An upper limit to the velocity dispersion of relaxed stellar systems without massive black holes
by Miller, M. Coleman and Davies, Melvyn B.
8 pages, 2 figures, accepted to the Astrophysical Journal
Massive black holes have been discovered in all closely examined galaxies with high velocity dispersion. The case is not as clear for lower-dispersion systems such as low-mass galaxies and globular clusters. Here we suggest that above a critical velocity dispersion of roughly 40 km/s, massive central black holes will form in relaxed stellar systems at any cosmic epoch. This is because above this dispersion primordial binaries cannot support the system against deep core collapse. If, as previous simulations show, the black holes formed in the cluster settle to produce a dense subcluster, then given the extremely high densities reached during core collapse the holes will merge with each other. For low velocity dispersions and hence low cluster escape speeds, mergers will typically kick out all or all but one of the holes due to three-body kicks or the asymmetric emission of gravitational radiation. If one hole remains, it will tidally disrupt stars at a high rate. If none remain, one is formed after runaway collisions between stars, then it tidally disrupts stars at a high rate. The accretion rate after disruption is many orders of magnitude above Eddington. If, as several studies suggest, the hole can accept matter at that rate because the generated radiation is trapped and advected, then it will grow quickly and form a massive central black hole.