematically exploit the rich diagnostic potential of the second solar spectrum. © European Southern Observatory (ESO) 1997 Online publication: May 26, 1998 |