Phenomenology of amplitude-corrected post-Newtonian gravitational waveforms for compact binary inspiral. I. Signal-to-noise ratios

Abstract

We study the phenomenological consequences of amplitude-corrected post-Newtonian (PN) gravitational waveforms, as opposed to the more commonly used restricted PN waveforms, for the quasi-circular, adiabatic inspiral of compact binary objects. In the case of initial detectors it has been shown that the use of amplitude-corrected waveforms for detection templates would lead to significantly lower signal-to-noise ratios (SNRs) than those suggested by simulations based exclusively on restricted waveforms. We further elucidate the origin of the effect by an in-depth analytic treatment. The discussion is extended to advanced detectors, where new features emerge. Non-restricted waveforms are linear combinations of harmonics in the orbital phase, and in the frequency domain the $k$th harmonic is cut off at $k f_{LSO}$, with $f_{LSO}$ the orbital frequency at the last stable orbit. As a result, with non-restricted templates it is possible to achieve sizeable signal-to-noise ratios in cases where the dominant harmonic (which is the one at twice the orbital phase) does not enter the detector's bandwidth. This will have important repercussions on the detection of binary inspirals involving intermediate-mass black holes. For sources at a distance of 100 Mpc, taking into account the higher harmonics will double the mass reach of Advanced LIGO, and that of EGO gets tripled. Conservative estimates indicate that the restricted waveforms underestimate detection rates for intermediate mass binary inspirals by at least a factor of twenty.