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

Abstract

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 ${50M}_{\ensuremath{\bigodot}}$ for initial LIGO interferometers, ${100M}_{\ensuremath{\bigodot}}$ for advanced, ${10}^{6}{M}_{\ensuremath{\bigodot}}$ 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 ${100M}_{\ensuremath{\bigodot}}--{700M}_{\ensuremath{\bigodot}}$ out to $\ensuremath{\sim}200\mathrm{Mpc}$ for initial LIGO interferometers, and in the mass range of $\ensuremath{\sim}{200M}_{\ensuremath{\bigodot}}$ to $\ensuremath{\sim}{3000M}_{\ensuremath{\bigodot}}$ out to about $z=1$ 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 $\ensuremath{\sim}4.$