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Register a new userGravitational Instabilities in Circumstellar Disks
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Authors
Kaitlin M. Kratter
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[Abridged] Star and planet formation are the complex outcomes of gravitational collapse and angular momentum transport mediated by protostellar and protoplanetary disks. In this review we focus on the role of gravitational instability in this process. We begin with a brief overview of the observational evidence for massive disks that might be subject to gravitational instability, and then highlight the diverse ways in which the instability manifests itself in protostellar and protoplanetary disks: the generation of spiral arms, small scale turbulence-like density fluctuations, and fragmentation of the disk itself. We present the analytic theory that describes the linear growth phase of the instability, supplemented with a survey of numerical simulations that aim to capture the non-linear evolution. We emphasize the role of thermodynamics and large scale infall in controlling the outcome of the instability. Despite apparent controversies in the literature, we show a remarkable level of agreement between analytic predictions and numerical results. We highlight open questions related to (1) the development of a turbulent cascade in thin disks, and (2) the role of mode-mode coupling in setting the maximum angular momentum transport rate in thick disks.
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We have conducted a survey of 17 wide (> 100 AU) young binary systems in Taurus with the Atacama Large Millimeter Array (ALMA) at two wavelengths. The observations were designed to measure the masses of circumstellar disks in these systems as an aid to understanding the role of multiplicity in star and planet formation. The ALMA observations had sufficient resolution to localize emission within the binary system. Disk emission was detected around all primaries and ten secondaries, with disk masses as low as $10^{-4} M_{odot}$. We compare the properties of our sample to the population of known disks in Taurus and find that the disks from this binary sample match the scaling between stellar mass and millimeter flux of $F_{mm} propto M_{ast}^{1.5-2.0}$ to within the scatter found in previous studies. We also compare the properties of the primaries to those of the secondaries and find that the secondary/primary stellar and disk mass ratios are not correlated; in three systems, the circumsecondary disk is more massive than the circumprimary disk, counter to some theoretical predictions.
Accurate temperature calculations for circumstellar disks are particularly important for their chemical evolution. Their temperature distribution is determined by the optical properties of the dust grains, which, among other parameters, depend on their radius. However, in most disk studies, only average optical properties and thus an average temperature is assumed to account for an ensemble of grains with different radii. We investigate the impact of subdividing the grain radius distribution into multiple sub-intervals on the resulting dust temperature distribution and spectral energy distribution (SED). These quantities were computed for two different scenarios: (1) Radius distribution represented by 16 logarithmically distributed radius intervals, and (2) radius distribution represented by a single grain species with averaged optical properties (reference). Within the considered parameter range, i.e., of grain radii between 5 nm and 1 mm and an optically thin and thick disk with a parameterized density distribution, we obtain the following results: In optically thin disk regions, the temperature spread can be as large as ~63% and the relative grain surface below a certain temperature is lower than in the reference disk. With increasing optical depth, the difference in the midplane temperature and the relative grain surface below a certain temperature decreases. Furthermore, below ~20K, this fraction is higher for the reference disk than for the case of multiple grain radii, while it shows the opposite behavior for temperatures above this threshold. The thermal emission in the case of multiple grain radii at short wavelengths is stronger than for the reference disk. The freeze-out radius is a function of grain radius, spanning a radial range between the coldest and warmest grain species of ~30AU.
We investigate the chance of detecting proto-planetary or debris disks in stars that induce microlensing events (lenses). The modification of the light curves shapes due to occultation and extinction by the disks as well as the additional gravitational deflection caused by the additional mass is considered. The magnification of gravitational microlensing events is calculated using the ray shooting method. The occultation is taken into account by neglecting or weighting the images on the lens plane according to a transmission map of the corresponding disk for a point source point lens (PSPL) model. The estimated frequency of events is obtained by taking the possible inclinations and optical depths of the disk into account. We conclude that gravitational microlensing can be used, in principle, as a tool for detecting debris disks beyond 1 kpc, but estimate that each year of the order of 1 debris disk is expected for lens stars of F, G, or K spectral type and of the order of 10 debris disks might have shown signatures in existing datasets.
The late stages of evolution of the primordial circumstellar disks surrounding young stars are poorly understood, yet vital to constrain theories of planet formation. We consider basic structural models for the disks around two ~10 Myr-old members of the nearby RCrA association, RX J1842.9-3532 and RX J1852.3-3700. We present new arcsecond-resolution maps of their 230 GHz continuum emission from the Submillimeter Array and unresolved CO(3-2) spectra from the Atacama Submillimeter Telescope Experiment. By combining these data with broadband fluxes from the literature and infrared fluxes and spectra from the catalog of the Formation and Evolution of Planetary Systems (FEPS) Legacy program on the Spitzer Space Telescope, we assemble a multiwavelength data set probing the gas and dust disks. Using the Monte Carlo radiative transfer code RADMC to model simultaneously the SED and millimeter continuum visibilities, we derive basic dust disk properties and identify an inner cavity of radius 16 AU in the disk around RX J1852.3-3700. We also identify an optically thin 5 AU cavity in the disk around RX J1842.9-3532, with a small amount of optically thick material close to the star. The molecular line observations suggest an intermediate disk inclination in RX J1842.9-3532, consistent with the continuum emission. In combination with the dust models, the molecular data allow us to derive a lower CO content than expected, suggesting that the process of gas clearing is likely underway in both systems, perhaps simultaneously with planet formation.
Motivated by recent observational and numerical studies suggesting that collapsing protostellar cores may be replenished from the local environment, we explore the evolution of protostellar cores submerged in the external counter-rotating environment. These models predict the formation of counter-rotating disks with a deep gap in the gas surface density separating the inner disk (corotating with the star) and the outer counter-rotating disk. The properties of these gaps are compared to those of planet-bearing gaps that form in disks hosting giant planets. We employ numerical hydrodynamics simulations of collapsing cores that are replenished from the local counter-rotating environment, as well as numerical hydrodynamic simulations of isolated disks hosting giant planets, to derive the properties of the gaps that form in both cases. Our numerical simulations demonstrate that counter-rotating disks can form for a wide range of mass and angular momentum available in the local environment. The gap that separates both disks has a depletion factor smaller than 1%, can be located at a distance from ten to over a hundred AU from the star, and can propagate inward with velocity ranging from 1 AU/Myr to >100 AU/Myr. Unlike our previous conclusion, the gap can therefore be a long-lived phenomenon, comparable in some cases to the lifetime of the disk itself. For a proper choice of the planetary mass, the viscous alpha-parameter and the disk mass, the planet-bearing gaps and the gaps in counter-rotating disks may show a remarkable similarity in the gas density profile and depletion factor, which may complicate their observational differentiation.
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