Radiative transfer in weakly polarizing media

We study radiative transfer through a weakly polarizing medium, i.e., a med ium in which the degree of polarization of the absorbed, retarded, and emit ted light is always weak. In this case, the general radiative transfer equa tion for the Stokes parameters yields very simple formal solutions. The int ensity does not depend on the polarization, and the other Stokes parameters are uncoupled from each other. It is shown how this simplified radiative t ransfer equation holds in many realistic cases relevant for solar and stell ar magnetometry. It can be applied whenever the weak magnetic held approxim ation works, i.e., for weakly split lines. In addition, it handles weak spe ctral lines, structures with complex magnetic topology, chromospheric lines formed under non-LTE conditions, etc. The merits of the approximation, whi ch we call the weakly polarizing medium (WPM) approximation, are illustrate d by means of several LTE and non-LTE line syntheses in realistic solar mod el atmospheres. The WPM approximation should be useful in planning and unde rstanding measurements based on polarization. It simplifies the relationshi p between the observed polarization and the physical structure that one tri es to retrieve. The approximation may also be used in numerical problems re quiring extensive polarized radiative transfer (inversion codes, syntheses of stellar spectra, self-consistent multilevel non-LTE Zeeman line transfer with atomic polarization, etc.).