*Astron. Astrophys. 318, 879-907 (1997)*
## 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*
**Abstract**
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 (), as well as
between the limits of small and large optical depth
(). 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 *µ*m, 100 *µ*m, 1.25 mm, and 1.3 mm. Model
visibilities fit very well the interferometry measurements at submm/mm
wavelengths (870 *µ*m, 2.73 mm) and confirm the presence of
a compact and very dense core (radius 50 AU,
) at the center of IRS 5. Model polarization maps
at 1 *µ*m 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
between the upper and lower conical surfaces can
naturally account for the cross-shaped pattern recently observed at
730 *µ*m. While the model of L1551 IRS 5 agrees well with
all the observations, it implies a massive envelope (8
) and a low luminosity of the central object (16
), 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 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 130.79.128.5 or via WWW http://cdsweb.u-strasbg.fr
*Send offprint requests to:* A.B. Men'shchikov
SIMBAD Objects
### Contents
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998
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