Near optimal angular quadratures for polarised radiative transfer^⋆

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

Received: 23 January 2020
Accepted: 27 February 2020

Abstract

In three-dimensional (3D) radiative transfer (RT) problems, the tensor product quadratures are generally not optimal in terms of the number of discrete ray directions needed for a given accuracy of the angular integration of the radiation field. In this paper, we derive a new set of angular quadrature rules that are more suitable for solving 3D RT problems with the short- and long-characteristics formal solvers. These quadratures are more suitable than the currently used ones for the numerical calculation of the radiation field tensors that are relevant in the problem of the generation and transfer of polarised radiation without assuming local thermodynamical equilibrium (non-LTE). We show that our new quadratures can save up to about 30% of computing time with respect to the Gaussian-trapezoidal product quadratures with the same accuracy.