The formation of polarized lines: factorization of the hanle phase matrix and vЄ law in a most general form

Abstract

Weconsidertheproblemof the transferpolarized radiationunderresonance scattering in a medium with a weak magnetic field, taking into account the Hanle effect. In the past, this problem has become very important in connection with the high degrees of polarization discovered in numerous Fraunhofer lines observed in the solar spectrum. The Hanle phase matrix describes redistribution of radiation in direction and polarization in a single scattering in cases when frequency redistribution can be separated from redistribution indirection and polarization, as for exampleinthe case of complete frequency redistribution. The Hanle phase matrix depends on the angular dependence of the Stokes parameters for incoming and scattered radiation, as well as on the direction and magnitude of the magnetic field. We derive the factorization of the Hanlephase matrix as a product of 3×6 and 6×6 matrices. Each of these matrices depends only on one of the angular dependences. This factorization greatly simplifies the problem of polarized radiative transfer in a weak magnetic field...

Keywords:

spectral lines, radiative transfer, polarization, magnetic fieldes, solar spectrum