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 ${g}_{\mathrm{cl}}$ of star formation occurs in clusters and that a significant fraction ${g}_{\mathrm{evap}}$ of clusters undergo this segregation and evaporation process. We predict future ground-based gravitational wave detectors could observe $\ensuremath{\sim}500({g}_{\mathrm{cl}}/0.5)({g}_{\mathrm{evap}}/0.1)$ 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.
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