Fragmentation of massive protostellar discs

We examine whether massive-star accretion discs are likely to fragment due to self-gravity. Rapid accretion and high angular momentum push these discs toward fragmentation, whereas viscous heating and the high protostellar luminosity stabilize them. We find that for a broad range of protostar masses and for reasonable accretion times, massive discs larger than similar to 150 au are prone to fragmentation. We develop an analytical estimate for the angular momentum of accreted material, extending the analysis of Matzner & Levin to account for strongly turbulent initial conditions. In a core-collapse model, we predict that discs are marginally prone to fragmentation around stars of about 4-15 M circle dot - even if we adopt conservative estimates of the discs' radii and tendency to fragment. More massive stars are progressively more likely to fragment, and there is a sharp drop in the stability of disc accretion at the very high accretion rates expected above 110 M circle dot. Fragmentation may starve accretion in massive stars, especially above this limit, and is likely to create swarms of small, coplanar companions.