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Register a new userInferring (Sub)millimeter Dust Opacities and Temperature Structure in Edge-on Protostellar Disks From Resolved Multi-Wavelength Continuum Observations: The Case of the HH 212 Disk
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(Sub)millimeter dust opacities are required for converting the observable dust continuum emission to the mass, but their values have long been uncertain, especially in disks around young stellar objects. We propose a method to constrain the opacity $kappa_ u$ in edge-on disks from a characteristic optical depth $tau_{0, u}$, the density $rho_0$ and radius $R_0$ at the disk outer edge through $kappa_ u=tau_{0, u}/(rho_0 R_0)$ where $tau_{0, u}$ is inferred from the shape of the observed flux along the major axis, $rho_0$ from gravitational stability considerations, and $R_0$ from direct imaging. We applied the 1D semi-analytical model to the embedded, Class 0, HH 212 disk, which has high-resolution data in ALMA Band 9, 7, 6, and 3 and VLA Ka band ($lambda$=0.43, 0.85, 1.3, 2.9, and 9.1 mm). The modeling of the HH 212 disk is extended to 2D through RADMC-3D radiative transfer calculations. We find a dust opacity of $kappa_ u approx $ $1.9times 10^{-2}$, $1.3times 10^{-2}$, and $4.9times 10^{-3}$ cm$^2$ per gram of gas and dust for ALMA Bands 7, 6, and 3, respectively with uncertainties dependent on the adopted stellar mass. The inferred opacities lend support to the widely used prescription $kappa_lambda=2.3times 10^{-2} (1.3 {rm mm}/lambda)$ cm$^2$ g$^{-1}$ advocated by Beckwith et al. (1990). We inferred a temperature of ~45K at the disk outer edge which increases radially inward. It is well above the sublimation temperatures of ices such as CO and N$_2$, which supports the notion that the disk chemistry cannot be completely inherited from the protostellar envelope.
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Eduard I. Vorobyov The Institute for Computational Astrophysics
, n Saint Marys University
, Halifax
2010
We perform a comparative numerical hydrodynamics study of embedded protostellar disks formed as a result of the gravitational collapse of cloud cores of distinct mass (M_cl=0.2--1.7 M_sun) and ratio of rotational to gravitational energy (beta=0.0028--0.023). An increase in M_cl and/or beta leads to the formation of protostellar disks that are more susceptible to gravitational instability. Disk fragmentation occurs in most models but its effect is often limited to the very early stage, with the fragments being either dispersed or driven onto the forming star during tens of orbital periods. Only cloud cores with high enough M_cl or beta may eventually form wide-separation binary/multiple systems with low mass ratios and brown dwarf or sub-solar mass companions. It is feasible that such systems may eventually break up, giving birth to rogue brown dwarfs. Protostellar disks of {it equal} age formed from cloud cores of greater mass (but equal beta) are generally denser, hotter, larger, and more massive. On the other hand, protostellar disks formed from cloud cores of higher beta (but equal M_cl) are generally thinner and colder but larger and more massive. In all models, the difference between the irradiation temperature and midplane temperature triangle T is small, except for the innermost regions of young disks, dense fragments, and disks outer edge where triangle T is negative and may reach a factor of two or even more. Gravitationally unstable, embedded disks show radial pulsations, the amplitude of which increases along the line of increasing M_cl and beta but tends to diminish as the envelope clears. We find that single stars with a disk-to-star mass ratio of order unity can be formed only from high-beta cloud cores, but such massive disks are unstable and quickly fragment into binary/multiple systems.
Theoretical models of grain growth predict dust properties to change as a function of protoplanetary disk radius, mass, age and other physical conditions. We lay down the methodology for a multi-wavelength analysis of (sub-)mm and cm continuum interferometric observations to constrain self-consistently the disk structure and the radial variation of the dust properties. The computational architecture is massively parallel and highly modular. The analysis is based on the simultaneous fit in the uv-plane of observations at several wavelengths with a model for the disk thermal emission and for the dust opacity. The observed flux density at the different wavelengths is fitted by posing constraints on the disk structure and on the radial variation of the grain size distribution. We apply the analysis to observations of three protoplanetary disks (AS 209, FT Tau, DR Tau) for which a combination of spatially resolved observations in the range ~0.88mm to ~10mm is available (from SMA, CARMA, and VLA), finding evidence of a decreasing maximum dust grain size (a_max) with radius. We derive large a_max values up to 1 cm in the inner disk between 15 and 30 AU and smaller grains with a_max~1 mm in the outer disk (R > 80AU). In this paper we develop a multi-wavelength analysis that will allow this missing quantity to be constrained for statistically relevant samples of disks and to investigate possible correlations with disk or stellar parameters.
We analyze a sample of 12 HST-selected edge-on protoplanetary disks for which the vertical extent of the emission layers can be constrained directly. We present ALMA high angular resolution continuum images (0.1arcsec) of these disks at two wavelengths, 0.89mm and 2.06mm (respectively ALMA bands 7 and 4), supplemented with archival band 6 data (1.33mm) where available. For most sources, the millimeter continuum emission is more compact than the scattered light, both in the vertical and radial directions. Six sources are resolved along their minor axis in at least one millimeter band, providing direct information on the vertical distribution of the millimeter grains. For the second largest disk of the sample, the significant difference in vertical extent between band 7 and band 4 suggests efficient size-selective vertical settling of large grains. Furthermore, the only Class I object in our sample shows evidence of flaring in the millimeter. Along the major axis, all disks are well resolved. Four of them are larger in band 7 than in band 4 in the radial direction, and three have a similar radial extent in all bands. For all disks, we also derive the millimeter brightness temperature and spectral index maps. We find that the disks are likely optically thick and that the dust emission reveals low brightness temperatures in most cases (<10K). The integrated spectral indices are similar to those of disks at lower inclination. The comparison of a generic radiative transfer disk model with our data shows that at least 3 disks are consistent with a small millimeter dust scale height, of a few au (measured at r=100au). This is in contrast with the more classical value of h_gsim10au derived from scattered light images and from gas line measurements. These results confirm, by direct observations, that large (millimeter) grains are subject to significant vertical settling in protoplanetary disks.
The large crescents imaged by ALMA in transition disks suggest that azimuthal dust trapping concentrates the larger grains, but centimetre-wavelengths continuum observations are required to map the distribution of the largest observable grains. A previous detection at ~1cm of an unresolved clump along the outer ring of MWC758 (Clump1), and buried inside more extended sub-mm continuum, motivates followup VLA observations. Deep multiconfiguration integrations reveal the morphology of Clump 1 and additional cm-wave components which we characterize via comparison with a deconvolution of recent 342GHz data (~1mm). Clump1, which concentrates ~1/3 of the whole disk flux density at ~1cm, is resolved as a narrow arc with a deprojected aspect ratio Chi>5.6, and with half the azimuthal width than at 342 GHz. The spectral trends in the morphology of Clump1 are quantitatively consistent with the Lyra-Lin prescriptions for dust trapping in an anticyclonic vortex, provided with porous grains (f~0.2+-0.2) in a very elongated (Chi~14+-3) and cold (T~23+-2K) vortex. The same prescriptions constrain the turbulence parameter alpha and the gas surface density Sigma_g through log10( alpha x Sigma_g /g/cm2)~-2.3+-0.4, thus requiring values for Sigma_g larger than a factor of a few compared to that reported in the literature from the CO isotopologues, if alpha <~ 1E-3. Such physical conditions imply an appreciably optically thick continuum even at cm-wavelengths (tau(33GHz)~0.2). A secondary and shallower peak at 342GHz is about twice fainter relative to Clump1 at 33GHz. Clump2 appears to be less efficient at trapping large grains.
Observations of the circumstellar disk in the Bok globule CB 26 at 110, 230, and 270 GHz are presented together with the results of the simulations and estimates of the disk parameters. These observations were obtained using the SMA, IRAM Plateau de Bure, and OVRO interferometers. The maps have relatively high angular resolutions (0.4-1), making it possible to study the spatial structure of the gas-dust disk. The disk parameters are reconstructed via a quantitative comparison of observational and theoretical intensity maps. The disk model used to construct the theoretical maps is based on the assumption of hydrostatic and radiative equilibrium in the vertical direction, while the radial surface density profile is described phenomenologically. The system of equations for the transfer of the infrared and ultraviolet radiation is solved in the vertical direction, in order to compute the thermal structure of the disk. The disk best-fit parameters are derived for each map and all the maps simultaneously, using a conjugate gradient method. The degrees of degeneracy of the parameters describing the thermal structure and density distribution of the disk are analyzed in detail. All three maps indicate the presence of an inner dust-free region with a radius of approximately 35 AU, in agreement with the conclusions of other studies. The inclination of the disk is 78 deg, which is smaller than the value adopted in our earlier study of rotating molecular outflows from CB 26. The model does not provide any evidence for the growth of dust particles above a_max=0.02 cm.
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