Illuminating black hole cusp populations in young star clusters

There is increasing evidence that globular clusters retain sizeable black hole populations at present day. This is supported by dynamical simulations of cluster evolution, which have unveiled the spatial distribution and mass spectrum of black holes in clusters across cosmic age. However, the black hole populations of young, high metallicity clusters remain unconstrained. The black holes hosted by these clusters are expected to rapidly mass segregate early in their evolutionary history, forming central cusps of hundreds to thousands of black holes. Here, we argue that the host young cluster can accumulate gas from its dense surroundings, from which the black hole cusp members can accrete at highly enhanced rates. Their collective accretion luminosity can be substantial and provides a novel observational constraint for nearby young massive clusters. We test this hypothesis by performing 3D hydrodynamic simulations where we embed discretized potentials, representing our black holes, within the core potential of a massive cluster. This system moves supersonically with respect to a gaseous medium from which it accretes. We study the accretion of this black hole cusp for different cusp populations and determine the integrated accretion luminosity of the black hole cusp. We apply our results to the young massive clusters of the Antennae Galaxies and find that a typical cusp accretion luminosity should be in excess of $\approx 10^{40}\,{\rm ergs\,\,s^{-1}}$. We argue that no strong candidates of this luminous signal have been observed, and constrain the cusp population of a typical cluster in the Antennae Galaxies to $\lesssim10-2\times10^2$ $10\,M_\odot$ black holes. This is in conflict with predictions of dynamical simulations, which suggest that these systems should harbor several hundred to thousands of black holes, and we explore the reasons for this discrepancy in our conclusions.