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Issue A&A Volume 395, Number 1, November III 2002 Page(s) 373 - 384 Section Computational methods DOI 10.1051/0004-6361:20021226

A&A 395, 373-384 (2002)
DOI: 10.1051/0004-6361:20021226

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

G.-J. van Zadelhoff¹, C. P. Dullemond², F. F. S. van der Tak³, J. A. Yates⁴, S. D. Doty⁵, V. Ossenkopf⁶, M. R. Hogerheijde⁷, M. Juvela⁸, H. Wiesemeyer⁹ and F. L. Schöier<sup>1

1</sup>  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

(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 J=4 population. The spread is largest at the radius where the transition from collisional to radiative excitation occurs. The resulting line profiles for the HCO ⁺ J=4-3 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.

Key words: stars: formation -- molecular processes

Offprint request: G. J. van Zadelhoff, zadelhof@strw.leidenuniv.nl

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