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

TL;DR

This paper models the gravitational wave background from black hole binary mergers, analyzing the inspiral, merger, and ring-down phases, and assesses detectability prospects for current and future gravitational wave detectors.

Contribution

It introduces hybrid waveforms from numerical simulations into background calculations and evaluates the impact of different binary population parameters on detectability.

Findings

Advanced LIGO/Virgo may detect the inspiral GWB only in optimistic scenarios.

Third-generation detectors like ET can detect the inspiral phase across models.

ET could observe the merger phase for certain merger rate predictions.

Abstract

We compute the gravitational wave background (GWB) generated by a cosmological population of (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 timescales). 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 Mpc$^{-3}$ Myr$^{-1}$. Third generation detectors, such as 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 $[0.053 - 0.85]$ Mpc$^{-3}$ Myr$^{-1}$, which are more than a factor 2 lower the the upper limit inferred from the analysis of the LIGO S5 run\cite{Abadieetal2011}.