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 g cl 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 (GW) detectors could observe ∼ 500(g cl /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.PACS numbers: 04.30. Db, 95.55.Ym, and 97.60.Lf Given our understanding of how isolated binary stars evolve, noninteracting stellar systems should produce relatively few double black hole (BH-BH) binaries tight enough to merge through the emission of GW within the age of the universe [1,2,3]. Portegies Zwart and McMillan [4] demonstrated that interactions between black holes (BHs) in dense cluster environments could produce merging BH-BH binaries much more efficiently than through the evolution of isolated binaries. As a result, the local binary black hole merger rate -the net rate both from isolated evolution of noninteracting stars and from dense clusters -can depend sensitively on the formation and evolution of young clusters through the entire history of the universe.An increasing number of galactic [5,6] and extragalactic [7,8] observations suggest at least 20% of stars form in dense, interacting stellar clusters. Over time, each cluster dissipates, both because hot young stars and supernovae (SN) heat and eject a significant fraction of the residual gas that gravitationally binds the cluster ("infant mortality"), and because the host galaxy's tidal field strips off stars as the cluster orbits it [9,10]. Thus any set of coeval clusters decrease in number and size, spewing stars into their hosts [11,12], with only a few of the most initially dense and orbitally-fortunate clusters surviving to the present.Unfortunately, electromagnetic observations of large young clusters in other galaxies cannot resolve their internal structure. These observations therefore only weakly constrain the fraction of young clusters that survive their first few Myr, during which the most massive young stars evolve, supernovae, and g...

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