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 ∼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_⊙ - 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 110M_⊙. Fragmentation may starve accretion in massive stars, especially above this limit, and is likely to create swarms of small, coplanar companions.