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Astron. Astrophys. 360, 1187-1202 (2000)

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An efficient algorithm for two-dimensional radiative transfer in axisymmetric circumstellar envelopes and disks

C.P. Dullemond 1 and R. Turolla 2

1 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, 85748 Garching, Germany (dullemon@mpa-garching.mpg.de)
2 Department of Physics, University of Padova, Via Marzolo 8, 35131 Padova, Italy (turolla@pd.infn.it)

Received 4 April 2000 / Accepted 9 June 2000


We present an algorithm for two-dimensional radiative transfer in axisymmetric, circumstellar media. The formal integration of the transfer equation is performed by a generalization of the short characteristics (SC) method to spherical coordinates. Accelerated Lambda Iteration (ALI) and Ng's algorithm are used to converge towards a solution. By taking a logarithmically spaced radial coordinate grid, the method has the natural capability of treating problems that span several decades in radius, in the most extreme case from the stellar radius up to parsec scale. Flux conservation is guaranteed in spherical coordinates by a particular choice of discrete photon directions and a special treatment of nearly-radially outward propagating radiation. The algorithm works well from zero up to very high optical depth, and can be used for a wide variety of transfer problems, including non-LTE line formation, dust continuum transfer and high temperature processes such as compton scattering. In this paper we focus on multiple scattering off dust grains and on non-LTE transfer in molecular and atomic lines. Line transfer is treated according to an ALI scheme for multi-level atoms/molecules, and includes both random and systematic velocity fields. The algorithms are implemented in a multi-purpose user-friendly radiative transfer program named RADICAL. We present two example computations: one of dust scattering in the Egg Nebula, and one of non-LTE line formation in rotational transitions of HCO+ in a flattened protostellar collapsing cloud.

Key words: radiative transfer – line: profiles – stars: circumstellar matter – stars: formation – infrared: stars – submillimeter

Send offprint requests to: C.P. Dullemond

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© European Southern Observatory (ESO) 2000

Online publication: August 23, 2000