Benchmark problems for continuum radiative transfer

High optical depths, anisotropic scattering, and polarisation

¹ School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK e-mail: pinte@astro.ex.ac.uk
² Sterrenkundig Instituut Anton Pannekoek, Universiteit Amsterdam, Kruislaan 403, 1098 Amsterdam, The Netherlands
³ Centro de Radioastronomía y Astrofsíca, Universidad Nacional Autóma de México, Morelia, Mich., Mexico
⁴ Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
⁵ UK Astronomy Technology Centre, Royal Observatory, Edinburgh, Blackford Hill, Edinburgh EH9 3HJ, UK
⁶ School of Physics & Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, UK
⁷ Laboratoire d'Astrophysique de Grenoble, CNRS/UJF UMR 5571, 414 rue de la Piscine, BP 53, 38041 Grenoble Cedex 9, France

Received: 19 December 2008
Accepted: 22 February 2009

Abstract

Aims. 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.

Methods. 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 10⁶, 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.

Results. 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.