Dynamical interactions and the black-hole merger rate of the Universe

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 gevap of clusters undergo this segregation and evaporation process. We predict future ground-based gravitational wave detectors could observe ∼500(gcl/0.5)(gevap/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.