Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era

Abstract

We present a new frequency-domain phenomenological model of the gravitational-wave signal from the inspiral, merger and ringdown of non-precessing (aligned-spin) black-hole binaries. The model is calibrated to 19 hybrid effective-one-body-numerical-relativity waveforms up to mass ratios of 1:18 and black-hole spins of |a/m| ∼ 0.85 (0.98 for equal-mass systems). The inspiral part of the model consists of an extension of frequency-domain post-Newtonian expressions, using higher-order terms fit to the hybrids. The merger-ringdown is based on a phenomenological ansatz that has been significantly improved over previous models. The model exhibits mismatches of typically less than 1% against all 19 calibration hybrids, and an additional 29 verification hybrids, which provide strong evidence that, over the calibration region, the model is sufficiently accurate for all relevant gravitational-wave astronomy applications with the Advanced LIGO and Virgo detectors. Beyond the calibration region the model produces physically reasonable results, although we recommend caution in assuming that any merger-ringdown waveform model is accurate outside its calibration region. As an example, we note that an alternative non-precessing model, SEOBNRv2 (calibrated up to spins of only 0.5 for unequal-mass systems), exhibits mismatch errors of up to 10% for high spins outside its calibration region. We conclude that waveform models would benefit most from a larger number of numerical-relativity simulations of high-aligned-spin unequal-mass binaries.PACS numbers:

Post-Newtonian templates for binary black-hole inspirals: the effect of the horizon fluxes and the secular change in the black-hole masses and spins

“…The explicit 3.5PN expression for Ψ F2 NS is given in (3.18) of [78]. Ψ F2 ∞ with all possible spin-dependent contributions up to 3.5PN order can be obtained from (6a) -(6c) in [54] together with (6.22) in [80] (see also [44,81]), but we repeat it here for completeness adopting our notation: …”

“…We view our templates as a direct extension of the so-called Taylor template families (TaylorT1, T2, T3, T4 and F2) without the BH absorption, which are available and implemented in the LALSuite: LSC Algorithm Library Suite; see, e.g., [75,76,77,78,79] for the non-spinning inspirals, and [54,80,81] for the spinning inspirals. Also, our templates could readily used for comparison with NR simulation for BBHs in the high-mass ratio and high-spin regime (e.g., [82,83,84]), or for refining more realistic search templates such as effective-one-body formalism [36,37] and phenomenological model [44], including inspiral, merger and ringdown phases as well.…”

“…While the main goal of this paper motivates us to limit the scope to the dominant (2, 2) mode, our work could be improved by the corrections from these higher modes, for instance, making use of the method recently proposed in [103]. Third, although there have been highly accurate predictions for inspiral, merger and ringdown gravitational waveforms for BBHs, we did not use the effective-one-body waveforms [37] or the phenomenological (so-called PhenomD) waveforms [44] as our reference GW signals. As seen in figures 3 and 4, the corrections to the template due to BH absorption become most significant in high-massratio regime with high aligned-spins, but very few NR simulation is currently available there.…”

“…For the late inspiral, merger and ringdown phases [8], the PN models are not applicable and it is mandatory to use the numerical-relativity (NR) simulations based on the breakthrough [21,22,23] (see also [24,25,26,27,28,29]) as well as other analytical treatments combined with NR waveforms, including effective-one-body formalism [30,31,32,33,34,35,36,37] and phenomenological models [38,39,40,41,42,43,44]. The BBH waveform models have been further improved over the years and many applications to detection have already followed.…”

“…Fortunately, our examination suggests v pole 0.70 for a broad range of the BBH parameters, where the PN expansion will lose accuracy [89,90,91], and it should be taken over by the result from NR simulations. Moreover, if we compare the value of v pole to the nominal value of the ISCO of the Kerr metric [recall (1.9)] with mass m and (dimensionless) effective spin χ eff adopted in the phenomenological ("Phenom") model [40,41,44] …”