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

TL;DR

This paper introduces a fast, accurate algorithm for computing the angle-averaged redistribution function in polarized radiation modeling, significantly reducing computational costs in complex atomic and magnetic scenarios.

Contribution

It develops a low-rank polynomial approximation method using Chebyshev basis functions to efficiently evaluate the redistribution function.

Findings

Algorithm is significantly faster than standard methods.

Achieves target accuracy between 10^-6 and 10^-2.

Applicable to complex atomic models and magnetic fields.

Abstract

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. We aim to develop an efficient algorithm to numerically evaluate the angle-averaged redistribution function for polarized radiation. Our proposed approach is based on a low-rank approximation via trivariate polynomials whose univariate components are represented in the Chebyshev basis. The resulting algorithm is significantly faster than standard quadrature-based schemes for any target accuracy in the range between 10^-6 and 10^-2.