Measuring gravitational waves from binary black hole coalescences. I. Signal to noise for inspiral, merger, and ringdown

We estimate the expected signal-to-noise ratios (SNRs) from the three phases (inspiral, merger, and ringdown) of coalescing binary black holes (BBHs) for initial and advanced ground-based interferometers (LIGO-VIRGO) and for the space-based interferometer LISA. Ground-based interferometers can do moderate SNR (a few tens), moderate accuracy studies of BBH coalescences in the mass range of a few to about 2000 solar masses; LISA can do high SNR (of order ${10}^4$), high accuracy studies in the mass range of about ${10}^5–{10}^8$ solar masses. BBHs might well be the first sources detected by LIGO-VIRGO: they are visible to much larger distances—up to 500 Mpc by initial interferometers—than coalescing neutron star binaries (heretofore regarded as the “bread and butter” workhorse source for LIGO-VIRGO, visible to about 30 Mpc by initial interferometers). Low-mass BBHs (up to ${50M}_{\odot }$ for initial LIGO interferometers, ${100M}_{\odot }$ for advanced, ${10}^6{M}_{\odot }$ for LISA) are best searched for via their well-understood inspiral waves; higher mass BBHs must be searched for via their poorly understood merger waves and/or their well-understood ringdown waves. A matched filtering search for massive BBHs based on ringdown waves should be capable of finding BBHs in the mass range of about ${100M}_{\odot }–{700M}_{\odot }$ out to $\sim 200\mathrm{Mpc}$ for initial LIGO interferometers, and in the mass range of $\sim {200M}_{\odot }$ to $\sim {3000M}_{\odot }$ out to about $z=1\mathrm{}$ for advanced interferometers. The required number of templates is of the order of 6000 or less. Searches based on merger waves could increase the number of detected massive BBHs by a factor of the order of 10 over those found from inspiral and ringdown waves, without detailed knowledge of the waveform shapes, using a noise monitoring search algorithm which we describe. A full set of merger templates from numerical relativity simulations could further increase the number of detected BBHs by an additional factor of up to $\sim 4.$