Estimates of the source parameters of gravitational-wave (GW) events produced by compact binary mergers rely on theoretical models for the GW signal. We present the first frequency-domain model for ...the inspiral, merger, and ringdown of the GW signal from precessing binary black hole systems that also includes multipoles beyond the leading-order quadrupole. Our model, PhenomPv3HM, is a combination of the higher-multipole nonprecessing model PhenomHM and the spin-precessing model PhenomPv3 that includes two-spin precession via a dynamical rotation of the GW multipoles. We validate the new model by comparing to a large set of precessing numerical-relativity simulations and find excellent agreement across the majority of the parameter space they cover. For mass ratios <5 the mismatch improves, on average, from ∼6% to ∼2% compared to PhenomPv3 when we include higher multipoles in the model. However, we find mismatches ∼8% for a mass-ratio-6 and highly spinning simulation. We quantify the statistical uncertainty in the recovery of binary parameters by applying standard Bayesian parameter estimation methods to simulated signals. We find that, while the primary black hole spin parameters should be measurable even at moderate signal-to-noise ratios (SNRs) ∼30, the secondary spin requires much larger SNRs ∼200. We also quantify the systematic uncertainty expected by recovering our simulated signals with different waveform models in which various physical effects-such as the inclusion of higher modes and/or precession-are omitted and find that even in the low-SNR case (∼17) the recovered parameters can be biased. Finally, as a first application of the new model we analyze the binary black hole event GW170729. We find larger values for the primary black hole mass of 58.25−12.53+11.73 M⊙ (90% credible interval). The lower limit (∼46 M⊙) is comparable to the proposed maximum black hole mass predicted by different stellar evolution models due to the pulsation pair-instability supernova (PPISN) mechanism. If we assume that the primary black hole in GW170729 formed through a PPISN, then out of the four PPISN models we consider only the model of Woosley 1 is consistent with our mass measurements at the 90% confidence level.
Measurements of black-hole spins from gravitational-wave observations of black-hole binaries with ground-based detectors are known to be hampered by partial degeneracies in the gravitational-wave ...phasing: between the two component spins, and between the spins and the binary's mass ratio, at least for signals that are dominated by the binary's inspiral. Through the merger and ringdown, however, a different set of degeneracies apply. This suggests the possibility that, if the inspiral, merger and ringdown are all within the sensitive frequency band of a detector, we may be able to break these degeneracies and more accurately measure both spins. In this work we investigate our ability to measure individual spins for nonprecessing binaries, for a range of configurations and signal strengths, and conclude that in general the spin of the larger black hole will be measurable (at best) with observations from Advanced LIGO and Virgo. This implies that in many applications waveform models parameterized by only one effective spin will be sufficient. Our work does not consider precessing binaries or subdominant harmonics, although we provide some arguments why we expect that these will not qualitatively change our conclusions.
Binary-black-hole orbits precess when the black-hole spins are misaligned with the binary's orbital angular momentum. The apparently complicated dynamics can in most cases be described as simple ...precession of the orbital angular momentum about an approximately fixed total angular momentum. However, the imprint of the precession on the observed gravitational-wave signal is yet more complicated, with a nontrivial time-varying dependence on the black-hole dynamics, the binary's orientation and the detector polarization. As a result, it is difficult to predict under which conditions precession effects are measurable in gravitational-wave observations, and their impact on both signal detection and source characterization. We show that the observed waveform can be simplified by decomposing it as a power series in a new precession parameter b = tan(β/2), where β is the opening angle between the orbital and total angular momenta. The power series is made up of five harmonics, with frequencies that differ by the binary's precession frequency, and individually do not exhibit amplitude and phase modulations. In many cases, the waveform can be well approximated by the two leading harmonics. In this approximation we are able to obtain a simple picture of precession as caused by the beating of two waveforms of similar frequency. This enables us to identify regions of the parameter space where precession is likely to have an observable effect on the waveform, and to propose a new approach to searching for signals from precessing binaries, based upon the two-harmonic approximation.
We present a new frequency-domain phenomenological model of the gravitational-wave signal from the inspiral, merger and ringdown of nonprecessing (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 nonprecessing 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.
In this paper we discuss the anatomy of frequency-domain gravitational-wave signals from nonprecessing black-hole coalescences with the goal of constructing accurate phenomenological waveform models. ...We first present new numerical-relativity simulations for mass ratios up to 18, including spins. From a comparison of different post-Newtonian approximants with numerical-relativity data we select the uncalibrated SEOBNRv2 model as the most appropriate for the purpose of constructing hybrid post-Newtonian/numerical-relativity waveforms, and we discuss how we prepare time-domain and frequency-domain hybrid data sets. We then use our data together with results in the literature to calibrate simple explicit expressions for the final spin and radiated energy. Equipped with our prediction for the final state we then develop a simple and accurate merger-ringdown model based on modified Lorentzians in the gravitational-wave amplitude and phase, and we discuss a simple method to represent the low frequency signal augmenting the TaylorF2 post-Newtonian approximant with terms corresponding to higher orders in the post-Newtonian expansion. We finally discuss different options for modelling the small intermediate frequency regime between inspiral and merger ringdown. A complete phenomenological model based on the present work is presented in a companion paper S. Khan et al., following paper, Phys. Rev. D 93 044007 (2016).
Gravitational-wave observations of binary black holes currently rely on theoretical models that predict the dominant multipoles (ℓ=2,|m|=2) of the radiation during inspiral, merger, and ringdown. We ...introduce a simple method to include the subdominant multipoles to binary black hole gravitational waveforms, given a frequency-domain model for the dominant multipoles. The amplitude and phase of the original model are appropriately stretched and rescaled using post-Newtonian results (for the inspiral), perturbation theory (for the ringdown), and a smooth transition between the two. No additional tuning to numerical-relativity simulations is required. We apply a variant of this method to the nonprecessing PhenomD model. The result, PhenomHM, constitutes the first higher-multipole model of spinning and coalescing black-hole binaries, and currently includes the (ℓ,|m|)=(2,2),(3,3),(4,4),(2,1),(3,2),(4,3) radiative moments. Comparisons with numerical-relativity waveforms demonstrate that PhenomHM is more accurate than dominant-multipole-only models for all binary configurations, and typically improves the measurement of binary properties.
Accurate gravitational-wave (GW) signal models exist for black hole binary (BBH) and neutron-star binary (BNS) systems, which are consistent with all of the published GW observations to date. ...Detections of a third class of compact-binary systems, neutron-star black hole (NSBH) binaries, have not yet been confirmed, but are eagerly awaited in the near future. For NSBH systems, GW models do not exist across the viable parameter space of signals. In this work we present the frequency-domain phenomenological model, phenomnsbh, for GWs produced by NSBH systems with mass ratios from equal-mass up to 15, spin on the black hole (BH) up to a dimensionless spin of | χ | = 0.5 , and tidal deformabilities ranging from 0 (the BBH limit) to 5000. We extend previous work on a phenomenological amplitude model for NSBH systems to produce an amplitude model that is parametrized by a single tidal deformability parameter. This amplitude model is combined with an analytic phase model describing tidal corrections. The resulting approximant is compared to publicly available NSBH numerical-relativity simulations and hybrid waveforms constructed from numerical-relativity simulations and tidal inspiral approximants. For most signals observed by second-generation ground-based detectors, it will be difficult to use the GW signal alone to distinguish single NSBH systems from either BNSs or BBHs, and therefore to unambiguously identify an NSBH system.
We perform an extensive numerical study of coalescing black-hole binaries to understand the gravitational-wave spectrum of quasinormal modes excited in the merged black hole. Remarkably, we find that ...the masses and spins of the progenitor are clearly encoded in the mode spectrum of the ringdown signal. Some of the mode amplitudes carry the signature of the binary's mass ratio, while others depend critically on the spins. Simulations of precessing binaries suggest that our results carry over to generic systems. Using Bayesian inference, we demonstrate that it is possible to accurately measure the mass ratio and a proper combination of spins even when the binary is itself invisible to a detector. Using a mapping of the binary masses and spins to the final black-hole spin allows us to further extract the spin components of the progenitor. Our results could have tremendous implications for gravitational astronomy by facilitating novel tests of general relativity using merging black holes.
Measurements of the properties of binary neutron star systems from gravitational-wave observations require accurate theoretical models for such signals. However, current models are incomplete, as ...they do not take into account all of the physics of these systems: some neglect possible tidal effects, others neglect spin-induced orbital precession, and no existing model includes the post-merger regime consistently. In this work, we explore the importance of two physical ingredients: tidal interactions during the inspiral and the imprint of the post-merger stage. We use complete inspiral–merger–post-merger waveforms constructed from a tidal effective-one-body approach and numerical-relativity simulations as signals against which we perform parameter estimates with waveform models of standard LIGO-Virgo analyses. We show that neglecting tidal effects does not lead to appreciable measurement biases in masses and spin for typical observations (small tidal deformability and signal-to-noise ratio ?25). However, with increasing signal-to-noise ratio or tidal deformability there are biases in the estimates of the binary parameters. The post-merger regime, instead, has no impact on gravitational-wave measurements with current detectors for the signal-to-noise ratios we consider.
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