Radiative transfer and molecular excitation in one and two dimensions

    Michiel Hogerheijde¹ & Floris van der Tak²

         This site presents a numerical method and computer code to calculate the radiative transfer and excitation of molecular lines. Our approach is based on the Monte Carlo method, and incorporates elements from Accelerated Lambda Iteration. It combines the flexibility of the former with the speed and accuracy of the latter. Convergence problems known to plague Monte Carlo methods at large optical depth (>100) are avoided by separating local contributions to the radiation field from the overall transfer problem. The random nature of the Monte Carlo method serves to verify the independence of the solution to the angular, spatial, and frequency sampling of the radiation field. This allows our method to be used in a wide variety of astrophysical problems without specific adaptations. Moreover, the code can be applied to all atoms or molecules for which collisional rate coefficients are available and any axially symmetric source model. Continuum emission and absorption by dust is explicitly taken into account but scattering is neglected. We expect this program to be an important tool in analyzing data from present and future infrared and (sub-)millimeter telescopes.

         A detailed description of our method, and a number of examples drawn from studies of star formation, are presented by Hogerheijde & van der Tak 2000, A&A 362, 697. Please refer to this paper if you publish results obtained with our program.

         Our code can treat both spherically symmetric (1D) and cylindrically symmetric (2D) source geometries. The 1D version of the code is publicly available; the 2D version is available on a collaborative basis with the authors, Michiel Hogerheijde (michiel @ strw.leidenuniv.nl) and Floris van der Tak (vdtak @ sron.nl). To obtain the source code distribution of the 1D version, see the link `Installation'. The source code is written in FORTRAN-77 and makes use of a C-shell script as front-end. It has been successfully compiled and run on Solaris, HP-Unix, AIX, and Linux systems. 

         More information on radiative transfer and molecular excitation methods can be found on the web site which resulted from the May 1999 workshop on Radiative Transfer in Molecular Lines. This site contains links to other radiative transfer codes, and several benchmark problems and their solutions.

         Although we have extensively tested our code, we do not claim it is free of errors or that it will give correct results in all situations. Especially the C-shell scripts that control the flow of the two main parts of the code (amc and sky) will generate cryptic error messages when the syntax of the input keyword file or model file is incorrect. If you have problems with the code, and you have convinced yourself that there are no such syntactical errors, send us a bug report, and include the input keyword file and model file as well as any screen output.

         Everyone is free to use the 1D version of our code. We do ask that if you publish results based on our code, that you reference our paper, Hogerheijde & van der Tak (2000, A&A 362, 697). The 1D code can be used as-is, but you are also free to make changes to the source code as you see fit, or use it as a starting point for your own radiative transfer and molecular excitation code. If you do so, please mark those changes clearly, and use a different name for the file(s); any changes to the source code fall outside our responsibility. The web site  from the May 1999 workshop on Radiative Transfer in Molecular Lines contains useful information on the development of such codes along with several benchmark problems.

    The authors would like to thank the following people for their help in improving the program: Neal Evans, Yaroslav Pavluchenkov, Frank Bensch, Jes Jørgensen, Simon Bruderer, Christian Brinch.

    ¹ Leiden Observatory, The Netherlands
    ² SRON Groningen, The Netherlands