Improved near optimal angular quadratures for polarised radiative transfer in 3D MHD models^⋆

¹ Instituto de Astrofísica de Canarias, Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain
e-mail: jjaumeb@iac.es
² Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
³ Astronomical Institute ASCR, v.v.i., Ondřejov, Czech Republic
e-mail: jiri.stepan@asu.cas.cz
⁴ Consejo Superior de Investigaciones Científicas, Madrid, Spain
e-mail: jtb@iac.es

Received: 14 September 2020
Accepted: 22 November 2020

Abstract

Accurate angular quadratures are crucial for the numerical solution of three-dimensional (3D) radiative transfer problems, especially when the spectral line polarisation produced by the scattering of anisotropic radiation is included. There are two requirements for obtaining an optimal quadrature and they are difficult to satisfy simultaneously: high accuracy and short computing time. By imposing certain symmetries, we were recently able to derive a set of near optimal angular quadratures. Here, we extend our previous investigation by considering other symmetries. Moreover, we test the performance of our new quadratures by numerically solving a radiative transfer problem of resonance line polarisation in a 3D model of the solar atmosphere resulting from a magneto-hydrodynamical simulation. The new angular quadratures derived here outperform the previous ones in terms of the number of rays needed to achieve any given accuracy.