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We study numerical convergence in local two-dimensional hydrodynamical simulations of self-gravitating accretion discs with a simple cooling law. It is well-known that there exists a steady gravito-turbulent state, in which cooling is balanced by dissipation of weak shocks, with a net outward transport of angular momentum. Previous results indicated that if cooling is too fast (typical time scale 3/Omega, where Omega is the local angular velocity), this steady state can not be maintained and the disc will fragment into gravitationally bound clumps. We show that, in the two-dimensional local approximation, this result is in fact not converged with respect to numerical resolution and longer time integration. Irrespective of the cooling time scale, gravito-turbulence consists of density waves as well as transient clumps. These clumps will contract because of the imposed cooling, and collapse into bound objects if they can survive for long enough. Since heating by shocks is very local, the destruction of clumps is a stochastic process. High numerical resolution and long integration times are needed to capture this behaviour. We have observed fragmentation for cooling times up to 20/Omega, almost a factor 7 higher than in previous simulations. Fully three-dimensional simulations with a more realistic cooling prescription are necessary to determine the effects of the use of the two-dimensional approximation and a simple cooling law.
We study the numerical convergence of hydrodynamical simulations of self-gravitating accretion discs, in which a simple cooling law is balanced by shock heating. It is well-known that there exists a critical cooling time scale for which shock heating
We study the stability of gaps opened by a giant planet in a self-gravitating protoplanetary disc. We find a linear instability associated with both the self-gravity of the disc and local vortensity maxima which coincide with gap edges. For our model
It is likely that most protostellar systems undergo a brief phase where the protostellar disc is self-gravitating. If these discs are prone to fragmentation, then they are able to rapidly form objects that are initially of several Jupiter masses and
The gravitational interaction between a protoplanetary disc and planetary sized bodies that form within it leads to the exchange of angular momentum, resulting in migration of the planets and possible gap formation in the disc for more massive planet
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 wo