Dynamical Interactions and the Black Hole Merger Rate of the Universe

Abstract

Binary black holes can form efficiently in dense young stellar clusters, such as the progenitors of globular clusters, via a combination of gravitational segregation and cluster evaporation. We use simple analytic arguments supported by detailed N-body simulations to determine how frequently black holes born in a single stellar cluster should form binaries, be ejected from the cluster, and merge through the emission of gravitational radiation. We then convolve this ``transfer function'' relating cluster formation to black hole mergers with (i) the distribution of observed cluster masses and (ii) the star formation history of the universe, assuming that a significant fraction gcl of star formation occurs in clusters and that a significant fraction gcand of clusters undergo this segregation and evaporation process. We predict future ground--based gravitational wave (GW) detectors could observe ~500 (gcl/0.5) (gcand/0.1) double black hole mergers per year, and the presently operating LIGO interferometer would have a chance (50%) at detecting a merger during its first full year of science data. More realistically, advanced LIGO and similar next-generation gravitational wave observatories provide unique opportunities to constrain otherwise inaccessible properties of clusters formed in the early universe.Comment: 4 pages, 2 figures. To appear in PRD Rapid Communication