Binary formation and mass function variations in fragmenting discs with short cooling times

Accretion discs at sub-pc distances around supermassive black holes are likely to cool rapidly enough that self-gravity results in fragmentation. Here, we use high-resolution hydrodynamic simulations of a simplified disc model to study how the outcome of fragmentation depends upon numerical resolution and cooling time, and to investigate the incidence of binary formation within fragmenting discs. We investigate a range of cooling times, from the relatively long cooling time-scales that are marginally unstable to fragmentation down to highly unstable cooling on a time-scale that is shorter than the local dynamical time. The characteristic mass of fragments decreases with reduced cooling time, though the effect is modest and dependent upon details of how rapidly bound clumps radiate. We observe a high incidence of capture binaries, though we are unable to determine their final orbits or probability of survival. The results suggest that faster cooling in the parent disc results in an increased binary fraction, and that a high primordial binary fraction may result from disc fragmentation. We discuss our results in terms of the young massive stars close to the Galactic Centre, and suggest that observations of some stellar binaries close to the Galactic Centre remain consistent with formation in a fragmenting accretion disc.