Recent Developments in Polarized Line Formation in Magnetic Fields

Abstract

The nature of solar surface magnetism has been an open problem in solar physics. In this paper we address three frontline problems of spectropolarimetry of the Sun. We first review the theoretical formulation and numerical solutions of Zeeman absorption and then the Hanle scattering phenomena in ‘turbulent magnetic fields’. We show that the mean emergent Stokes profiles cannot be obtained by simply averaging the scattering and absorption opacities, respectively, over a given distribution of the random field (except when the micro-turbulence prevails). A new formulation of the transfer equation is necessary to study the astrophysically interesting meso-turbulence case. Such formulations of the stochastic polarized radiative transfer problems for absorbing and scattering media are developed only in recent years. We review them and show some results computed by our new formulations.Until recent years the solution of the polarized line radiative transfer equation in LTE (Zeeman absorption in strong fields), and its NLTE counterpart (Hanle scattering in weak fields), were treated as two disparate problems. The reason for this artificial division was more due to the theoretical and numerical difficulties encountered in the solution of the combined Hanle-Zeeman radiative transfer equation. A very general form of the transfer equation was formulated only a decade ago, for the case of complete frequency redistribution. A more difficult case of partial frequency redistribution is explored by us recently. We review these developments through a study of the Hanle-Zeeman effect in arbitrary strength magnetic fields.