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Binary black-hole systems are expected to be important sources of gravitational waves for upcoming gravitational-wave detectors. If the spins are not colinear with each other or with the orbital angular momentum, these systems exhibit complicated precession dynamics that are imprinted on the gravitational waveform. We develop a new procedure to match the precession dynamics computed by post-Newtonian (PN) theory to those of numerical binary black-hole simulations in full general relativity. For numerical relativity (NR) simulations lasting approximately two precession cycles, we find that the PN and NR predictions for the directions of the orbital angular momentum and the spins agree to better than ~1° with NR during the inspiral, increasing to 5° near merger. Nutation of the orbital plane on the orbital time scale agrees well between NR and PN, whereas nutation of the spin direction shows qualitatively different behavior in PN and NR. We also examine how the PN equations for precession and orbital-phase evolution converge with PN order, and we quantify the impact of various choices for handling partially known PN terms. [ABSTRACT FROM AUTHOR]

We extract gravitational waveforms from numerical simulations of black hole binaries computed using the Spectral Einstein Code. We compare two extraction methods: direct construction of the Newman-Penrose (NP) scalar ψ4 at a finite distance from the source and Cauchy-characteristic extraction (CCE). The direct NP approach is simpler than CCE, but NP waveforms can be contaminated by near-zone effects--unless the waves are extracted at several distances from the source and extrapolated to infinity. Even then, the resulting waveforms can in principle be contaminated by gauge effects. In contrast, CCE directly provides, by construction, gauge-invariant waveforms at future null infinity. We verify the gauge invariance of CCE by running the same physical simulation using two different gauge conditions. We find that these two gauge conditions produce the same CCE waveforms but show differences in extrapolated-ψ4 waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-ψ4 and CCE waveforms. In some cases, we find that NP waveforms extrapolated to infinity agree with the corresponding CCE waveforms to within the estimated error bars. However, we find that in other cases extrapolated and CCE waveforms disagree, most notably for m = 0 "memory" modes. [ABSTRACT FROM AUTHOR]

A general method is presented for estimating the uncertainty in hybrid models of gravitational waveforms from binary black-hole systems with arbitrary physical parameters, and thence the highest allowable initial orbital frequency for a numerical-relativity simulation such that the combined analytical and numerical waveform meets some minimum desired accuracy. The key strength of this estimate is that no prior numerical simulation in the relevant region of parameter space is needed, which means that these techniques can be used to direct future work. The method is demonstrated for a selection of extreme physical parameters. It is shown that optimal initial orbital frequencies depend roughly linearly on the mass of the binary, and therefore useful accuracy criteria must depend explicitly on the mass. The results indicate that accurate estimation of the parameters of stellar-mass black-hole binaries in Advanced LIGO data or calibration of waveforms for detection will require much longer numerical simulations than are currently available, or more accurate post-Newtonian approximations--or both--especially for comparable-mass systems with high spin. [ABSTRACT FROM AUTHOR]

We present a detailed study of the center-of-mass (c.m.) motion seen in simulations produced by the Simulating eXtreme Spacetimes (SXS) collaboration. We investigate potential physical sources for the large c.m. motion in binary black hole simulations and find that a significant fraction of the c.m. motion cannot be explained physically, thus concluding that it is largely a gauge effect. These large c.m. displacements cause mode mixing in the gravitational waveform, most easily recognized as amplitude oscillations caused by the dominant (2,±2) modes mixing into subdominant modes. This mixing does not diminish with increasing distance from the source; it is present even in asymptotic waveforms, regardless of the method of data extraction. We describe the current c.m.-correction method used by the SXS collaboration, which is based on counteracting the motion of the c.m. as measured by the trajectories of the apparent horizons in the simulations, and investigate potential methods to improve that correction to the waveform. We also present a complementary method for computing an optimal c.m. correction or evaluating any other c.m. transformation based solely on the asymptotic waveform data. [ABSTRACT FROM AUTHOR]

The availability of accurate numerical waveforms is an important requirement for the creation and calibration of reliable waveform models for gravitational wave astrophysics. For black hole-neutron star binaries (BHNS), very few accurate waveforms are however publicly available. Most recent models are calibrated to a large number of older simulations with good parameter space coverage for low-spin nonprecessing binaries but limited accuracy, and a much smaller number of longer, more recent simulations limited to nonspinning black holes. In this paper, we present long, accurate numerical waveforms for three new systems that include rapidly spinning black holes, and one precessing configuration. We study in detail the accuracy of the simulations, and in particular perform for the first time in the context of BHNS binaries a detailed comparison of waveform extrapolation methods to the results of Cauchy characteristic extraction. The new waveforms have < 0.1     rad phase errors during inspiral, rising to ∼ (0.2-0.4)     rad errors at merger, and ≲1 % error in their amplitude. We compute the faithfulness of recent analytical models to these numerical results for the late inspiral and merger phases covered by the numerical simulations, and find that models specifically designed for BHNS binaries perform well (faithfulness F>0.99) for binaries seen face on. For edge-on observations, particularly for precessing systems, disagreements between models and simulations increase, and models that include precession and/or higher-order modes start to perform better than BHNS models that currently lack these features. [ABSTRACT FROM AUTHOR]

Gravitational waves from coalescing stellar-mass black hole binaries (BBHs) are expected to be detected by the Advanced Laser Interferometer gravitational-wave observatory and Advanced Virgo. Detection searches operate by matched filtering the detector data using a bank of waveform templates. Traditionally, template banks for BBHs are constructed from intermediary analytical waveform models which are calibrated against numerical relativity simulations and which can be evaluated for any choice of BBH parameters. This paper explores an alternative to the traditional approach, namely, the construction of template banks directly from numerical BBH simulations. Using nonspinning BBH systems as an example, we demonstrate which regions of the mass-parameter plane can be covered with existing numerical BBH waveforms. We estimate the required number and required length of BBH simulations to cover the entire nonspinning BBH parameter plane up to mass ratio 10, thus illustrating that our approach can be used to guide parameter placement of future numerical simulations. We derive error bounds which are independent of analytical waveform models; therefore, our formalism can be used to independently test the accuracy of such waveform models. The resulting template banks are suitable for advanced LIGO searches. [ABSTRACT FROM AUTHOR]

Initial data for numerical evolutions of binary-black holes have been dominated by "conformally flat" (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated "conformally curved" initial data (i.e., initial data in which the background metric is not explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using superposed Kerr-Schild initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within δɸ≲10-2 radians and the amplitudes agree to within δA/A ≲ 5 X 10-3, which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in 105. [ABSTRACT FROM AUTHOR]

Understanding the Bondi-Metzner-Sachs (BMS) frame of the gravitational waves produced by numerical relativity is crucial for ensuring that analyses on such waveforms are performed properly. It is also important that models are built from waveforms in the same BMS frame. Up until now, however, the BMS frame of numerical waveforms has not been thoroughly examined, largely because the necessary tools have not existed. In this paper, we show how to analyze and map to a suitable BMS frame for numerical waveforms calculated with the Spectral Einstein Code (SpEC). However, the methods and tools that we present are general and can be applied to any numerical waveforms. We present an extensive study of 13 binary black hole systems that broadly span parameter space. From these simulations, we extract the strain and also the Weyl scalars using both SpECTRE's Cauchy-characteristic extraction module and also the standard extrapolation procedure with a displacement memory correction applied during postprocessing. First, we show that the current center-of-mass correction used to map these waveforms to the center-of-mass frame is not as effective as previously thought. Consequently, we also develop an improved correction that utilizes asymptotic Poincaré charges instead of a Newtonian center-of-mass trajectory. Next, we map our waveforms to the post-Newtonian (PN) BMS frame using a PN strain waveform. This helps us find the unique BMS transformation that minimizes the L2 norm of the difference between the numerical and PN strain waveforms during the early inspiral phase. We find that once the waveforms are mapped to the PN BMS frame, they can be hybridized with a PN strain waveform much more effectively than if one used any of the previous alignment schemes, which only utilize the Poincaré transformations. [ABSTRACT FROM AUTHOR]

We present a new study of remnant black hole properties from 13 binary black hole systems, numerically evolved using the Spectral Einstein Code. The mass, spin, and recoil velocity of each remnant were determined quasilocally from apparent horizon data and asymptotically from Bondi data (h,ψ4,ψ3,ψ2,ψ1) computed at future null infinity using SpECTRE's Cauchy characteristic evolution. We compare these independent measurements of the remnant properties in the bulk and on the boundary of the spacetime, giving insight into how well asymptotic data are able to reproduce local properties of the remnant black hole in numerical relativity. We also discuss the theoretical framework for connecting horizon quantities to asymptotic quantities and how it relates to our results. This study recommends a simple improvement to the recoil velocities reported in the Simulating eXtreme Spacetimes waveform catalog, provides an improvement to future surrogate remnant models, and offers new analysis techniques for evaluating the physical accuracy of numerical simulations. [ABSTRACT FROM AUTHOR]

Accurate models of gravitational waves from merging binary black holes are crucial for detectors to measure events and extract new science. One important feature that is currently missing from the Simulating eXtreme Spacetimes (SXS) Collaboration's catalog of waveforms for merging black holes, and other waveform catalogs, is the gravitational memory effect: a persistent, physical change to spacetime that is induced by the passage of transient radiation. We find, however, that by exploiting the Bondi-van der Burg-Metzner-Sachs (BMS) balance laws, which come from the extended BMS transformations, we can correct the strain waveforms in the SXS catalog to include the missing displacement memory. Our results show that these corrected waveforms satisfy the BMS balance laws to a much higher degree of accuracy. Furthermore, we find that these corrected strain waveforms coincide especially well with the waveforms obtained from Cauchy-characteristic extraction (CCE) that already exhibit memory effects. These corrected strain waveforms also evade the transient junk effects that are currently present in CCE waveforms. Last, we make our code for computing these contributions to the BMS balance laws and memory publicly available as a part of the python package sxs, thus enabling anyone to evaluate the expected memory effects and violation of the BMS balance laws. [ABSTRACT FROM AUTHOR]

We present the first numerical relativity waveforms for binary black hole mergers produced using spectral methods that show both the displacement and the spin memory effects. Explicitly, we use the SXS (Simulating eXtreme Spacetimes) Collaboration's spec code to run a Cauchy evolution of a binary black hole merger and then extract the gravitational wave strain using spectre's version of a Cauchy-characteristic extraction. We find that we can accurately resolve the strain's traditional m=0 memory modes and some of the m≠0 oscillatory memory modes that have previously only been theorized. We also perform a separate calculation of the memory using equations for the Bondi-Metzner-Sachs charges as well as the energy and angular momentum fluxes at asymptotic infinity. Our new calculation uses only the gravitational wave strain and two of the Weyl scalars at infinity. Also, this computation shows that the memory modes can be understood as a combination of a memory signal throughout the binary's inspiral and merger phases, and a quasinormal mode signal near the ringdown phase. Additionally, we find that the magnetic memory, up to numerical error, is indeed zero as previously conjectured. Last, we find that signal-to-noise ratios of memory for LIGO, the Einstein Telescope, and the Laser Interferometer Space Antenna with these new waveforms and new memory calculation are larger than previous expectations based on post-Newtonian or minimal waveform models. [ABSTRACT FROM AUTHOR]

As gravitational-wave detectors become more sensitive and broaden their frequency bandwidth, we will access a greater variety of signals emitted by compact binary systems, shedding light on their astrophysical origin and environment. A key physical effect that can distinguish among different formation scenarios is the misalignment of the spins with the orbital angular momentum, causing the spins and the binary's orbital plane to precess. To accurately model such precessing signals, especially when masses and spins vary in the wide astrophysical range, it is crucial to include multipoles beyond the dominant quadrupole. Here, we develop the first multipolar precessing waveform model in the effective-one-body (EOB) formalism for the entire coalescence stage (i.e., inspiral, merger and ringdown) of binary black holes: SEOBNRv4PHM. In the nonprecessing limit, the model reduces to SEOBNRv4HM, which was calibrated to numerical-relativity (NR) simulations, and waveforms from black-hole perturbation theory. We validate SEOBNRv4PHM by comparing it to the public catalog of 1405 precessing NR waveforms of the Simulating eXtreme Spacetimes (SXS) collaboration, and also to 118 SXS precessing NR waveforms, produced as part of this project, which span mass ratios 1-4 and (dimensionless) black-hole's spins up to 0.9. We stress that SEOBNRv4PHM is not calibrated to NR simulations in the precessing sector. We compute the unfaithfulness against the 1523 SXS precessing NR waveforms, and find that, for 94% (57%) of the cases, the maximum value, in the total mass range 20-200 M⊙, is below 3% (1%). Those numbers change to 83% (20%) when using the inspiral-merger-ringdown, multipolar, precessing phenomenological model IMRPhenomPv3HM. We investigate the impact of such unfaithfulness values with two Bayesian, parameter-estimation studies on synthetic signals. We also compute the unfaithfulness between those waveform models as a function of the mass and spin parameters to identify in which part of the parameter space they differ the most. We validate them also against the multipolar, precessing NR surrogate model NRSur7dq4, and find that the SEOBNRv4PHM model outperforms IMRPhenomPv3HM. [ABSTRACT FROM AUTHOR]

After the discovery of gravitational waves from binary black holes (BBHs) and binary neutron stars (BNSs) with the LIGO and Virgo detectors, neutron-star black holes (NSBHs) are the natural next class of binary systems to be observed. In this work, we develop a waveform model for aligned-spin NSBHs combining a BBH baseline waveform (available in the effective-one-body approach) with a phenomenological description of tidal effects (extracted from numerical-relativity simulations) and correcting the amplitude during the late inspiral, merger and ringdown to account for the NS tidal disruption. In particular, we calibrate the amplitude corrections using NSBH waveforms obtained with the numerical-relativity spectral Einstein code (spec) and the sacra code. The model was calibrated using simulations with NS masses in the range 1.2-1.4 M⊙, tidal deformabilities up to 4200 (for a 1.2 M⊙ NS), and dimensionless BH spin magnitude up to 0.9. Based on the simulations used and on checking that sensible waveforms are produced, we recommend our model to be employed with a NS mass in the range 1-3 M⊙, tidal deformability 0-5000, and (dimensionless) BH spin magnitude up to 0.9. We also validate our model against two new, highly accurate NSBH waveforms with BH spin 0.9 and mass ratios 3 and 4, characterized by tidal disruption, produced with SpEC, and find very good agreement. Furthermore, we compute the unfaithfulness between waveforms from NSBH, BBH, and BNS systems, finding that it will be challenging for the Advanced LIGO-Virgo detector network at design sensitivity to distinguish different source classes. We perform a Bayesian parameter-estimation analysis on a synthetic numerical-relativity signal in zero noise to study parameter biases. Finally, we reanalyze GW170817, with the hypothesis that it is a NSBH. We do not find evidence to distinguish the BNS and NSBH hypotheses; however, the posterior for the mass ratio is shifted to less equal masses under the NSBH hypothesis. [ABSTRACT FROM AUTHOR]

Gravitational-wave (GW) detectors have begun to observe coalescences of heavy black hole binaries (M≳50 M⊙) at a consistent pace for the past few years. Accurate models of gravitational waveforms are essential for unbiased and precise estimation of source parameters, such as masses and spins of component black holes. Recently developed surrogate models based on high-accuracy numerical relativity (NR) simulations provide ideal models for constraining physical parameters describing these heavy black hole merger events. In this paper, we first demonstrate the viability of these multi-modal surrogate models as reliable parameter estimation tools. We show that within a fully Bayesian framework, NR surrogates can help extract additional information from GW observations that is inaccessible to traditional models. We demonstrate this by analyzing a set of synthetic signals with NR surrogate templates and comparing against contemporary approximate models. We then consider the case of two of the earliest binary black holes detected by the LIGO observatories, GW150914 and GW170104. We reanalyze their data with the generically precessing NR-based surrogate model and freely provide the resulting posterior samples as supplemental material. We find that our refined analysis is able to extract information from sub-dominant GW harmonics in data, and therefore better resolve the degeneracy in measuring source luminosity distance and orbital inclination for both events. Our analysis estimates the sources of both events to be 20%-25% further away than was previously estimated. Our analysis also constrains their orbital orientations more tightly around face-on or face-off configurations than before. Additionally, for GW150914 we constrain the effective inspiral spin χeff more tightly around zero. This work is one of the first to unambiguously extract sub-dominant GW mode information from real events. It is also a first step toward eliminating the approximations used in semi-analytic waveform models from GW parameter estimation. It strongly motivates that NR surrogates be extended to cover more of the binary black hole parameter space. [ABSTRACT FROM AUTHOR]

A generic, noneccentric binary black hole (BBH) system emits gravitational waves (GWs) that are completely described by seven intrinsic parameters: the black hole spin vectors and the ratio of their masses. Simulating a BBH coalescence by solving Einstein's equations numerically is computationally expensive, requiring days to months of computing resources for a single set of parameter values. Since theoretical predictions of the GWs are often needed for many different source parameters, a fast and accurate model is essential. We present the first surrogate model for GWs from the coalescence of BBHs including all seven dimensions of the intrinsic noneccentric parameter space. The surrogate model, which we call NRSur7dq2, is built from the results of 744 numerical relativity simulations. NRSur7dq2 covers spin magnitudes up to 0.8 and mass ratios up to 2, includes all ℓ ≤ 4 modes, begins about 20 orbits before merger, and can be evaluated in ~ 50 ms. We find the largest NRSur7dq2 errors to be comparable to the largest errors in the numerical relativity simulations, and more than an order of magnitude smaller than the errors of other waveform models. Our model, and more broadly the methods developed here, will enable studies that were not previously possible when using highly accurate waveforms, such as parameter inference and tests of general relativity with GW observations. [ABSTRACT FROM AUTHOR]

Initial data for numerical evolutions of binary-black holes have been dominated by “conformally flat” (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated “conformally curved” initial data (i.e., initial data in which the background metric is not explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using superposed Kerr-Schild initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within δϕ≲10-2 radians and the amplitudes agree to within δA/A≲5×10-3, which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in 105. [ABSTRACT FROM AUTHOR]