Imprint of the merger and ring-down on the gravitational wave background from black hole binaries coalescence

Abstract

We compute the gravitational wave background (GWB) generated by a cosmological population of black hole-black hole (BH-BH) binaries using hybrid waveforms recently produced by numerical simulations of (BH-BH) coalescence, which include the inspiral, merger, and ring-down contributions. A large sample of binary systems is simulated using the population synthesis code SeBa, and we extract fundamental statistical information on (BH-BH) physical parameters (primary and secondary BH masses, orbital separations and eccentricities, formation, and merger time scales). We then derive the binary birth and merger rates using the theoretical cosmic star formation history obtained from a numerical study which reproduces the available observational data at redshifts $z<8$. We evaluate the contributions of the inspiral, merger, and ring-down signals to the GWB, and discuss how these depend on the parameters which critically affect the number of coalescing (BH-BH) systems. We find that Advanced LIGO/Virgo have a chance to detect the GWB signal from the inspiral phase with a $(S/N)=10$ only for the most optimistic model, which predicts the highest local merger rate of $0.85\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}\text{ }{\mathrm{Myr}}^{\ensuremath{-}1}$. Third generation detectors, such as the Einstein Telescope (ET), could reveal the GWB from the inspiral phase predicted by any of the considered models. In addition, ET could sample the merger phase of the evolution at least for models which predict local merger rates between $[0.053--0.85]\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}3}\text{ }{\mathrm{Myr}}^{\ensuremath{-}1}$, which are more than a factor 2 lower than the upper limit inferred from the analysis of the LIGO S5 run [J. Abadie et al., Phys. Rev. D 83, 122005 (2011)]. The frequency dependence and amplitude of the GWB generated during the coalescence is very sensitive to the adopted core mass threshold for BH formation. This opens up the possibility to better understand the final stages of the evolution of massive stellar binaries using observational constraints on the associated gravitational wave emission.