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Register a new userConvergence of simulations of self-gravitating accretion discs II: Sensitivity to the implementation of radiative cooling and artificial viscosity
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Recently it has been suggested that the fragmentation boundary in Smoothed Particle Hydrodynamic (SPH) and FARGO simulations of self-gravitating accretion discs with beta-cooling do not converge as resolution is increased. Furthermore, this recent work suggests that by carefully optimising the artificial viscosity parameters in these codes it can be shown that fragmentation may occur for much longer cooling times than earlier work suggests. If correct, this result is intriguing as it suggests that gas giant planets could form, via direct gravitational collapse, reasonably close to their parent stars. This result is, however, slightly surprising and there have been a number of recent studies suggesting that the result is likely an indication of a numerical problem with the simulations. One suggestion, in particular, is that the SPH results are influenced by the manner in which the cooling is implemented. We extend this work here and show that if the cooling is implemented in a manner that removes a known numerical artefact in the shock regions, the fragmentation boundary converges to a value consistent with earlier work and that fragmentation is unlikely for the long cooling times suggested by this recent work. We also investigate the optimisation of the artificial viscosity parameters and show that the values that appear optimal are likely introducing numerical problems in both the SPH and FARGO simulations. We therefore conclude that earlier predictions for the cooling times required for fragmentation are likely correct and that, as suggested by this earlier work, fragmentation cannot occur in the inner parts (r < 50 au) of typical protostellar discs.
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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.
Gas giant planets may form early-on during the evolution of protostellar discs, while these are relatively massive. We study how Jupiter-mass planet-seeds (termed protoplanets) evolve in massive, but gravitationally stable (Q>1.5), discs using radiative hydrodynamic simulations. We find that the protoplanet initially migrates inwards rapidly, until it opens up a gap in the disc. Thereafter, it either continues to migrate inwards on a much longer timescale or starts migrating outwards. Outward migration occurs when the protoplanet resides within a gap with gravitationally unstable edges, as a high fraction of the accreted gas is high angular momentum gas from outside the protoplanets orbit. The effect of radiative heating from the protoplanet is critical in determining the direction of the migration and the eccentricity of the protoplanet. Gap opening is facilitated by efficient cooling that may not be captured by the commonly used beta-cooling approximation. The protoplanet initially accretes at a high rate (1e-3Mj/yr), and its accretion luminosity could be a few tenths of the host stars luminosity, making the protoplanet easily observable (albeit only for a short time). Due to the high gas accretion rate, the protoplanet generally grows above the deuterium-burning mass-limit. Protoplanet radiative feedback reduces its mass growth so that its final mass is near the brown dwarf-planet boundary. The fate of a young planet-seed is diverse and could vary from a gas giant planet on a circular orbit at a few AU from the central star to a brown dwarf on an eccentric, wide orbit.
We present a 3D semi-analytic model of self-gravitating discs, and include a prescription for dust trapping in the disc spiral arms. Using Monte-Carlo radiative transfer we produce synthetic ALMA observations of these discs. In doing so we demonstrate that our model is capable of producing observational predictions, and able to model real image data of potentially self-gravitating discs. For a disc to generate spiral structure that would be observable with ALMA requires that the discs dust mass budget is dominated by millimetre and centimetre-sized grains. Discs in which grains have grown to the grain fragmentation threshold may satisfy this criterion, thus we predict that signatures of gravitational instability may be detectable in discs of lower mass than has previously been suggested. For example, we find that discs with disc-to-star mass ratios as low as $0.10$ are capable of driving observable spiral arms. Substructure becomes challenging to detect in discs where no grain growth has occurred or in which grain growth has proceeded well beyond the grain fragmentation threshold. We demonstrate how we can use our model to retrieve information about dust trapping and grain growth through multi-wavelength observations of discs, and using estimates of the opacity spectral index. Applying our disc model to the Elias 27, WaOph 6 and IM Lup systems we find gravitational instability to be a plausible explanation for the observed substructure in all 3 discs, if sufficient grain growth has indeed occurred.
It has recently been suggested that in the presence of driven turbulence discs may be much less stable against gravitational collapse than their non turbulent analogs, due to stochastic density fluctuations in turbulent flows. This mode of fragmentation would be especially important for gas giant planet formation. Here we argue, however, that stochastic density fluctuations due to turbulence do not enhance gravitational instability and disc fragmentation in the long cooling time limit appropriate for planet forming discs. These fluctuations evolve adiabatically and dissipate away by decompression faster than they could collapse. We investigate these issues numerically in 2D via shearing box simulations with driven turbulence and also in 3D with a model of instantaneously applied turbulent velocity kicks. In the former setting turbulent driving leads to additional disc heating that tends to make discs more, rather than less, stable to gravitational instability. In the latter setting, the formation of high density regions due to convergent velocity kicks is found to be quickly followed by decompression, as expected. We therefore conclude that driven turbulence does not promote disc fragmentation in protoplanetary discs and instead tends to make the discs more stable. We also argue that sustaining supersonic turbulence is very difficult in discs that cool slowly.
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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