  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
black hole 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 10^(-10)/yr for the Milky-Way-like
galaxies and weakly dependent on the mass of MBH as M^(3/28). We estimate the
detection rate of 0.02-14/yr 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.
