Convergence of SPH simulations of self-gravitating accretion discs: Sensitivity to the implementation of radiative cooling

Abstract

Recent simulations of self-gravitating accretion discs, carried out using a three-dimensional Smoothed Particle Hydrodynamics (SPH) code by Meru and Bate, have been interpreted as implying that three-dimensional global discs fragment much more easily than would be expected from a two-dimensional local model. Subsequently, global and local two-dimensional models have been shown to display similar fragmentation properties, leaving it unclear whether the three-dimensional results reflect a physical effect or a numerical problem associated with the treatment of cooling or artificial viscosity in SPH. Here, we study how fragmentation of self-gravitating disc flows in SPH depends upon the implementation of cooling. We run disc simulations that compare a simple cooling scheme, in which each particle loses energy based upon its internal energy per unit mass, with a method in which the cooling is derived from a smoothed internal energy density field. For the simple per particle cooling scheme, we find a significant increase in the minimum cooling time scale for fragmentation with increasing resolution, matching previous results. Switching to smoothed cooling, however, results in lower critical cooling time scales, and tentative evidence for convergence at the highest spatial resolution tested. We conclude that precision studies of fragmentation using SPH require careful consideration of how cooling (and, probably, artificial viscosity) is implemented, and that the apparent non-convergence of the fragmentation boundary seen in prior simulations is likely a numerical effect. In real discs, where cooling is physically smoothed by radiative transfer effects, the fragmentation boundary is probably displaced from the two-dimensional value by a factor that is only of the order of unity.

9 pages, 11 figures, MNRAS in press

References in corpus (9)

• Characterising the Gravitational Instability in Cooling Accretion Discs
• Star Formation Around Super-Massive Black Holes
• Fragmentation of gravitationally unstable gaseous protoplanetary disks with radiative transfer
• The Thermal Regulation of Gravitational Instabilities in Protoplanetary Disks III. Simulations with Radiative Cooling and Realistic Opacities
• Radiative transfer and the energy equation in SPH simulations of star formation
• Can giant planets form by gravitational fragmentation of discs?
• Introducing a Hybrid Method of Radiative Transfer for Smoothed Particle Hydrodynamics
• The Nature of Angular Momentum Transport in Radiative Self-Gravitating Protostellar Discs
• Resolution requirements for Smoothed Particle Hydrodynamics simulations of self-gravitating accretion discs

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