arXiv subjects

Michael Boyle

Publications and source records attributed to Michael Boyle.

At least 73 records · Page 4Linked to original sources

arXiv2018

Gravitational waveforms from SpEC simulations : neutron star-neutron star and low-mass black hole-neutron star binaries

Gravitational waveforms from numerical simulations are a critical tool to test and analytically calibrate the waveform models used to study the properties of merging compact objects. In this paper, we present a series of high-accuracy waveforms produced with the SpEC code for systems involving at least one neutron star. We provide for the first time waveforms with sub-radian accuracy over more than twenty cycles for low-mass black hole-neutron star binaries, including binaries with non-spinning objects, and binaries with rapidly spinning neutron stars that maximize the impact on the gravitational wave signal of the near-resonant growth of the fundamental excitation mode of the neutron star (f-mode). We also provide for the first time with SpEC a high-accuracy neutron star-neutron star waveform. These waveforms are made publicly available as part of the SxS catalogue. We compare our results to analytical waveform models currently implemented in data analysis pipelines. For most simulations, the models lie outside of the predicted numerical errors in the last few orbits before merger, but do not show systematic deviations from the numerical results: comparing different models appears to provide reasonable estimates of the modeling errors. The sole exception is the equal-mass simulation using a rapidly counter-rotating neutron star to maximize the impact of the excitation of the f-mode, for which all models perform poorly. This is however expected, as even the single model that takes f-mode excitation into account ignores the significant impact of the neutron star spin on the f-mode excitation frequency.

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arXiv2018

A Numerical Relativity Waveform Surrogate Model for Generically Precessing Binary Black Hole Mergers

A generic, non-eccentric binary black hole (BBH) system emits gravitational waves (GWs) that are completely described by 7 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 $7$ dimensions of the intrinsic non-eccentric 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 $\ell \leq 4$ modes, begins about $20$ orbits before merger, and can be evaluated in $\sim~50\,\mathrm{ms}$. 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 would otherwise require millions of numerical relativity waveforms, such as parameter inference and tests of general relativity with GW observations.

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arXiv2018

Detection and characterization of spin-orbit resonances in the advanced gravitational wave detectors era

In this paper, we test the performance of templates in detection and characterization of Spin-orbit resonant (SOR) binaries. We use precessing SEOBNRv3 waveforms as well as {\it four} numerical relativity (NR) waveforms to model GWs from SOR binaries and filter them through IMRPhenomD, SEOBNRv4 (non-precessing) and IMRPhenomPv2 (precessing) approximants. We find that IMRPhenomD and SEOBNRv4 recover only $\sim70\%$ of injections with fitting factor (FF) higher than 0.97 (or 90\% of injections with ${\rm FF} >0.9$).However, using the sky-maxed statistic, IMRPhenomPv2 performs magnificently better than their non-precessing counterparts with recovering $99\%$ of the injections with FFs higher than 0.97. Interestingly, injections with $Δϕ= 180^{\circ}$ have higher FFs ($Δϕ$ is the angle between the components of the black hole spins in the plane orthogonal to the orbital angular momentum) as compared to their $Δϕ=0^{\circ}$ and generic counterparts. This implies that we will have a slight observation bias towards $Δϕ=180^{\circ}$ SORs while using non-precessing templates for searches. All template approximants are able to recover most of the injected NR waveforms with FFs $>0.95$. For all the injections including NR, the error in estimating chirp mass remains below $<10\%$ with minimum error for $Δϕ= 180^{\circ}$ resonant binaries. The symmetric mass ratio can be estimated with errors below $15\%$. The effective spin parameter $χ_{\rm eff}$ is measured with maximum absolute error of 0.13. The in-plane spin parameter $χ_p$ is mostly underestimated indicating that a precessing signal will be recovered as a relatively less precessing signal. Based on our findings, we conclude that we not only need improvements in waveform models towards precession and non-quadrupole modes but also better search strategies for precessing GW signals.

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arXiv2018

Measuring the properties of nearly extremal black holes with gravitational waves

Characterizing the properties of black holes is one of the most important science objectives for gravitational-wave observations. Astrophysical evidence suggests that black holes that are nearly extremal (i.e. spins near the theoretical upper limit) might exist and thus might be among the merging black holes observed with gravitational waves. In this paper, we explore how well current gravitational wave parameter estimation methods can measure the spins of rapidly spinning black holes in binaries. We simulate gravitational-wave signals using numerical-relativity waveforms for nearly-extremal, merging black holes. For simplicity, we confine our attention to binaries with spins parallel or antiparallel with the orbital angular momentum. We find that recovering the holes' nearly extremal spins is challenging. When the spins are nearly extremal and parallel to each other, the resulting parameter estimates do recover spins that are large, though the recovered spin magnitudes are still significantly smaller than the true spin magnitudes. When the spins are nearly extremal and antiparallel to each other, the resulting parameter estimates recover the small effective spin but incorrectly estimate the individual spins as nearly zero. We study the effect of spin priors and argue that a commonly used prior (uniform in spin magnitude and direction) hinders unbiased recovery of large black-hole spins.

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arXiv2017

Targeted numerical simulations of binary black holes for GW170104

In response to LIGO's observation of GW170104, we performed a series of full numerical simulations of binary black holes, each designed to replicate likely realizations of its dynamics and radiation. These simulations have been performed at multiple resolutions and with two independent techniques to solve Einstein's equations. For the nonprecessing and precessing simulations, we demonstrate the two techniques agree mode by mode, at a precision substantially in excess of statistical uncertainties in current LIGO's observations. Conversely, we demonstrate our full numerical solutions contain information which is not accurately captured with the approximate phenomenological models commonly used to infer compact binary parameters. To quantify the impact of these differences on parameter inference for GW170104 specifically, we compare the predictions of our simulations and these approximate models to LIGO's observations of GW170104.

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arXiv2017

A Parameter Estimation Method that Directly Compares Gravitational Wave Observations to Numerical Relativity

We present and assess a Bayesian method to interpret gravitational wave signals from binary black holes. Our method directly compares gravitational wave data to numerical relativity simulations. This procedure bypasses approximations used in semi-analytical models for compact binary coalescence. In this work, we use only the full posterior parameter distribution for generic nonprecessing binaries, drawing inferences away from the set of NR simulations used, via interpolation of a single scalar quantity (the marginalized log-likelihood, $\ln {\cal L}$) evaluated by comparing data to nonprecessing binary black hole simulations. We also compare the data to generic simulations, and discuss the effectiveness of this procedure for generic sources. We specifically assess the impact of higher order modes, repeating our interpretation with both $l\le2$ as well as $l\le3$ harmonic modes. Using the $l\le3$ higher modes, we gain more information from the signal and can better constrain the parameters of the gravitational wave signal. We assess and quantify several sources of systematic error that our procedure could introduce, including simulation resolution and duration; most are negligible. We show through examples that our method can recover the parameters for equal mass, zero spin; GW150914-like; and unequal mass, precessing spin sources. Our study of this new parameter estimation method demonstrates we can quantify and understand the systematic and statistical error. This method allows us to use higher order modes from numerical relativity simulations to better constrain the black hole binary parameters.

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arXiv2017

The integration of angular velocity

A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential equations. Several possible approaches are examined, along with various improvements over previous efforts. These are then evaluated numerically by comparison to a complicated but analytically known rotation that is motivated by the important astrophysical problem of precessing black-hole binaries. It is shown that a straightforward solution directly using quaternions is most efficient and accurate, and that the norm of the quaternion is irrelevant. Integration of the generator of the rotation can also be made roughly as efficient as integration of the rotation. Both methods will typically be twice as efficient as naive vector- or matrix-based methods. Implementation by means of standard general-purpose numerical integrators is stable and efficient, so that such problems can be readily solved as part of a larger system of differential equations. Possible generalization to integration in other Lie groups is also discussed.

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arXiv2017

An improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors

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 towards 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 $\gtrsim 4$ and double spin $\gtrsim 0.8$ will be crucial to resolve 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.

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arXiv2017

Complete waveform model for compact binaries on eccentric orbits

We present a time domain waveform model that describes the inspiral-merger-ringdown (IMR) of compact binary systems whose components are non-spinning, 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 non-linear 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 incorporate higher-order post-Newtonian corrections for the energy flux of quasi-circular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced inspiral evolution prescription is combined with an analytical prescription for the merger-ringdown evolution using a catalog of numerical relativity simulations. This IMR waveform model reproduces effective-one-body waveforms for systems with mass-ratios between 1 to 15 in the zero eccentricity limit. Using a set of eccentric numerical relativity simulations, not used during calibration, we show that our eccentric model accurately reproduces the features of eccentric compact binary coalescence throughout the merger. Using this model we show that the gravitational wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasi-circular, spin-aligned waveforms if the eccentricity $e_0$ of these systems when they enter the aLIGO band at a gravitational wave frequency of 14 Hz satisfies $e_0^{\rm GW150914}\leq0.15$ and $e_0^{\rm GW151226}\leq0.1$.

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arXiv2016

On the accuracy and precision of numerical waveforms: Effect of waveform extraction methodology

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 to 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 finite length of the numerical waveforms are of similar magnitude, with gravitational wave extraction errors somewhat dominating at noise-weighted mismatches of $\sim 3\times 10^{-4}$. This set of waveforms will serve to validate and improve aligned-spin waveform models for gravitational wave science.

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arXiv2016

Modeling the source of GW150914 with targeted numerical-relativity simulations

In fall of 2015, the two LIGO detectors measured the gravitational wave signal GW150914, which originated from a pair of merging black holes. In the final 0.2 seconds (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. 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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arXiv2016

Transformations of asymptotic gravitational-wave data

Gravitational-wave data is gauge dependent. While we can restrict the class of gauges in which such data may be expressed, there will still be an infinite-dimensional group of transformations allowed while remaining in this class, and almost as many different---though physically equivalent---waveforms as there are transformations. This paper presents a method for calculating the effects of the most important transformation group, the Bondi-Metzner-Sachs (BMS) group, consisting of rotations, boosts, and supertranslations (which include time and space translations as special cases). To a reasonable approximation, these transformations result in simple coupling between the modes in a spin-weighted spherical-harmonic decomposition of the waveform. It is shown that waveforms from simulated compact binaries in the publicly available SXS waveform catalog contain unmodeled effects due to displacement and drift of the center of mass, accounting for mode-mixing at typical levels of 1%. However, these effects can be mitigated by measuring the average motion of the system's center of mass for a portion of the inspiral, and applying the opposite transformation to the waveform data. More generally, controlling the BMS transformations will be necessary to eliminate the gauge ambiguity inherent in gravitational-wave data for both numerical and analytical waveforms. Open-source code implementing BMS transformations of waveforms is included along with this paper in the supplemental materials.

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arXiv2016

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 $ρ$, 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 $ρ\lesssim 15$. PhenomD's modeling errors are found to be smaller than SEOBNRv2's, and are generally irrelevant for $ρ\lesssim 20$. 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.

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arXiv2015

Improvements to the construction of binary black hole initial data

Construction of binary black hole initial data is a prerequisite for numerical evolutions of binary black holes. This paper reports improvements to the binary black hole initial data solver in the Spectral Einstein Code, to allow robust construction of initial data for mass-ratio above 10:1, and for dimensionless black hole spins above 0.9, while improving efficiency for lower mass-ratios and spins. We implement a more flexible domain decomposition, adaptive mesh refinement and an updated method for choosing free parameters. We also introduce a new method to control and eliminate residual linear momentum in initial data for precessing systems, and demonstrate that it eliminates gravitational mode mixing during the evolution. Finally, the new code is applied to construct initial data for hyperbolic scattering and for binaries with very small separation.

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arXiv2015

Comparing Post-Newtonian and Numerical-Relativity Precession Dynamics

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 $\sim 1^{\circ}$ with NR during the inspiral, increasing to $5^{\circ}$ 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.

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arXiv2014

Improved methods for simulating nearly extremal binary black holes

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 $S/m^2=0.93$. We present improved methods that enable us to simulate merging, nearly extremal black holes more robustly and more efficiently. We use these methods to simulate an unequal-mass, precessing binary black hole coalescence, where the larger black hole has $S/m^2=0.99$. We also use these methods to simulate a non-precessing binary black hole coalescence, where both black holes have $S/m^2=0.994$, 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).

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arXiv2014

Gravitational-wave modes from precessing black-hole binaries

Gravitational waves from precessing black-hole binaries exhibit features that are absent in nonprecessing systems. The most prominent of these is a parity-violating asymmetry that beams energy and linear momentum preferentially along or opposite to the orbital angular momentum, leading to recoil of the binary. The asymmetry will appear as amplitude and phase modulations at the orbital frequency. For strongly precessing systems, it accounts for at least 3% amplitude modulation for binaries in the sensitivity band of ground-based gravitational-wave detectors, and can exceed 50% for massive systems. Such asymmetric features are also clearly visible when the waves are decomposed into modes of spin-weighted spherical harmonics, and are inherent in the waves themselves---rather than resulting from residual eccentricity in numerical simulations, or from mode-mixing due to precession. In particular, there is generically no instantaneous frame for which the mode decomposition will have any symmetry. We introduce a method to simplify the expressions for waveforms given in analytical relativity, which can be used to combine existing high-order waveforms for nonprecessing systems with expressions for the precessing contributions, leading to improved accuracy and a unified treatment of precessing and nonprecessing binaries. Using this method, it is possible to clarify the nature and the origins of the asymmetries and show the effects of asymmetry on recoils more clearly. We present post-Newtonian (PN) expressions for the waveform modes that include these terms, complete to the relative 2PN level in spin (proportional to $v^4/c^4$ times a certain combination of the spins). Comparing the results of those expressions to numerical results, we find good qualitative agreement. We also demonstrate how these expressions can be used to efficiently calculate waveforms for gravitational-wave astronomy.

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arXiv2013

A catalog of 174 binary black-hole simulations for gravitational-wave astronomy

This paper 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.

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