  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.
