Black hole binaries in galactic nuclei and gravitational wave sources

Stellar black hole (BH) binaries are one of the most promising gravitational wave (GW) sources for GW detection by the ground-based detectors. Nuclear star clusters (NCs) located at the centre of galaxies are known to harbour massive black holes (MBHs) and to be bounded by a gravitational potential by other galactic components such as the galactic bulge. Such an environment of NCs provides a favourable conditions for the BH-BH binary formation by the gravitational radiation capture due to the high BH number density and velocity dispersion. We carried out detailed numerical study of the formation of BH binaries in the NCs using a series of N-body simulations for equal-mass cases. There is no mass segregation introduced. We have derived scaling relations of the binary formation rate with the velocity dispersion of the stellar system beyond the radius of influence and made estimates of the rate of formation of BH binaries per unit comoving volume and thus expected detection rate by integrating the binary formation rate over galaxy population within the detection distance of the advanced detectors. We find that the overall formation rates for BH-BH binaries per NC is similar to 10(-10) yr(-1) for the Milky Way-like galaxies and weakly dependent on the mass of MBH as Gamma proportional to M-MBH(3/28). We estimate the detection rate of 0.02-14 yr(-1) for advanced LIGO/Virgo considering several factors such as the dynamical evolution of NCs, the variance of the number density of stars and the mass range of MBH giving uncertainties.