Binary black hole late inspiral: Simulations for gravitational wave observations

Coalescing binary black hole mergers are expected to be the strongest gravitational wave sources for ground-based interferometers, such as the LIGO, VIRGO, and GEO600, as well as the space-based interferometer LISA. Until recently it has been impossible to reliably derive the predictions of general relativity for the final merger stage, which takes place in the strong-field regime. Recent progress in numerical relativity simulations is, however, revolutionizing our understanding of these systems. We examine here the specific case of merging equal-mass Schwarzschild black holes in detail, presenting new simulations in which the black holes start in the late-inspiral stage on orbits with very low eccentricity and evolve for $\sim 1200M$ through $\sim 7$ orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass $\sim 14\mathrm{cycle}$ before merger, and highlight the importance of using frequency (rather than time) to set the physical reference when comparing models. Matching our results to post-Newtonian (PN) calculations for the earlier parts of the inspiral provides a combined waveform with less than one cycle of accumulated phase error through the entire coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs) for iLIGO, adLIGO, and LISA, highlighting the contributions from the late-inspiral and merger-ringdown parts of the waveform, which can now be simulated numerically. Contour plots of SNR as a function of $z$ and $M$ show that adLIGO can achieve $\mathrm{SNR}\gtrsim 10$ for some intermediate mass binary black holes (IMBBHs) out to $z\sim 1$, and that LISA can see massive binary black holes (MBBHs) in the range $3\times {10}^4\lesssim M/M_{\odot }\lesssim {10}^7$ at $\mathrm{SNR}>100$ out to the earliest epochs of structure formation at $z>15$.