Benchmark problems for continuum radiative transfer. High optical depths, anisotropic scattering, and polarisation

TL;DR

This paper presents a benchmark for radiative transfer codes in high-opacity protoplanetary disc models, evaluating their accuracy in complex scenarios involving anisotropic scattering and polarization.

Contribution

It introduces a set of challenging benchmark problems for radiative transfer in high optical depth media and compares the performance of seven different codes.

Findings

Codes agree within good accuracy across test cases

Monte Carlo methods show specific advantages and limitations

Benchmark results support reliable interpretation of disc observations

Abstract

Solving the continuum radiative transfer equation in high opacity media requires sophisticated numerical tools. In order to test the reliability of such tools, we present a benchmark of radiative transfer codes in a 2D disc configuration. We test the accuracy of seven independently developed radiative transfer codes by comparing the temperature structures, spectral energy distributions, scattered light images, and linear polarisation maps that each model predicts for a variety of disc opacities and viewing angles. The test cases have been chosen to be numerically challenging, with midplane optical depths up 10^6, a sharp density transition at the inner edge and complex scattering matrices. We also review recent progress in the implementation of the Monte Carlo method that allow an efficient solution to these kinds of problems and discuss the advantages and limitations of Monte Carlo codes compared to those of discrete ordinate codes. For each of the test cases, the predicted results from the radiative transfer codes are within good agreement. The results indicate that these codes can be confidently used to interpret present and future observations of protoplanetary discs.