Halo-imbedded-Disk. The system consists of a star of radius R * and effective temperature T * , surrounded by a disk and a spherical envelope.
The system consists of a star of radius R* and effective temperature T*, surrounded by a disk and a spherical envelope.
The envelope extends from an inner radius R1 to some outer radius Rh, with overall radial optical depth tV at visual. Thanks to general scaling properties (MNRAS, 287, 799, 1997), only a small set of parameters is relevant.
With standard interstellar dust and sublimation temperature of 1500K, R1/R*100 for T*=10000K and R1/R*15 for T*=5000K.
We assume a geometrically thin passive disk. Because of its potentially large optical depth, the disk can extend inside the dust sublimation where its optical depth comes from the gaseous component. The disk extends from the surface of the star to an outer radius Rd.
The spectral energy distribution of AB Aur modeled with a halo-imbedded-disk. IRAS LRS and ISO data are marked with thin lines, all other data (de-reddened with AV=0.2) with points. The theoretical model (thick full line) is the sum of the star+envelope component (dotted line) and the disk (dashed line).
The dust spectral features originate from the envelope, whose grains can be expected to have different evolution and chemistry than those of the disk interior and/or surface. Therefore, dust properties derived from a halo-free model may be inappropriate.
Detailed radiative transfer modeling is performed with a hybrid 1D/2D version of the code DUSTY (www.pa.uky.edu/~moshe/dusty) which accounts for energy exchange between the star, envelope, and the disk, including scattering, absorption and emission. Because the envelope optical depth is typically tV1, the envelope is transparent to the disk emission in all the models we consider, and the disk effect on the envelope is neglected.
The spherical-halo – flared-disk equivalence
Locations in the envelope can be characterized by the dimensionless radius y=r/R1.
The dust density distribution is specified by the dimensionless profile:
Radial distance from the axis can be characterized by the dimensionless radius: a=ra/R1.
The disk surface is specified by the geometrical height H(a), which yields the surface normal n , the grazing angle a, and the flaring angle bH/ra.
Visual & near infrared (ApJ, 523, L151 (1999)): large, optically thin, circularly symmetric envelope (or a large disk with inclination < 45O)
Millimeter wavelengths (ApJ, 490, 792 (1997)): small, optically thick disk with inclination > 45O.
TOP: Temperature profiles of a disk when heated only by a central star with T*=10,000K (full line), and when adding a spherical dusty halo with tV=0.1 (thin lines) or tV=1.0 (thick lines). The halo starts at dust sublimation temperature of 1,500K and its density profile is r-2. The temperature profile of the halo is also shown in each case (dotted lines).
BOTTOM: The fractional contributions of the halo (dashed lines) and (attenuated) stellar components (full lines) to the heating of the disk.
Conversion from flared disk (b) to envelope (h,tV):
Conversion from envelope (h,tV) to flared disk (b):
Theoretical imaging of AB Aur (halo-imbedded-disk model)
Theoretical imaging of flared disks
Spherical halos are indistinguish-able from face-on disks in either imaging or flux observations.
Inclined flared disks, though, have an asymmetric appearance. Points on the surface of a flared disk at equal distance from the star lie on a circle centered on the disk axis. The circle retains its shape in pole-on viewing but is deformed into an off-center ellipse in view from inclination angle i.
In addition to that, the optical depth of the disk surface layer toward the observer varies around the contour. This creates additional brightness asymmetry.
Theoretical images of the inner regions of the circumstellar environment around AB Aur at various wavelengths and disk incli-nation of 76O.
AB Aur, the best-studied massive young star (Herbig Ae/Be star), is an example where the widely used CG-model is inconsistent with the imaging.
Our halo-imbedded-disk model uses a geometrically thin, optically thick disk imbedded in an optically thin spherical halo. The halo density profile is r–2
Contours start at 10 Jy/arcsec2 and decrease by factor 3.3.
Short wavelength emission is dominated by the halo, resulting in circular images. The switch from scattering- to emission-dominance between 0.6mm and 5mm explains the change in brightness profile.
At longer wavelengths the disk becomes dominant and the image becomes smaller and non-circular.
This asymmetry is the only practical way to distinguish between these two geometries.
A convenient measure of the asymmetry is the ratio of brightness at diametric locations relative to the star:
This asymmetry parameter vanishes for flat disks at all inclination angles and for pole-on viewing irrespective of the flaring. A non-vanishing A is a hallmark of an inclined flared disk, and each flaring profile produces its own characteristic signature.
DISKS AND HALOS IN PRE-MAIN-SEQUENCE STARS
Moshe Elitzur, Dejan Vinković (University of Kentucky)
Anatoly S. Miroshnichenko (University of Toledo)
Željko Ivezić (Princeton University)
The flared disk model by Chiang & Goldreich (ApJ, 490, 368, 1997) for the circumstellar dust distribution around YSOs is supported by successful modeling of spectral energy distributions (SED). However, imaging suggests that optically thin halos are present through most of the pre-main-sequence phase. These halos play an important role in the diagnostics of circumstellar dust properties and must be included in modeling efforts.
Our study shows that:
A) Ignoring the halo in radiative transfer models leads to erroneous interpretation of the dust properties and evolution.
B) The halo dominates the system IR excess, and provides heating that affects the disk temperature profile. The disk emission emerges only at longer (sub-mm and mm) wavelengths.
C) A mathematical equivalence exists between the flux from optically thin spherical halos and flared disks. Therefore it is impossible to distinguish a flared disk from a spherical halo with flux measurements (SED) alone. Only imaging can distinguish between these two configurations.
D) Inclined flared disks produce off-center elliptical images with brightness asymmetry, while optically thin haloes appear circularly symmetric. This distinction can be used for deriving directly from the observed images an objective level of confidence in the applicability of the flared disk hypothesis.
SED and Dust Properties
Observations of AB Aur
For every flared disk there is an equivalent spherical halo, and vice versa, with mathematically identical flux