Resolution requirements for smoothed particle hydrodynamics simulations of self-gravitating accretion discs

Stimulated by recent results by Meru & Bate, we revisit the issue of resolution requirements for simulating self-gravitating accretion discs with smoothed particle hydrodynamics (SPH). We show that all the results by Meru & Bate are actually consistent if they are 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 million (for a disc mass of the order of 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 of 2 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.