Formal Solutions for Polarized Radiative Transfer. IV. Numerical Performances in Practical Problems

TL;DR

This paper evaluates the performance of various numerical schemes for synthesizing polarized spectra in solar physics, focusing on accuracy, grid density, and the differences between high-order and low-order formal solvers.

Contribution

It provides a comparative analysis of formal solvers' performance in polarized radiative transfer, highlighting their accuracy and computational requirements in practical solar physics problems.

Findings

High-order formal solvers achieve better accuracy with fewer grid points.

Low-order solvers require denser grids for similar accuracy levels.

Performance varies significantly depending on spectral lines and atmospheric models.

Abstract

The numerical computation of reliable and accurate Stokes profiles is of great relevance in solar physics. In the synthesis process, many actors play a relevant role: among them the formal solver, the discrete atmospheric model, and the spectral line. This paper tests the performances of different numerical schemes in the synthesis of polarized spectra for different spectral lines and atmospheric models. The hierarchy between formal solvers is enforced, stressing the peculiarities of high-order and low-order formal solvers. The density of grid points necessary for reaching a given accuracy requirement is quantitatively described for specific situations.