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I review recent progresses in the dynamics and the evolution of self-gravitating accretion discs. Accretion discs are a fundamental component of several astrophysical systems on very diverse scales, and can be found around supermassive black holes in Active Galactic Nuclei (AGN), and also in our Galaxy around stellar mass compact objects and around young stars. Notwithstanding the specific differences arising from such diversity in physical extent, all these systems share a common feature where a central object is fed from the accretion disc, due to the effect of turbulence and disc instabilities, which are able to remove the angular momentum from the gas and allow its accretion. In recent years, it has become increasingly apparent that the gravitational field produced by the disc itself (the discs self-gravity) is an important ingredient in the models, especially in the context of protostellar discs and of AGN discs. Indeed, it appears that in many cases (and especially in the colder outer parts of the disc) the development of gravitational instabilities can be one of the main agents in the redistribution of angular momentum. In some cases, the instability can be strong enough to lead to the formation of gravitationally bound clumps within the disc, and thus to determine the disc fragmentation. As a result, progress in our understanding of the dynamics of self-gravitating discs is essential to understand the processes that lead to the feeding of both young stars and of supermassive black holes in AGN. At the same time, understanding the fragmentation conditions is important to determine under which conditions AGN discs would fragment and form stars and whether protostellar discs might form giant gaseous planets through disc fragmentation.
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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.
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.
In this paper we examine the issue of characterising the transport associated with gravitational instabilities in relatively cold discs, discussing in particular the conditions under which it can be described within a local, viscous framework. We present the results of global, three-dimensional, SPH simulations of self-gravitating accretion discs, in which the disc is cooled using a simple parametrisation for the cooling function. Our simulations show that the disc settles in a ``self-regulated state, where the axisymmetric stability parameter $Qapprox 1$ and where transport and energy dissipation are dominated by self-gravity. We have computed the gravitational stress tensor and compared our results with expectations based on a local theory of transport. We find that, as long as the disc mass is smaller than $0.25M_{star}$ and the aspect ratio $H/Rlesssim 0.1$, transport is determined locally, thus allowing for a viscous treatment of the disc evolution.
The steady-state structure of a disc with a corona is analyzed when the vertical component of the gravitational force due to the self-gravity of the disc is considered. For the energy exchange between the disc and the corona, we assume a fraction f of the dissipated energy inside the accretion disc is transported to the corona via the magnetic tubes. Analytical solutions corresponding to a prescription for f (in which this parameter directly depends on the ratio of the gas pressure to the total pressure) or free f are presented and their physical properties are studied in detail. We show that the existence of the corona not only decreases the temperature of the disc, but also increases the surface density.The vertical component of the gravitational force due to the self-gravity of the disc decreases the self-gravitating radius and the mass of the fragments at this radius. However, as more energy is transported from the disc to the corona, the effect of the vertical component of the gravitational force due to the self-gravity of the disc on the self-gravitating radius becomes weaker, though the mass of the fragments is reduced irrespective of the amount of the energy exchange from the disc to the corona.
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.
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