Production of intermediate-mass black holes in globular clusters

The discovery of numerous non-nuclear X-ray point sources with luminosities L>1039 erg s−1 in several starburst galaxies has stimulated speculation about their nature and origin. The strong variability seen in several sources points to massive black holes as the central engines. If the flux is isotropic, the luminosities range up to ≈1041 erg s−1, implying masses of M≳103 M⊙ if the luminosity is sub-Eddington. Here we explore a model for these sources. We suggest that in some tens of per cent of globular clusters a very massive black hole, M≳50 M⊙, is formed. This black hole sinks in ≲106 yr to the centre of the cluster, where in the ∼1010 yr lifetime of the cluster it accretes ∼103 M⊙, primarily in the form of lighter black holes. Unlike less-massive black holes in binaries, which are flung from clusters by recoil before they can merge gravitationally, a ≳50 M⊙ black hole has enough inertia that it remains bound to the cluster. We suggest that ∼103 M⊙ black holes may be common in the centres of dense globular clusters, and may therefore exist in some tens of per cent of current globulars. If the cluster later merges with its host galaxy, accretion from young star clusters in molecular clouds by the black hole can generate luminosity consistent with that observed. We also consider the detectability of massive black holes in globular clusters with gravitational wave detectors, and speculate on future observations that may test our predictions.