Assessment of the CRD approximation for the observer’s frame R^III redistribution matrix

¹ Euler Institute, Università della Svizzera italiana (USI), East Campus, Sector D, Via la Santa 1, 6962 Lugano, Switzerland
e-mail: simone.riva@usi.ch
² Istituto ricerche solari Aldo e Cele Daccò (IRSOL), Faculty of Informatics, Università della Svizzera italiana (USI), Via Patocchi 57, 6605 Locarno, Switzerland
³ Institute for Computational and Mathematical Engineering, Stanford University, Center for Turbulence Research, Room 204, 481 Panama Mall, Stanford, CA 94305-3024, USA
⁴ Simula Research Laboratory, Kristian Augusts gate 23, 0164 Oslo, Norway
⁵ FernUni, Schinerstrasse 18, 3900 Brig, Switzerland
⁶ Leibniz-Institut für Sonnenphysik (KIS), Schöneckstrasse 6, 79104 Freiburg i. Br., Germany

Received: 7 April 2023
Accepted: 2 September 2023

Abstract

Context. Approximated forms of the R^II and R^III 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 R^III is to consider its expression under the assumption of complete frequency redistribution (CRD) in the observer’s frame (R^III−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 R^III−CRD approximation in the modeling of scattering polarization.

Methods. We first present an analytic comparison between R^III and R^III−CRD. We then compare the results of radiative transfer calculations, out of local thermodynamic equilibrium, performed with R^III and R^III−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 R^III−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 R^III−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.