Binary Black Hole Waveforms Research Articles

Phenomenological relationship between eccentric and quasicircular orbital binary black hole waveform

Phenomenological relationship between eccentric and quasicircular orbital binary black hole waveform

High-accuracy high-mass-ratio simulations for binary neutron stars and their comparison to existing waveform models

The subsequent observing runs of the advanced gravitational-wave detector network will likely provide us with various gravitational-wave observations of binary neutron star systems. For an accurate interpretation of these detections, we need reliable gravitational-wave models. To test and to point out how existing models could be improved, we perform a set of high-resolution numerical relativity simulations for four different physical setups with mass ratios $q=1.25$, 1.50, 1.75, 2.00, and total gravitational mass $M=2.7\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. Each configuration is simulated with five different resolutions to allow a proper error assessment. Overall, we find approximately second-order converging results for the dominant (2,2) mode, but also the subdominant (2,1), (3,3), and (4,4) modes, while generally, the convergence order reduces slightly for an increasing mass ratio. Our simulations allow us to validate waveform models, where we find generally good agreement between state-of-the-art models and our data, and to prove that scaling relations for higher modes currently employed for binary black hole waveform modeling also apply for the tidal contribution. Finally, we also test if the current nrtidal model used to describe tidal effects is a valid description for high-mass-ratio systems. We hope that our simulation results can be used to further improve and test waveform models in preparation for the next observing runs.

Black-hole perturbation theory with post-Newtonian theory: Towards hybrid waveforms for neutron-star binaries

We consider the motion of nonspinning, compact objects orbiting around a Kerr black hole with tidal couplings. The tide-induced quadrupole moment modifies both the orbital energy and outgoing fluxes, so that over the inspiral timescale there is an accumulative shift in the orbital and gravitational wave phase. Previous studies on compact object tidal effects have been carried out in the Post-Newtonian (PN) and Effective-One-Body (EOB) formalisms. In this work, within the black hole perturbation framework, we propose to characterize the tidal influence in the expansion of mass ratios, while higher-order PN corrections are naturally included. For the equatorial and circular orbit, we derive the leading order, frequency dependent tidal phase shift which agrees with the Post-Newtonian result at low frequencies but deviates at high frequencies. We also find that such phase shift has weak dependence ($\le 10\%$) on the spin of the primary black hole. Combining this black hole perturbation waveform with the Post-Newtonian waveform, we propose a frequency-domain, hybrid waveform that shows comparable accuracy as the EOB waveform in characterizing the tidal effects, as calibrated by numerical relativity simulations. Further improvement is expected as the next-leading order in mass ratio and the higher-PN tidal corrections are included. This hybrid approach is also applicable for generating binary black hole waveforms.

Extraction of binary black hole gravitational wave signals from detector data using deep learning

Accurate extractions of the detected gravitational wave (GW) signal waveforms are essential to validate a detection and to probe the astrophysics behind the sources producing the GWs. This however could be difficult in realistic scenarios where the signals detected by existing GW detectors could be contaminated with non-stationary and non-Gaussian noise. While the performance of existing waveform extraction methods are optimal, they are not fast enough for online application, which is important for multi-messenger astronomy. In this paper, we demonstrate that a deep learning architecture consisting of Convolutional Neural Network and bidirectional Long Short-Term Memory components can be used to extract binary black hole (BBH) GW waveforms from realistic noise in a few milli-seconds. We have tested our network systematically on injected GW signals, with component masses uniformly distributed in the range of 10 to 80 solar masses, on Gaussian noise and LIGO detector noise. We find that our model can extract GW waveforms with overlaps of more than 0.95 with pure Numerical Relativity templates for signals with signal-to-noise ratio (SNR) greater than six, and is also robust against interfering glitches. We then apply our model to all ten detected BBH events from the first (O1) and second (O2) observation runs, obtaining greater than 0.97 overlaps for all ten extracted BBH waveforms with the corresponding pure templates. We discuss the implication of our result and its future applications to GW localization and mass estimation.

Improved analysis of GW190412 with a precessing numerical relativity surrogate waveform model

The recent observation of GW190412, the first high-mass ratio binary black-hole (BBH) merger, by the LIGO-Virgo Collaboration (LVC) provides a unique opportunity to probe the impact of subdominant harmonics and precession effects encoded in a gravitational wave signal. We present refined estimates of source parameters for GW190412 using \texttt{NRSur7dq4}, a recently developed numerical relativity waveform surrogate model that includes all $\ell \leq 4$ spin-weighted spherical harmonic modes as well as the full physical effects of precession. We compare our results with two different variants of phenomenological precessing BBH waveform models, \texttt{IMRPhenomPv3HM} and \texttt{IMRPhenomXPHM}, as well as to the LVC results. Our results are broadly in agreement with \texttt{IMRPhenomXPHM} results and the reported LVC analysis compiled with the \texttt{SEOBNRv4PHM} waveform model, but in tension with \texttt{IMRPhenomPv3HM}. Using the \texttt{NRSur7dq4} model, we provide a tighter constraint on the mass-ratio ($0.26^{+0.08}_{-0.06}$) as compared to the LVC estimate of $0.28^{+0.13}_{-0.07}$ (both reported as median values withs 90\% credible intervals). We also constrain the binary to be more face-on, and find a broader posterior for the spin precession parameter. We further find that even though $\ell=4$ harmonic modes have negligible signal-to-noise ratio, omission of these modes will influence the estimated posterior distribution of several source parameters including chirp mass, effective inspiral spin, luminosity distance, and inclination. We also find that commonly used model approximations, such as neglecting the asymmetric modes (which are generically excited during precession), have negligible impact on parameter recovery for moderate SNR-events similar to GW190412.

Gravitational-wave surrogate models powered by artificial neural networks

Inferring the properties of black holes and neutron stars is a key science goal of gravitational-wave (GW) astronomy. To extract as much information as possible from GW observations we must develop methods to reduce the cost of Bayesian inference. In this paper, we use artificial neural networks (ANNs) and the parallelisation power of graphics processing units (GPUs) to improve the surrogate modelling method, which can produce accelerated versions of existing models. As a first application of our method, ANN-Sur, we build a time-domain surrogate model of the spin-aligned binary black hole (BBH) waveform model SEOBNRv4. We achieve median mismatches of 2e-5 and mismatches no worse than 2e-3. For a typical BBH waveform generated from 12 Hz with a total mass of $60 M_\odot$ the original SEOBNRv4 model takes 1812 ms. Existing bespoke code optimisations (SEOBNRv4opt) reduced this to 91.6 ms and the interpolation based, frequency-domain surrogate SEOBNRv4ROM can generate this waveform in 6.9 ms. Our ANN-Sur model, when run on a CPU takes 2.7 ms and just 0.4 ms when run on a GPU. ANN-Sur can also generate large batches of waveforms simultaneously. We find that batches of up to 10^4 waveforms can be evaluated on a GPU in just 163 ms, corresponding to a time per waveform of 0.016 ms. This method is a promising way to utilise the parallelisation power of GPUs to drastically increase the computational efficiency of Bayesian parameter estimation.

Gravitational waveforms of binary neutron star inspirals using post-Newtonian tidal splicing

The tidal deformations of neutron stars within an inspiraling compact binary alter the orbital dynamics, imprinting a signature on the gravitational wave signal. Modeling this signal could be done with numerical-relativity simulations, but these are too computationally expensive for many applications. Analytic post-Newtonian treatments are limited by unknown higher-order nontidal terms. This paper further builds upon the "tidal splicing" model in which post-Newtonian tidal terms are "spliced" onto numerical relativity simulations of black-hole binaries. We improve on previous treatments of tidal splicing by including spherical harmonic modes beyond the (2,2) mode, expanding the post-Newtonian expressions for tidal effects to 2.5 order, including dynamical tide corrections, and adding a partial treatment of the spin-tidal dynamics. Furthermore, instead of numerical relativity simulations, we use the spin-aligned binary black hole (BBH) surrogate model "NRHybSur3dq8" to provide the BBH waveforms that are input into the tidal slicing procedure. This allows us to construct spin-aligned, inspiraling TaylorT2 and TaylorT4 splicing waveform models that can be evaluated quickly. These models are tested against existing binary neutron star and black hole-neutron star simulations. We implement the TaylorT2 splicing model as an extension to "NRHybSur3dq8," creating a model that we call "NRHybSur3dq8Tidal."

Probing Einstein-dilaton Gauss-Bonnet gravity with the inspiral and ringdown of gravitational waves

Gravitational waves from extreme gravity events such as the coalescence of two black holes in a binary system fill our observable universe, bearing with them the underlying theory of gravity driving their process. One compelling alternative theory of gravity -- known as Einstein-dilaton Gauss-Bonnet gravity motivated by string theory -- describes the presence of an additional dilaton scalar field coupled directly to higher orders of the curvature, effectively describing a "fifth force" interaction and the emission of scalar dipole radiation between two scalarized black holes. Most previous studies focused on considering only the leading correction to the inspiral portion of the binary black hole waveforms. In our recent paper, we carried out inspiral-merger-ringdown consistency tests in this string-inspired gravity by including corrections to both the inspiral and ringdown portions, as well as those to the mass and spin of remnant black holes, valid to quadratic order in spin. We here extend the analysis by directly computing bounds on the theoretical coupling constant using the full inspiral-merger-ringdown waveform rather than treating the inspiral and merger-ringdown portions separately. We also consider the corrections valid to quartic order in spin to justify the validity of black hole's slow-rotation approximation. We find the quasinormal mode corrections to the waveform to be particularly important for high-mass events such as GW170729, in which the dilaton fields' small-coupling approximation fails without such effects included. We also show that future space-based and multiband gravitational-wave observations have the potential to go beyond existing bounds on the theory. The bounds presented here are comparable to those found in via the inspiral-merger-ringdown consistency tests.

Stability of rotating black holes in Einstein dilaton Gauss-Bonnet gravity

In order to perform model-dependent tests of general relativity with gravitational wave observations, we must have access to numerical relativity binary black hole waveforms in theories beyond general relativity (GR). In this study, we focus on order-reduced Einstein dilaton Gauss-Bonnet gravity (EDGB), a higher curvature beyond-GR theory with motivations in string theory. The stability of single, rotating black holes in EDGB is unknown, but is a necessary condition for being able to simulate binary black hole systems (especially the early-inspiral and late ringdown stages) in EDGB. We thus investigate the stability of rotating black holes in order-reduced EDGB. We evolve the leading-order EDGB scalar field and EDGB spacetime metric deformation on a rotating black hole background, for a variety of spins. We find that the EDGB metric deformation exhibits linear growth, but that this level of growth exponentially converges to zero with numerical resolution. Thus, we conclude that rotating black holes in EDGB are numerically stable to leading-order, thus satisfying our necessary condition for performing binary black hole simulations in EDGB.

Improving the NRTidal model for binary neutron star systems

Accurate and fast gravitational waveform (GW) models are essential to extract information about the properties of compact binary systems that generate GWs. Building on previous work, we present an extension of the NRTidal model for binary neutron star (BNS) waveforms. The upgrades are: (i) a new closed-form expression for the tidal contribution to the GW phase which includes further analytical knowledge and is calibrated to more accurate numerical relativity data than previously available; (ii) a tidal correction to the GW amplitude; (iii) an extension of the spin-sector incorporating equation-of-state-dependent finite size effects at quadrupolar and octupolar order; these appear in the spin-spin tail terms and cubic-in-spin terms, both at 3.5PN. We add the new description to the precessing binary black hole waveform model IMRPhenomPv2 to obtain a frequency-domain precessing binary neutron star model. In addition, we extend the SEOBNRv4_ROM and IMRPhenomD aligned-spin binary black hole waveform models with the improved tidal phase corrections. Focusing on the new IMRPhenomPv2_NRTidalv2 approximant, we test the model by comparing with numerical relativity waveforms as well as hybrid waveforms combining tidal effective-one-body and numerical relativity data. We also check consistency against a tidal effective-one-body model across large regions of the BNS parameter space.

Surrogate model of hybridized numerical relativity binary black hole waveforms

Numerical relativity (NR) simulations provide the most accurate binary black hole gravitational waveforms, but are prohibitively expensive for applications such as parameter estimation. Surrogate models of NR waveforms have been shown to be both fast and accurate. However, NR-based surrogate models are limited by the training waveforms' length, which is typically about 20 orbits before merger. We remedy this by hybridizing the NR waveforms using both post-Newtonian and effective one body waveforms for the early inspiral. We present NRHybSur3dq8, a surrogate model for hybridized nonprecessing numerical relativity waveforms, that is valid for the entire LIGO band (starting at $20~\text{Hz}$) for stellar mass binaries with total masses as low as $2.25\,M_{\odot}$. We include the $\ell \leq 4$ and $(5,5)$ spin-weighted spherical harmonic modes but not the $(4,1)$ or $(4,0)$ modes. This model has been trained against hybridized waveforms based on 104 NR waveforms with mass ratios $q\leq8$, and $|\chi_{1z}|,|\chi_{2z}| \leq 0.8$, where $\chi_{1z}$ ($\chi_{2z}$) is the spin of the heavier (lighter) BH in the direction of orbital angular momentum. The surrogate reproduces the hybrid waveforms accurately, with mismatches $\lesssim 3\times10^{-4}$ over the mass range $2.25M_{\odot} \leq M \leq 300 M_{\odot}$. At high masses ($M\gtrsim40M_{\odot}$), where the merger and ringdown are more prominent, we show roughly two orders of magnitude improvement over existing waveform models. We also show that the surrogate works well even when extrapolated outside its training parameter space range, including at spins as large as 0.998. Finally, we show that this model accurately reproduces the spheroidal-spherical mode mixing present in the NR ringdown signal.

Observational tests of the black hole area increase law

The black hole area theorem implies that when two black holes merge, the area of the final black hole should be greater than the sum of the areas of the two original black holes. We examine how this prediction can be tested with gravitational-wave observations of binary black holes. By separately fitting the early inspiral and final ringdown stages, we calculate the posterior distributions for the masses and spins of the two initial and the final black holes. This yields posterior distributions for the change in the area and thus a statistical test of the validity of the area increase law. We illustrate this method with a GW150914-like binary black hole waveform calculated using numerical relativity, and detector sensitivities representative of both the first observing run and the design configuration of Advanced LIGO. We obtain a $\sim74.6\%$ probability that the simulated signal is consistent with the area theorem with current sensitivity, improving to $\sim99.9\%$ when Advanced LIGO reaches design sensitivity. An important ingredient in our test is a method of estimating when the post-merger signal is well-fit by a damped sinusoid ringdown waveform.

Accuracy of binary black hole waveform models for aligned-spin binaries

Coalescing binary black holes are among the primary science targets for second generation ground-based gravitational wave (GW) detectors. Reliable GW models are central to detection of such systems and subsequent parameter estimation. This paper performs a comprehensive analysis of the accuracy of recent waveform models for binary black holes with aligned spins, utilizing a new set of $84$ high-accuracy numerical relativity simulations. Our analysis covers comparable mass binaries ($1\le m_1/m_2\le 3$), and samples independently both black hole spins up to dimensionless spin-magnitude of $0.9$ for equal-mass binaries and $0.85$ for unequal mass binaries. Furthermore, we focus on the high-mass regime (total mass $\gtrsim 50M_\odot$). The two most recent waveform models considered (PhenomD and SEOBNRv2) both perform very well for signal detection, losing less than 0.5\% of the recoverable signal-to-noise ratio $\rho$, except that SEOBNRv2's efficiency drops mildly for both black hole spins aligned with large magnitude. For parameter estimation, modeling inaccuracies of SEOBNRv2 are found to be smaller than systematic uncertainties for moderately strong GW events up to roughly $\rho\lesssim 15$. PhenomD's modeling errors are found to be smaller than SEOBNRv2's, and are generally irrelevant for $\rho\lesssim 20$. Both models' accuracy deteriorates with increased mass-ratio, and when at least one black hole spin is large and aligned. The SEOBNRv2 model shows a pronounced disagreement with the numerical relativity simulation in the merger phase, for unequal masses and simultaneously both black hole spins very large and aligned. Two older waveform models (PhenomC and SEOBNRv1) are found to be distinctly less accurate than the more recent PhenomD and SEOBNRv2 models. Finally, we quantify the bias expected from all GW models during parameter estimation for recovery of binary's masses and spins.

Merging ``real'' neutron stars for gravitational waves and electromagnetic counterparts

Having more-or-less succeeded in learning to stably evolve Einstein’s equations, numerical relativity is taking the leap to including the physics of neutron stars, which will enable us to construct truly realistic pictures of neutron star-neutron star and black hole-neutron star binary mergers. The neutron star profile affects late inspirals and mergers, leaving its imprint on gravitational waveforms and electromagnetic counterpart signals. Furthermore, we expect neutrino radiation, magnetic field, and nuclear recombination effects to drive the post-merger evolution. In this talk, I will describe some recent neutron star merger simulations combining nuclear physics and general relativity. The goal is to connect assumptions about the nuclear equation of state and the premerger binary to resulting binary trajectories, matter outflows, accretion disk dynamics, and neutrino energy output. These can then hopefully be connected to observable signals in the form of gravitational waves, kilonovae, and gamma ray bursts. It is found that an interesting variety of disks, outflows, and neutrino bursts are possible. Connections to observables are being attempted by tracking nuclear reactions in tidal ejecta and estimating energy injection to gamma ray bursts from neutrino annihilation and other sources. Meanwhile, non-vacuum inspiral simulations are finally approaching the length and accuracy needed for interesting comparisons with binary black hole waveforms and post-Newtonian predictions, these being steps toward a reliable characterization of the imprint of the nuclear equation of state on the gravitational waves.

Impact of higher-order modes on the detection of binary black hole coalescences

The inspiral and merger of black hole binary systems are a promising source of gravitational waves for the array of advanced interferometric ground-based gravitational-wave detectors currently being commissioned. The most effective method to look for a signal with a well understood waveform, such as the binary black hole signal, is matched filtering against a library of model waveforms. While current model waveforms are comprised solely of the dominant radiation mode, the quadrupole mode, it is known that there can be significant power in the higher-order modes for a broad range of physically relevant source parameters during the merger of the black holes. The binary black hole waveforms produced by numerical relativity are accurate through late inspiral, merger, and ringdown and include the higher-order modes. The available numerical-relativity waveforms span an increasing portion of the physical parameter space of unequal mass, spin and precession. In this paper, we investigate the degree to which gravitational-wave searches could be improved by the inclusion of higher modes in the model waveforms, for signals with a variety of initial mass ratios and generic spins. Our investigation studies how well the quadrupole-only waveform model matches the signal as a function of the inclination and orientation of the source and how the modes contribute to the distance reach into the Universe of Advanced LIGO for a fixed set of internal source parameters. The mismatch between signals and quadrupole-only waveforms can be large, dropping below 0.97 for up to 65% of the source sky for the nonprecessing cases we studied, and over a larger area in one precessing case. There is a corresponding 30% increase in detection volume that could be achieved by adding higher modes to the search; however, this is mitigated by the fact that the mismatch is largest for signals which radiate the least energy and to which the search is therefore least sensitive. Likewise, the mismatch is largest in the directions from the source along which the least energy is radiated.

Binary black hole waveform extraction at null infinity

In this paper, we present a work in progress toward an efficient and economical computational module which interfaces between Cauchy and characteristic evolution codes. Our goal is to provide a standardized waveform extraction tool for the numerical relativity community which will allow CCE to be readily applied to a generic Cauchy code. The tool provides a means of unambiguous comparison between the waveforms generated by evolution codes based upon different formulations of the Einstein equations and different numerical approximation.

A burst search for gravitational waves from binary black holes

Compact binary coalescence (CBC) is one of the most promising sources of gravitational waves. These sources are usually searched for with matched filters which require accurate calculation of the GW waveforms and generation of large template banks. We present a complementary search technique based on algorithms used in un-modeled searches. Initially designed for detection of un-modeled bursts, which can span a very large set of waveform morphologies, the search algorithm presented here is constrained for targeted detection of the smaller subset of CBC signals. The constraint is based on the assumption of elliptical polarization for signals received at the detector. We expect that the algorithm is sensitive to CBC signals in a wide range of masses, mass ratios and spin parameters. In preparation for the analysis of data from the fifth LIGO-Virgo science run (S5), we performed preliminary studies of the algorithm on test data. We present the sensitivity of the search to different types of simulated binary black hole waveforms. Also, we discuss how to extend the results of the test run into a search over all of the current LIGO-Virgo data set.

General relativistic simulations of black-hole–neutron-star mergers: Effects of black-hole spin

Black-hole--neutron-star (BHNS) binary mergers are candidate engines for generating both short-hard gamma-ray bursts and detectable gravitational waves. Using our most recent conformal thin-sandwich BHNS initial data and our fully general relativistic hydrodynamics code, which is now adaptive mesh refinement capable, we are able to efficiently and accurately simulate these binaries from large separations through inspiral, merger, and ringdown. We evolve the metric using the Baumgarte-Shapiro-Shibata-Nakamura formulation with the standard moving puncture gauge conditions, and handle the hydrodynamics with a high-resolution shock-capturing scheme. We explore the effects of BH spin (aligned and antialigned with the orbital angular momentum) by evolving three sets of initial data with BH:NS mass ratio $q=3$: the data sets are nearly identical, except the BH spin is varied between $a/{M}_{\mathrm{BH}}=\ensuremath{-}0.5$ (antialigned), 0.0, and 0.75. The number of orbits before merger increases with $a/{M}_{\mathrm{BH}}$, as expected. We also study the nonspinning BH case in more detail, varying $q$ between 1, 3, and 5. We calculate gravitational waveforms for the cases we simulate and compare them to binary black-hole waveforms. Only a small disk ($<0.01{M}_{\ensuremath{\bigodot}}$) forms for the antialigned spin case ($a/{M}_{\mathrm{BH}}=\ensuremath{-}0.5$) and for the most extreme-mass-ratio case ($q=5$). By contrast, a massive (${M}_{\mathrm{disk}}\ensuremath{\approx}0.2{M}_{\ensuremath{\bigodot}}$) hot disk forms in the rapidly spinning ($a/{M}_{\mathrm{BH}}=0.75$) aligned BH case. Such a disk could drive a short-hard gamma-ray burst, possibly by, e.g., producing a copious flux of neutrino-antineutrino pairs.

Gravitational-wave data analysis using binary black-hole waveforms

While the inspiral and ring-down stages of the binary black-hole coalescence are well modelled by analytical approximation methods in general relativity, the recent progress in numerical relativity has enabled us to compute accurate waveforms from the merger stage also. This has an important impact on the search for gravitational waves from binary black holes. ‘Complete’ binary black-hole waveforms can now be produced by matching post-Newtonian waveforms with those computed by numerical relativity, which can be parametrized to produce analytical waveform templates. The ‘complete’ waveforms can also be used to estimate the efficiency of different search methods aiming to detect signals from black-hole coalescences. This paper summarizes some recent efforts in this direction.