The effect of cooling on the global stability of self-gravitating protoplanetary discs

Using a local model, Gammie has shown that accretion discs with cooling times t_cool ≤ 3Ω^-1 fragment into gravitationally bound objects, while those with cooling times t_cool > 3Ω^-1 evolve into a quasi-steady state. We use three-dimensional smoothed particle hydrodynamic simulations of protoplanetary accretion discs to test if the local results hold globally. We find that for disc masses appropriate for T Tauri discs, the fragmentation boundary still occurs at a cooling time close to t_cool = 3Ω^-1 For more massive discs, which are likely to be present at an earlier stage of the star formation process, fragmentation occurs for longer cooling times, but still within a factor of 2 of that predicted using a local model. These results have implications not only for planet formation in protoplanetary discs and star formation in active galactic nucleus discs, but also for the redistribution of angular momentum which could be driven by the presence of relatively massive objects within the accretion disc.