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

The coalescences of binary black hole systems, here taken to be nonspinning, 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 binary black holes 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 the 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 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, for both 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 NR-calibrated effective-one-body 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 effective-one-body formalism instead of PN theory.