Fast and accurate approximation of the angle-averaged redistribution function for polarized radiation

¹ School of Mathematics and Actuarial Science, University of Leicester, LE1 7RH Leicester, UK
² Department of Mathematics, Shiraz University of Technology, Modarres BLVD, Shiraz 71555-313, Iran
³ School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box: 19395-5746, Tehran, Iran
⁴ Istituto Ricerche Solari Locarno, 6605 Locarno-Monti, Switzerland
e-mail: ernest@irsol.ch
⁵ Leibniz-Institut für Sonnenphysik (KIS), 79104 Freiburg, Germany

Received: 20 November 2019
Accepted: 20 September 2020

Abstract

Context. Modeling spectral line profiles taking frequency redistribution effects into account is a notoriously challenging problem from the computational point of view, especially when polarization phenomena (atomic polarization and polarized radiation) are taken into account. Frequency redistribution effects are conveniently described through the redistribution function formalism, and the angle-averaged approximation is often introduced to simplify the problem. Even in this case, the evaluation of the emission coefficient for polarized radiation remains computationally costly, especially when magnetic fields are present or complex atomic models are considered.

Aims. We aim to develop an efficient algorithm to numerically evaluate the angle-averaged redistribution function for polarized radiation.

Methods. The proposed approach is based on a low-rank approximation via trivariate polynomials whose univariate components are represented in the Chebyshev basis.

Results. The resulting algorithm is significantly faster than standard quadrature-based schemes for any target accuracy in the range [10⁻⁶, 10⁻²].