Resolution requirements for Smoothed Particle Hydrodynamics simulations of self-gravitating accretion discs

TL;DR

This paper investigates the resolution requirements for simulating self-gravitating accretion discs with SPH, showing that higher resolution (up to 10 million particles) is needed for reliable thermodynamic results, especially regarding fragmentation criteria.

Contribution

It demonstrates that the resolution criterion for cooling gaseous discs depends on the cooling rate and suggests that current simulations are approaching convergence at very high particle counts.

Findings

Resolution approaching 10 million particles for convergence.

Critical cooling time for fragmentation is about 15Ω^{-1}.

Thermodynamic results are sensitive to resolution, while dynamical results are robust.

Abstract

Stimulated by recent results by Meru and Bate (2010a,b), we revisit the issue of resolution requirements for simulating self-gravitating accretion discs with Smoothed Particle Hydrodynamics (SPH). We show that the results by Meru and Bate (2010a) are consistent with those of Meru and Bate (2010b) if they are both interpreted as driven by resolution effects, therefore implying that the resolution criterion for cooling gaseous discs is a function of the imposed cooling rate. We discuss two possible numerical origins of such dependence, which are both consistent with the limited number of available data. Our results tentatively indicate that convergence for current simulations is being reached for a number of SPH particles approaching 10 millions (for a disc mass of order 10 per cent of the central object mass), which would set the critical cooling time for fragmentation at about $15\Omega^{-1}$, roughly a factor two larger than previously thought. More in general, we discuss the extent to which the large number of recent numerical results are reliable or not. We argue that those results that pertain to the dynamics associated with gravitational instabilities (such as the locality of angular momentum transport, and the relationship between density perturbation and induced stress) are robust, while those pertaining to the thermodynamics of the system (such as the determination of the critical cooling time for fragmentation) can be affected by poor resolution.