The transfer of polarized radiation in spectral lines: Formalism and solutions in simple cases

A general treatment of the transfer of polarized radiation in spectral lines assuming a Rayleigh phase function and a general law of frequency redistribution is derived. It is shown how nine families of coupled integral equations for the moments of the radiation field arise which are necessary to fully describe the state of polarization of the emergent radiation from a plane-parallel, semi-infinite atmosphere. The special case of angle independent redistribution functions is derived from the general formalism, and it is shown how the nine families of integral equations reduce to the six linearly independent integral equations derived by Collins (1972). To serve as a test of the formulation, solutions for isothermal atmospheres are given.