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 similar to 1200M through similar to 7 orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass similar to 14 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 SNR greater than or similar to 10 for some intermediate mass binary black holes (IMBBHs) out to z similar to 1, and that LISA can see massive binary black holes (MBBHs) in the range 3x10(4)less than or similar to M/M less than or similar to 10(7) at SNR > 100 out to the earliest epochs of structure formation at z > 15.