Accuracy and effectualness of closed-form, frequency-domain waveforms for nonspinning black hole binaries

Abstract

The coalescences of binary black hole (BBH) systems, here taken to be non-spinning, are among the most promising sources for gravitational wave (GW) ground-based detectors, such as LIGO and Virgo. To detect the GW signals emitted by BBHs, and measure the parameters of the source, one needs to have in hand a bank of GW templates that are both effectual (for detection), and accurate (for measurement). We study the effectualness and the accuracy of the two types of parametrized banks of templates that are directly defined in the frequency-domain by means of closed-form expressions, namely 'post-Newtonian' (PN) and 'phenomenological' models. In absence of knowledge of the (continuous family of) exact waveforms, our study assumes as fiducial, target waveforms the ones generated by the most accurate version of the effective-one-body (EOB) formalism, calibrated upon a few high-accuracy numerical relativity (NR) waveforms. We find that, for initial GW detectors the use, at each point of parameter space, of the best closed-form template (among PN and phenomenological models) leads to an effectualness > 97% over the entire mass range and > 99% in an important fraction of parameter space; however, when considering advanced detectors, both of the closed-form frequency-domain models fail to be effectual enough in significant domains of the two-dimensional [total mass and mass ratio] parameter space. Moreover, we find that, both for initial and advanced detectors, the two closed-form frequency-domain models fail to satisfy the minimal required accuracy standard in a very large domain of the two-dimensional parameter space. In addition, a side result of our study is the determination, as a function of the mass ratio, of the maximum frequency at which a frequency-domain PN waveform can be 'joined' onto a NRcalibrated EOB waveform without undue loss of accuracy. In the case of mass ratios larger than 4:1 this maximum frequency occurs well before the last stable orbit, leaving probably too many orbital cycles to be covered by current NR techniques if one wanted to construct accurate enough hybrid PN-NR waveforms. This problem will, however, be probably greatly alleviated, or even solved, by using the EOB formalism instead of PN theory.

Catalog of 174 Binary Black Hole Simulations for Gravitational Wave Astronomy

“…GW detection [condition (iii)] requires 10 orbits for straightforward simulations (mass ratio q 4, dimensionless spins χ ≡ S/M 2 0.7 aligned with the orbital angular momentum) [15]; parameter estimation can benefit from well over 100 orbits [15][16][17][18]. These numbers increase with more extreme mass ratio and BH spins [17], and analogous estimates have not even been performed for precessing binaries.…”

Sources of Gravitational Waves: Theory and Observations

“…One could try to directly combine PN-computed waveforms with NR waveforms, thus building a hybrid waveform. However, if the goal is to produce highly accurate templates, this method would still require high computational cost, because the different PN approximants agree sufficiently well with each other only at large separations, thus the hybridisation should start hundreds of GW cycles before merger [342][343][344]. An alternative avenue is provided by the EOB approach.…”

Approaching the Post-Newtonian Regime with Numerical Relativity: A Compact-Object Binary Simulation Spanning 350 Gravitational-Wave Cycles

“…For example, waveforms computed at the currently known PN order become unreliable possibly hundreds of orbits before merger for unequal-mass binaries [24,25] and even earlier when one of the objects is spinning [26]. [Several PN waveforms (or approximants) with different PN-truncation error are available in the literature.…”