Publications
of the
MPIfR
Optical & Infrared
Interferometry Group
A.B. Men'shchikov, T. Henning and O.
Fischer:
Self-consistent model of the dusty torus
around HL Tau
Astrophysical Journal 519, 257-278 (1999)
Abstract.
We present the first comprehensive two-dimensional radiative transfer
modeling of the circumstellar dusty environment of HL Tau, a remarkable
embedded young stellar object often considered a prototype low-mass
star with
a circumstellar disk resembling the solar nebula at the early stages of
planet
formation. To recover its general structure and physical parameters, we
used
entire beam-matched spectral energy distribution from optical to
millimeter
wavelengths, the high-resolution intensity and linear polarization maps
at
0.7 micron, 1.25 micron, 1.65 micron, 2.2 micron (R, J, H, K bands),
aperture synthesis maps at 1.36 mm, 2.7 mm, 3.06 mm, and 7 mm,
visibilities at 650 micron, 870 micron, and 1.36 mm, and large-aperture
linear polarization measurements in the optical and near-infrared bands
as
observational constraints.
Our detailed model of HL Tau explains all these observations well,
making the
overall picture much more certain. The central radiation source, with a
bolometric luminosity of 11 Lsun, is embedded in a compact, dense torus
having a 1/r^1.25 density distribution and containing
predominantly very large dust particles (radii a > 0.1 mm). With two
wide bipolar cones excavated by the outflow along the symmetry axis,
the model
torus has an opening angle of 90 degree, radius of 100 AU, maximum
molecular hydrogen density of 1.6 x 10^12 cm^-3, and a mass
of 0.03 Msun (assuming a dust-to-gas mass ratio of 0.01). A relatively
large reservoir of circumstellar material, containing dust grains of
submicron
sizes, resides in an extended toroidal envelope of a similar mass,
having a
1/r^2 density profile to the adopted outer radius of 10^4 AU.
The model of HL Tau strongly suggests that only the bright parts of the
dense
compact torus inclined towards us by 43 degree can be seen by observers
at any relevant wavelength. Direct light from the central source is
heavily
diluted even in the highest-resolution 0.2 arcsec images. The dusty
torus is
optically thick up to millimeter wavelengths, with the total optical
depth of
tau_v = 33 towards the invisible central object. The optical depth
is partly due to the gray extinction by very large particles in the
dense torus
(tau_v = 10) and to the wavelength-dependent extinction by
submicron-sized grains in the extended envelope (tau_v = 20). If
the very broad size distribution of solid particles indeed exists in
the dense
torus, this might indicate that in HL Tau we are observing initial
phases of
accumulation of larger bodies, which may eventually lead to planet
formation.
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