Polarized Line Formation in Spherically Symmetric Atmospheres with Velocity Fields

The plane-parallel approximation of the stellar atmospheres cannot be applied to model the formation of optically thick lines formed in extended atmospheres. To a good approximation these atmospheres can be represented by a spherically symmetric medium. Such extended stellar atmospheres are dynamic, in general, due to the systematic motions present in their layers. Macroscopic velocity fields in the spectral line forming regions produce Doppler shift, aberration of photons, and also give rise to advection. All of these effects can modify the amplitudes and shapes of the emergent Stokes profiles. In the present paper we consider the problem of polarized line formation in spherically symmetric media, in the presence of velocity fields. Solving the radiative transfer problem in the observer's frame is a straightforward approach to handle the presence of velocity fields. This method, however, becomes computationally prohibitive when large velocity fields are considered, particularly in the case of the line formation with partial frequency redistribution (PFR). In this paper we present a polarized comoving frame method to solve the problem at hand. We consider nonrelativistic radial velocity fields, thereby accounting only for Doppler shift effects and neglecting advection and aberration of photons. We study the effects of extendedness, velocity fields, and PFR on the polarized line profiles formed in highly extended atmospheres.