Testing general relativity in the nonlinear, dynamical, strong-field regime of gravity is one of the major goals of gravitational wave astrophysics. Performing precision tests of general relativity ...(GR) requires numerical inspiral, merger, and ringdown waveforms for binary black hole (BBH) systems in theories beyond GR. Currently, GR and scalar-tensor gravity are the only theories amenable to numerical simulations. In this article, we present a well-posed perturbation scheme for numerically integrating beyond-GR theories that have a continuous limit to GR. We demonstrate this scheme by simulating BBH mergers in dynamical Chern-Simons gravity (dCS), to linear order in the perturbation parameter. We present mode waveforms and energy fluxes of the dCS pseudoscalar field from our numerical simulations. We find good agreement with analytic predictions at early times, including the absence of pseudoscalar dipole radiation. We discover new phenomenology only accessible through numerics: a burst of dipole radiation during merger. We also quantify the self-consistency of the perturbation scheme. Finally, we estimate bounds that GR-consistent LIGO detections could place on the new dCS length scale, approximately ℓ≲O(10) km.
We present the first surrogate model for gravitational waveforms from the coalescence of precessing binary black holes. We call this surrogate model NRSur4d2s. Our methodology significantly extends ...recently introduced reduced-order and surrogate modeling techniques, and is capable of directly modeling numerical relativity waveforms without introducing phenomenological assumptions or approximations to general relativity. Motivated by GW150914, LIGO’s first detection of gravitational waves from merging black holes, the model is built from a set of 276 numerical relativity (NR) simulations with mass ratios q≤2, dimensionless spin magnitudes up to 0.8, and the restriction that the initial spin of the smaller black hole lies along the axis of orbital angular momentum. It produces waveforms which begin ∼30 gravitational wave cycles before merger and continue through ringdown, and which contain the effects of precession as well as all ℓ∈{2,3} spin-weighted spherical-harmonic modes. We perform cross-validation studies to compare the model to NR waveforms not used to build the model and find a better agreement within the parameter range of the model than other, state-of-the-art precessing waveform models, with typical mismatches of 10−3. We also construct a frequency domain surrogate model (called NRSur4d2s_FDROM) which can be evaluated in 50 ms and is suitable for performing parameter estimation studies on gravitational wave detections similar to GW150914.
Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we ...construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from nonspinning binary black hole coalescences with mass ratios in 1, 10 and durations corresponding to about 15 orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms not used for the surrogate's training with errors nearly as small as the numerical error of the NR code. Our model includes all spherical-harmonic _{-2}Y_{ℓm} waveform modes resolved by the NR code up to ℓ=8. We compare our surrogate model to effective one body waveforms from 50M_{⊙} to 300M_{⊙} for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases).
This Letter presents a publicly available catalog of 174 numerical binary black hole simulations following up to 35 orbits. The catalog includes 91 precessing binaries, mass ratios up to 8∶1, orbital ...eccentricities from a few percent to 10(-5), black hole spins up to 98% of the theoretical maximum, and radiated energies up to 11.1% of the initial mass. We establish remarkably good agreement with post-Newtonian precession of orbital and spin directions for two new precessing simulations, and we discuss other applications of this catalog. Formidable challenges remain: e.g., precession complicates the connection of numerical and approximate analytical waveforms, and vast regions of the parameter space remain unexplored.
We improve the accuracy of the effective-one-body (EOB) waveforms that were employed during the first observing run of Advanced LIGO for binaries of spinning, nonprecessing black holes by calibrating ...them to a set of 141 numerical-relativity (NR) waveforms. The NR simulations expand the domain of calibration toward larger mass ratios and spins, as compared to the previous EOBNR model. Merger-ringdown waveforms computed in black-hole perturbation theory for Kerr spins close to extremal provide additional inputs to the calibration. For the inspiral-plunge phase, we use a Markov-chain Monte Carlo algorithm to efficiently explore the calibration space. For the merger-ringdown phase, we fit the NR signals with phenomenological formulae. After extrapolation of the calibrated model to arbitrary mass ratios and spins, the (dominant-mode) EOBNR waveforms have faithfulness-at design Advanced-LIGO sensitivity-above 99% against all the NR waveforms, including 16 additional waveforms used for validation, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling for these binary configurations. We find that future NR simulations at mass ratios ≳4 and double spin ≳0.8 will be crucial to resolving discrepancies between different ways of extrapolating waveform models. We also find that some of the NR simulations that already exist in such region of parameter space are too short to constrain the low-frequency portion of the models. Finally, we build a reduced-order version of the EOBNR model to speed up waveform generation by orders of magnitude, thus enabling intensive data-analysis applications during the upcoming observation runs of Advanced LIGO.
We present a new set of 95 numerical relativity simulations of non-precessing binary black holes (BBHs). The simulations sample comprehensively both black-hole spins up to spin magnitude of 0.9, and ...cover mass ratios 1-3. The simulations cover on average 24 inspiral orbits, plus merger and ringdown, with low initial orbital eccentricities e < 10 − 4 . A subset of the simulations extends the coverage of non-spinning BBHs up to mass ratio q = 10. Gravitational waveforms at asymptotic infinity are computed with two independent techniques: extrapolation and Cauchy characteristic extraction. An error analysis based on noise-weighted inner products is performed. We find that numerical truncation error, error due to gravitational wave extraction, and errors due to the Fourier transformation of signals with finite length of the numerical waveforms are of similar magnitude, with gravitational wave extraction errors dominating at noise-weighted mismatches of ∼ 3 × 10 − 4 . This set of waveforms will serve to validate and improve aligned-spin waveform models for gravitational wave science.
Coalescing binary black holes are among the primary science targets for second generation ground-based gravitational wave detectors. Reliable gravitational waveform 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, and samples independently both black hole spins up to a dimensionless spin magnitude of 0.9 for equal-mass binaries and 0.85 for unequal mass binaries. 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 four waveform models during parameter estimation for several recovered binary parameters: chirp mass, mass ratio, and effective spin.
We present a time domain waveform model that describes the inspiral, merger and ringdown of compact binary systems whose components are nonspinning, and which evolve on orbits with low to moderate ...eccentricity. The inspiral evolution is described using third-order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to nonlinear memory. This framework reduces to the post-Newtonian approximant TaylorT4 at third post-Newtonian order in the zero-eccentricity limit. To improve phase accuracy, we also incorporate higher-order post-Newtonian corrections for the energy flux of quasicircular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced prescription for the inspiral evolution is combined with a fully analytical prescription for the merger-ringdown evolution constructed using a catalog of numerical relativity simulations. We show that this inspiral-merger-ringdown waveform model reproduces the effective-one-body model of Ref. Y. Pan et al., Phys. Rev. D 89, 061501 (2014). for quasicircular black hole binaries with mass ratios between 1 to 15 in the zero-eccentricity limit over a wide range of the parameter space under consideration. Using a set of eccentric numerical relativity simulations, not used during calibration, we show that our new eccentric model reproduces the true features of eccentric compact binary coalescence throughout merger. We use this model to show that the gravitational-wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasicircular, spin-aligned waveforms if the eccentricity e0 of these systems when they enter the aLIGO band at a gravitational-wave frequency of 14 Hz satisfies e0GW150914≤0.15 and e0GW151226≤0.1. We also find that varying the spin combinations of the quasicircular, spin-aligned template waveforms does not improve the recovery of nonspinning, eccentric signals when e0≥0.1. This suggests that these two signal manifolds are predominantly orthogonal.
Astrophysical black holes could be nearly extremal (that is, rotating nearly as fast as possible); therefore, nearly extremal black holes could be among the binaries that current and future ...gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass m and spin S exceeding the Bowen-York limit of . We present improved methods that enable us to simulate merging, nearly extremal black holes (i.e., black holes with ) more robustly and more efficiently. We use these methods to simulate an unequal-mass, precessing binary black hole (BBH) coalescence, where the larger black hole has . We also use these methods to simulate a non-precessing BBH coalescence, where both black holes have , nearly reaching the Novikov-Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; we compare the evolution of the black hole masses and spins with analytic predictions; and we explore the effect of increasing spin magnitude on the orbital dynamics (the so-called 'orbital hangup' effect).
In fall of 2015, the two LIGO detectors measured the gravitational wave signal GW150914, which originated from a pair of merging black holes (Abbott et al Virgo, LIGO Scientific 2016 Phys. Rev. Lett. ...116 061102). In the final 0.2 s (about 8 gravitational-wave cycles) before the amplitude reached its maximum, the observed signal swept up in amplitude and frequency, from 35 Hz to 150 Hz. The theoretical gravitational-wave signal for merging black holes, as predicted by general relativity, can be computed only by full numerical relativity, because analytic approximations fail near the time of merger. Moreover, the nearly-equal masses, moderate spins, and small number of orbits of GW150914 are especially straightforward and efficient to simulate with modern numerical-relativity codes. In this paper, we report the modeling of GW150914 with numerical-relativity simulations, using black-hole masses and spins consistent with those inferred from LIGO's measurement (Abbott et al LIGO Scientific Collaboration, Virgo Collaboration 2016 Phys. Rev. Lett. 116 241102). In particular, we employ two independent numerical-relativity codes that use completely different analytical and numerical methods to model the same merging black holes and to compute the emitted gravitational waveform; we find excellent agreement between the waveforms produced by the two independent codes. These results demonstrate the validity, impact, and potential of current and future studies using rapid-response, targeted numerical-relativity simulations for better understanding gravitational-wave observations.
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