Astron. Astrophys. 362, 697-710 (2000)

An accelerated Monte Carlo method to solve two-dimensional radiative transfer and molecular excitation

With applications to axisymmetric models of star formation

M.R. Hogerheijde ¹ and F.F.S. van der Tak <sup>2

1</sup> Radio Astronomy Laboratory, University of California at Berkeley, Astronomy Department, 601 Campbell Hall # 3411, Berkeley, CA 94720-3411, USA (michiel@astro.berkeley.edu)
² Sterrewacht Leiden, Postbus 9513, 2300 RA Leiden, The Netherlands (vdtak@strw.leidenuniv.nl)

Received 13 June 2000 / Accepted 21 July 2000

Abstract

We present a numerical method and computer code to calculate the radiative transfer and excitation of molecular lines. Formulating the Monte Carlo method from the viewpoint of cells rather than photons allows us to separate local and external contributions to the radiation field. This separation is critical to accurate and fast performance at high optical depths (). 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. These features allow use of our method in a wide variety of astrophysical problems without specific adaptations: in any axially symmetric source model and for all atoms or molecules for which collisional rate coefficients are available. Continuum emission and absorption by dust is explicitly taken into account but scattering is neglected. We illustrate these features in calculations of (i) the HCO⁺ J=1-0 and 3-2 emission from a flattened protostellar envelope with infall and rotation, (ii) the CO, HCO⁺, CN and HCN emission from a protoplanetary disk and (iii) HCN emission from a high-mass young stellar object, where infrared pumping is important. The program can be used for optical depths up to , depending on source model. We expect this program to be an important tool in analysing data from present and future infrared and (sub) millimetre telescopes.

Key words: line: formation radiative transfer methods: numerical stars: formation ISM: molecules

Send offprint requests to: M.R. Hogerheijde

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Contents

• 1. Introduction
• 2. An illustrative, one-dimensional model
• 3. Solving radiative transfer and molecular excitation
  • 3.1. The coupled problem
  • 3.2. Constructing and the -operator
  • 3.3. The Monte Carlo method
  • 3.4. Convergence and acceleration
  • 3.5. The role of variance in Monte Carlo calculations
  • 3.6. Implementation and performance characteristics
  • 3.7. Alternative accelerators
• 4. Astrophysically relevant examples
  • 4.1. A young stellar object with rotation
  • 4.2. A circumstellar disk
  • 4.3. A high mass young stellar object
• 5. Conclusion
• Acknowledgements
• Appendices
  • A: the code
  • B: comparison with other codes
    • B.1. Bernes' CO cloud
    • B.2. Model for B 335 by Choi et al.
• References

© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000
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