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Astron. Astrophys. 318, 879-907 (1997)

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Radiation transfer in circumstellar disks *

A.B. Men'shchikov and Th. Henning

Max-Planck-Gesellschaft, AG "Staub in Sternentstehungsgebieten", Schillergäßchen 3, D-07745 Jena, Germany (sascha@astro.uni-jena.de, henning@astro.uni-jena.de)

Received 26 July 1994 / Accepted 30 March 1996


We describe a new approach to the solution of the frequency-dependent stationary radiative transfer equation for axially-symmetric circumstellar dust disks. We apply our method to flared disks which are considered here as spheres with the polar cones removed. We have simplified the problem by computing the moments of the specific intensity only for the midplane and the surface of the flared disk. At the same time, we solve the radiative transfer equation exactly for an "equivalent" spherical envelope. The basic assumption is that density distribution in the disk depends only on the radial distance from the central star. This results in significantly faster calculations, reduces necessary computer memory, and allows incorporation of the algorithm into a hydrodynamical code.

Extensive calculations have been performed, to test the method and to compute the radiation field between the limits of small and large opening angle for the flared disk ([FORMULA]), as well as between the limits of small and large optical depth ([FORMULA]). We demonstrate that significant differences in spectral appearance can be attributed to the optical depths, geometry, and viewing angles. Quantitative comparisons with results obtained with another method applied to the same geometry show very good agreement, in terms of the spectral energy distributions (SEDs), intensity maps, and temperature profiles. Since our method is much faster than a general two-dimensional (2D) program, it enables calculations with high radial and angular resolutions.

We apply our 2D radiative transfer code to a detailed modeling of the deeply embedded young stellar object (YSO) L1551 IRS 5. The thick flared disk model fits perfectly the broad-band photometry in the whole spectral range from visual to millimeter wavelengths. Intensity maps are in a very good agreement with available linear scans and maps at 50 µm, 100 µm, 1.25 mm, and 1.3 mm. Model visibilities fit very well the interferometry measurements at submm/mm wavelengths (870 µm, 2.73 mm) and confirm the presence of a compact and very dense core (radius [FORMULA] 50 AU, [FORMULA]) at the center of IRS 5. Model polarization maps at 1 µm  predicting both the polarization degree and overall pattern are in agreement with the observed ones. The thick flared disk model of IRS 5 with the opening angle [FORMULA] between the upper and lower conical surfaces can naturally account for the cross-shaped pattern recently observed at 730 µm. While the model of L1551 IRS 5 agrees well with all the observations, it implies a massive envelope (8 [FORMULA]) and a low luminosity of the central object (16 [FORMULA]), in contrast to previous models.

Our modeling demonstrates the danger of deriving source parameters by fitting only spectral energy distributions. Depending on the unknown geometry, density structure, dust properties, optical depths, and viewing angle, derived luminosities and masses of the sources can be in error by a factor of [FORMULA] 30 or even more. An intrinsic ambiguity of a solution of the inverse problem by fitting only a featureless continuum makes this standard method useless or at least implies huge error bars in derived parameters. The only way to estimate reliable parameters of embedded objects is to use all of the spatial information coded in observations and to fit many different data sets, in the frame of a self-consistent model. We emphasize that photometry made with different beam sizes is a readily available (but often ignored) source of spatial information which can help to test model predictions and constrain source parameters, and which is especially important for a large number of objects with no high-resolution observations.

Key words: radiative transfer – methods: numerical – circumstellar matter – stars: individual: L1551 IRS 5

* In the journal version of the paper, Appendices A, B, and C will not appear; they are only available in in electronic form at the CDS via anonymous ftp or via WWW http://cdsweb.u-strasbg.fr

Send offprint requests to: A.B. Men'shchikov

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998