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

TL;DR

This paper investigates how amplitude-corrected post-Newtonian gravitational waveforms affect signal detection, revealing that including higher harmonics significantly improves detection capabilities, especially for intermediate-mass black hole binaries.

Contribution

It provides a detailed analysis of the impact of amplitude corrections and higher harmonics on gravitational wave detection, highlighting improvements over traditional restricted waveforms.

Findings

Amplitude-corrected waveforms yield lower SNRs for initial detectors compared to restricted waveforms.

Including higher harmonics can double or triple the mass reach of advanced detectors.

Restricted waveforms underestimate detection rates for intermediate-mass binary inspirals by at least twenty times.

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.