RADIATION TRANSFER IN CIRCUMSTELLAR DISKS

We describe a new approach to the solution of the frequency-dependent stationary radiative transfer equation for axially-symmetric circumste llar dust disks. We apply our method to flared disks which are conside red here as spheres with the polar cones removed. We have simplified t he 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'' s pherical envelope. The basic assumption is that density distribution i n the disk depends only on the radial distance from the central star. This results in significantly faster calculations, reduces necessary c omputer memory, and allows incorporation of the algorithm into a hydro dynamical code. Extensive calculations have been performed, to test th e method and to compute the radiation field between the limits of smal l and large opening angle for the flared disk (0.001 degrees less than or equal to psi less than or equal to 180 degrees), as well as betwee n the limits of small and large optical depth (0.01 less than or equal to tau(V) less than or equal to 2150). We demonstrate that significan t differences in spectral appearance can be attributed to the optical depths, geometry, and viewing angles. Quantitative comparisons with re sults obtained with another method applied to the same geometry show v ery good agreement, in terms of the spectral energy distributions (SED s), intensity maps, and temperature profiles. Since our method is much faster than a general two-dimensional (2D) program, it enables calcul ations with high radial and angular resolutions. We apply our 2D radia tive transfer code to a detailed modeling of the deeply embedded young stellar object (YSO) L1551 IRS 5. The thick flared disk model fits pe rfectly the broad-band photometry in the whole spectral range from vis ual to millimeter wavelengths. Intensity maps are in a very good agree ment with available linear scans and maps at 50 mu m, 100 mu m, 1.25 m m, and 1.3 mm. Model visibilities fit very well the interferometry mea surements at submm/mm wavelengths (870 mu m, 2.73 mm) and confirm the presence of a compact and very dense core (radius approximate to 50 AU , n(H2) approximate to 2 . 10(9) cm(-3)) at the center of IRS 5. Model polarization maps at 1 mu m predicting both the polarization degree a nd overall pattern are in agreement with the observed ones. The thick flared disk model of IRS 5 with the opening angle psi = 90 degrees bet ween the upper and lower conical surfaces can naturally account for th e cross-shaped pattern recently observed at 730 mu m. While the model of L1551 IRS 5 agrees well with all the observations, it implies a mas sive envelope (8 M.) and a low luminosity of the central object (16 L. ), in contrast to previous models. Our modeling demonstrates the dange r of deriving source parameters by fitting only spectral energy distri butions. Depending on the unknown geometry, density structure, dust pr operties, optical depths, and viewing angle, derived luminosities and masses of the sources can be in error by a factor of similar to 30 or even more. An intrinsic ambiguity of a solution of the inverse problem by fitting only a featureless continuum makes this standard method us eless or at least implies huge error bars in derived parameters. The o nly way to estimate reliable parameters of embedded objects is to use all of the spatial information coded in observations and to fit many d ifferent data sets, in the frame of a self-consistent model. We emphas ize that photometry made with different beam sizes is a readily availa ble (but often ignored) source of spatial information which can help t o test model predictions and constrain source parameters, and which is especially important for a large number of objects with no high-resol ution observations.