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Register a new userVortex stretching in self-gravitating protoplanetary discs
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Horseshoe-shaped brightness asymmetries of several transitional discs are thought to be caused by large-scale vortices. Anticyclonic vortices are efficiently collect dust particles, therefore they can play a major role in planet formation. Former studies suggest that the disc self-gravity weakens vortices formed at the edge of the gap opened by a massive planet in discs whose masses are in the range of 0.01<=M_disc/M_*<=0.1. Here we present an investigation on the long-term evolution of the large-scale vortices formed at the viscosity transition of the discs dead zone outer edge by means of two-dimensional hydrodynamic simulations taking disc self-gravity into account. We perform a numerical study of low mass, 0.001<=M_disc/M_*<=0.01, discs, for which cases disc self-gravity was previously neglected. The large-scale vortices are found to be stretched due to disc self-gravity even for low-mass discs with M_disc/M_*>=0.005 where initially the Toomre Q-parameter was <=50 at the vortex distance. As a result of stretching, the vortex aspect ratio increases and a weaker azimuthal density contrast develops. The strength of the vortex stretching is proportional to the disc mass. The vortex stretching can be explained by a combined action of a non-vanishing gravitational torque caused by the vortex, and the Keplerian shear of the disc. Self-gravitating vortices are subject to significantly faster decay than non-self-gravitating ones. We found that vortices developed at sharp viscosity transitions of self-gravitating discs can be described by a GNG model as long as the disc viscosity is low, i.e. alpha_dz<=10^-5.
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Self-gravity becomes competitive as an angular momentum transport process in accretion discs at large radii, where the temperature is low enough that external irradiation likely contributes to the thermal balance. Irradiation is known to weaken the strength of disc self-gravity, and can suppress it entirely if the disc is maintained above the threshold for linear instability. However, its impact on the susceptibility of the disc to fragmentation is less clear. We use two-dimensional numerical simulations to investigate the evolution of self-gravitating discs as a function of the local cooling time and strength of irradiation. In the regime where the disc does not fragment, we show that local thermal equilibrium continues to determine the stress - which can be represented as an effective viscous alpha - out to very long cooling times (at least 240 dynamical times). In this regime, the power spectrum of the perturbations is uniquely set by the effective viscous alpha and not by the cooling rate. Fragmentation occurs for cooling times tau < beta_crit / Omega, where beta_crit is a weak function of the level of irradiation. We find that beta_crit declines by approximately a factor of two, as irradiation is increased from zero up to the level where instability is almost quenched. The numerical results imply that irradiation cannot generally avert fragmentation of self-gravitating discs at large radii; if other angular momentum transport sources are weak mass will build up until self-gravity sets in, and fragmentation will ensue.
It is quite likely that self-gravity will play an important role in the evolution of accretion discs, in particular those around young stars, and those around supermassive black holes. We summarise, here, our current understanding of the evolution of such discs, focussing more on discs in young stellar system, than on discs in active galactic nuclei. We consider the conditions under which such discs may fragment to form bound objects, and when they might, instead, be expected to settle into a quasi-steady, self-regulated state. We also discuss how this understanding may depend on the mass of the disc relative to the mass of the central object, and how it might depend on the presence of external irradiation. Additionally, we consider whether or not fragmentation might be stochastic, where we might expect it to occur in an actual protostellar disc, and if there is any evidence for fragmentation actually playing a role in the formation of planetary-mass bodies. Although there are still a number of outstanding issue, such as the convergence of simulations of self-gravitating discs, whether or not there is more than one mode of fragmentation, and quite what role self-gravitating discs may play in the planet formation process, our general understanding of these systems seems quite robust.
In this paper we present simulated observations of massive self-gravitating circumstellar discs using the Atacama Large Millimetre/sub-millimetre Array (ALMA). Using a smoothed particle hydrodynamics model of a $0.2M_{odot}$ disc orbiting a $1M_{odot}$ protostar, with a cooling model appropriate for discs at temperatures below $sim 160$K and representative dust opacities, we have constructed maps of the expected emission at sub-mm wavelengths. We have then used the CASA ALMA simulator to generate simulated images and visibilities with various array configurations and observation frequencies, taking into account the expected thermal noise and atmospheric opacities. We find that at 345 GHz (870 $mu$m) spiral structures at a resolution of a few AU should be readily detectable in approximately face-on discs out to distances of the Taurus-Auriga star-forming complex.
Large-scale, dust-trapping vortices may account for observations of asymmetric protoplanetary discs. Disc vortices are also potential sites for accelerated planetesimal formation by concentrating dust grains. However, in 3D discs vortices are subject to destructive `elliptic instabilities, which reduces their viability as dust traps. The survival of vortices in 3D accretion discs is thus an important issue to address. In this work, we perform shearing box simulations to show that disc self-gravity enhances the survival of 3D vortices, even when self-gravity is weak in the classic sense (e.g. with a Toomre $Qsimeq5$). We find a 3D, self-gravitating vortex can grow on secular timescales in spite of the elliptic instability. The vortex aspect-ratio decreases as it strengthens, which feeds the elliptic instability. The result is a 3D vortex with a turbulent core that persists for $sim 10^{3}$ orbits. We find when gravitational and hydrodynamic stresses become comparable, the vortex may undergo episodic bursts, which we interpret as interaction between elliptic and gravitational instabilities. We estimate the distribution of dust particles in self-gravitating, turbulent vortices. Our results suggest large-scale vortices in protoplanetary discs are more easily observed at large radii.
We investigate how the detectability of signatures of self-gravity in a protoplanetary disc depends on its temporal evolution. We run a one-dimensional model for secular timescales to follow the disc mass as a function of time. We then combine this with three-dimensional global hydrodynamics simulations that employ a hybrid radiative transfer method to approximate realistic heating and cooling. We simulate ALMA continuum observations of these systems, and find that structures induced by the gravitational instability (GI) are readily detectable when $q=M_mathrm{disc}/M_*gtrsim 0.25$ and $R_mathrm{outer}lesssim 100$ au. The high accretion rate generated by gravito-turbulence in such a massive disc drains its mass to below the detection threshold in $sim10^4$ years, or approximately 1 % of the typical disc lifetime. Therefore, discs with spiral arms detected in ALMA dust observations, if generated by self-gravity, must either be still receiving infall to maintain a high $q$ value, or have just emerged from their natal envelope. Detection of substructure in systems with lower $q$ is possible, but would require a specialist integration with the most extended configuration over several days. This disfavours the possibility of GI-caused spiral structure in systems with $q<0.25$ being detected in relatively short integration times, such as those found in the DSHARP ALMA survey (Andrews et al. 2018; Huang et al. 2018). We find no temporal dependence of detectability on dynamical timescales
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