期刊
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
卷 427, 期 3, 页码 2022-2046出版社
WILEY-BLACKWELL
DOI: 10.1111/j.1365-2966.2012.22035.x
关键词
accretion; accretion discs; gravitation; hydrodynamics; instabilities; planets and satellites: formation; protoplanetary discs
资金
- Ministry for Education and Research (Bundesministerium fuer Bildung und Forschung)
- Ministry for Science, Research and Arts Baden-Wuerttemberg (Ministerium fuer Wissenschaft, Forschung und Kunst Baden-Wuerttemberg)
- EURYI
- EC
- German Research Foundation (DFG) within the Collaborative Research Group FOR 759 [KL 650/8-2]
- ETH Zurich Postdoctoral Fellowship Programme
- Marie Curie Actions for People COFUND programme
- Science and Technology Facilities Council [PP/C50707X/1, PP/D508220/1, ST/H008535/1, ST/K000373/1] Funding Source: researchfish
- STFC [ST/K000373/1, ST/H008535/1, PP/C50707X/1, PP/D508220/1] Funding Source: UKRI
We carry out simulations of gravitationally unstable discs using a smoothed particle hydrodynamics (SPH) code and a grid-based hydrodynamics code, fargo, to understand the previous non-convergent results reported by Meru & Bate. We obtain evidence that convergence with increasing resolution occurs with both SPH and fargo and in both cases we find that the critical cooling time-scale is larger than previously thought. We show that SPH has a first-order convergence rate, while fargo converges with a second-order rate. We show that the convergence of the critical cooling time-scale for fragmentation depends largely on the numerical viscosity employed in both SPH and fargo. With SPH, particle velocity dispersion may also play a role. We show that reducing the dissipation from the numerical viscosity leads to larger values of the critical cooling time at a given resolution. For SPH, we find that the effect of the dissipation due to the numerical viscosity is somewhat larger than had previously been appreciated. In particular, we show that using a quadratic term in the SPH artificial viscosity (beta SPH) that is too low appears to lead to excess dissipation in gravitationally unstable discs, which may affect any results that sensitively depend on the thermodynamics, such as disc fragmentation. We show that the two codes converge to values of the critical cooling time-scale, beta crit > 20 (for a ratio of specific heats of ? = 5/3), and perhaps even as large as beta crit similar to 30. These are approximately three to five times larger than has been found by most previous studies. This is equivalent to a maximum gravitational stress that a disc can withstand without fragmenting of aGI, crit similar to 0.013 - 0.02, which is much smaller than the values typically used in the literature. It is therefore easier for self-gravitating discs to fragment than has been concluded from most past studies.
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