Numerical methods for non-LTE line radiative transfer: Performance and convergence characteristics

¹ Leiden Observatory, PO Box 9513, 2300 RA Leiden, The Netherlands
² Max Planck Institut für Astrophysik, Postfach 1317, 85741 Garching, Germany
³ Max Planck Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
⁴ University College London, Gower Street, London WC1E 6BT, UK
⁵ Department of Physics and Astronomy, Denison University, Granville, OH 43023, USA
⁶ 1. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937, Köln, Germany
⁷ Steward Observatory, The University of Arizona, 933 N. Cherry Ave. Tucson AZ 85721, USA
⁸ Helsinki University Observatory, Tähtitorninmäki, PO Box 14, 00014 University of Helsinki, Finland
⁹ Institut de Radio-Astronomie Millimétrique, 300 rue de la piscine, Domaine Universitaire, 38406 St. Martin d'Hères, France

Corresponding author: G. J. van Zadelhoff, zadelhof@strw.leidenuniv.nl

Received: 3 January 2002
Accepted: 22 August 2002

Abstract

Comparison is made between a number of independent computer programs for radiative transfer in molecular rotational lines. The test models are spherically symmetric circumstellar envelopes with a given density and temperature profile. The first two test models have a simple power law density distribution, constant temperature and a fictive 2-level molecule, while the other two test models consist of an inside-out collapsing envelope observed in rotational transitions of HCO⁺. For the 2-level molecule test problems all codes agree well to within 0.2%, comparable to the accuracy of the individual codes, for low optical depth and up to 2% for high optical depths (). The problem of the collapsing cloud in HCO⁺ has a larger spread in results, ranging up to 12% for the population. The spread is largest at the radius where the transition from collisional to radiative excitation occurs. The resulting line profiles for the HCO⁺ –3 transition agree to within 10%, i.e., within the calibration accuracy of most current telescopes. The comparison project and the results described in this paper provide a benchmark for future code development, and give an indication of the typical accuracy of present day calculations of molecular line transfer.