Assessment of the CRD approximation for the observer’s frame RIII redistribution matrix

Abstract

Context. Approximated forms of the RII and RIII redistribution matrices are frequently applied to simplify the numerical solution of the radiative transfer problem for polarized radiation, taking partial frequency redistribution (PRD) effects into account. A widely used approximation for RIII is to consider its expression under the assumption of complete frequency redistribution (CRD) in the observer’s frame (RIII−CRD). The adequacy of this approximation for modeling the intensity profiles has been firmly established. By contrast, its suitability for modeling scattering polarization signals has only been analyzed in a few studies, considering simplified settings. Aims. In this work, we aim to quantitatively assess the impact and the range of validity of the RIII−CRD approximation in the modeling of scattering polarization. Methods. We first present an analytic comparison between RIII and RIII−CRD. We then compare the results of radiative transfer calculations, out of local thermodynamic equilibrium, performed with RIII and RIII−CRD in realistic one-dimensional atmospheric models. We focus on the chromospheric Ca I line at 4227 Å and on the photospheric Sr I line at 4607 Å. Results. The RIII−CRD approximation provides accurate results for the Ca I 4227 Å line. Only when velocities are included can some appreciable discrepancies be found, especially for lines of sight close to the disk center. The approximation performs well also for the Sr I 4607 Å line, especially in the absence of magnetic fields or when a micro-turbulent field is included. However, some appreciable errors appear when deterministic magnetic fields or bulk velocities are considered. Conclusions. Our results show that the RIII−CRD approximation is suited for the PRD modeling of the scattering polarization signals of strong chromospheric lines, both in the core and wings. With a few minor exceptions, this approximation is also suitable for photospheric lines, although PRD effects generally play a minor role in their modeling.