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GipsyX/RTGx is the Jet Propulsion Laboratory's (JPL) next generation software package for positioning, navigation, timing, and Earth science using measurements from three geodetic techniques: Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS); with Very Long Baseline Interferometry (VLBI) under development. The software facilitates combined estimation of geodetic and geophysical parameters using a Kalman filter approach on real or simulated data in both post-processing and in real-time. The estimated parameters include station coordinates and velocities, satellite orbits and clocks, Earth orientation, ionospheric and tropospheric delays. The software is also capable of full realization of a dynamic terrestrial reference through analysis and combination of time series of ground station coordinates. We present some key aspects of its new architecture, and describe some of its major applications, including Real-time orbit determination and ephemeris predictions in the U.S. Air Force Next Generation GPS Operational Control Segment (OCX), as well as in JPL's Global Differential GPS (GDGPS) System, supporting User Range Error (URE) of $<$ 5 cm RMS; precision post-processing GNSS orbit determination, including JPL's contributions to the International GNSS Service (IGS) with URE in the 2 cm RMS range; Precise point positioning (PPP) with ambiguity resolution, both statically and kinematically, for geodetic applications with 2 mm horizontal, and 6.5 mm vertical repeatability for static positioning; Operational orbit and clock determination for Low Earth Orbiting (LEO) satellites, such as NASA's Gravity Recovery and Climate Experiment (GRACE) mission with GRACE relative clock alignment at the 20 ps level., Comment: 65 pages, 14 figures

As gravitational-wave detectors become more sensitive, 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 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 systems, 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 inspiral, merger and ringdown (IMR) 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 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 new 118 precessing NR waveforms, which span mass ratios 1-4 and 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 $20-200 M_\odot$, is below $3\%$ ($1\%$). Those numbers become $83\%$ ($20\%$) when using the IMR, multipolar, precessing phenomenological model IMRPhenomPv3HM. We investigate the impact of such unfaithfulness values with two parameter-estimation studies on synthetic signals. We also compute the unfaithfulness between those waveform models and 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., Comment: 24 pages, 18 figures. Abstract abridged

We present an improved spectral algorithm for Cauchy-characteristic extraction and characteristic evolution of gravitational waves in numerical relativity. The new algorithms improve spectral convergence both at the poles of the spherical-polar grid and at future null infinity, as well as increase the temporal resolution of the code. The key to the success of these algorithms is a new set of high-accuracy tests, which we present here. We demonstrate the accuracy of the code and compare with the existing PittNull implementation., Comment: 26 pages, 8 figures, published version

Accurate models of gravitational waves from merging black holes are necessary for detectors to observe as many events as possible while extracting the maximum science. Near the time of merger, the gravitational waves from merging black holes can be computed only using numerical relativity. In this paper, we present a major update of the Simulating eXtreme Spacetimes (SXS) Collaboration catalog of numerical simulations for merging black holes. The catalog contains 2018 distinct configurations (a factor of 11 increase compared to the 2013 SXS catalog), including 1426 spin-precessing configurations, with mass ratios between 1 and 10, and spin magnitudes up to 0.998. The median length of a waveform in the catalog is 39 cycles of the dominant $\ell=m=2$ gravitational-wave mode, with the shortest waveform containing 7.0 cycles and the longest 351.3 cycles. We discuss improvements such as correcting for moving centers of mass and extended coverage of the parameter space. We also present a thorough analysis of numerical errors, finding typical truncation errors corresponding to a waveform mismatch of $\sim 10^{-4}$. The simulations provide remnant masses and spins with uncertainties of 0.03% and 0.1% ($90^{\text{th}}$ percentile), about an order of magnitude better than analytical models for remnant properties. The full catalog is publicly available at https://www.black-holes.org/waveforms ., Comment: 33+18 pages, 13 figures, 4 tables, 2,018 binaries. Catalog metadata in ancillary JSON file. v2: Matches version accepted by CQG. Catalog available at https://www.black-holes.org/waveforms

We present a detailed investigation into the properties of GW170729, the gravitational wave with the most massive and distant source confirmed to date. We employ an extensive set of waveform models, including new improved models that incorporate the effect of higher-order waveform modes which are particularly important for massive systems. We find no indication of spin-precession, but the inclusion of higher-order modes in the models results in an improved estimate for the mass ratio of $(0.3-0.8)$ at the 90\% credible level. Our updated measurement excludes equal masses at that level. We also find that models with higher-order modes lead to the data being more consistent with a smaller effective spin, with the probability that the effective spin is greater than zero being reduced from $99\%$ to $94\%$. The 90\% credible interval for the effective spin parameter is now $(-0.01-0.50)$. Additionally, the recovered signal-to-noise ratio increases by $\sim0.3$ units compared to analyses without higher-order modes. We study the effect of common spin priors on the derived spin and mass measurements, and observe small shifts in the spins, while the masses remain unaffected. We argue that our conclusions are robust against systematic errors in the waveform models. We also compare the above waveform-based analysis which employs compact-binary waveform models to a more flexible wavelet- and chirplet-based analysis. We find consistency between the two, with overlaps of $\sim 0.9$, typical of what is expected from simulations of signals similar to GW170729, confirming that the data are well-described by the existing waveform models. Finally, we study the possibility that the primary component of GW170729 was the remnant of a past merger of two black holes and find this scenario to be indistinguishable from the standard formation scenario., Comment: 14 pages, 8 figures, final published version, samples available at https://git.ligo.org/katerina.chatziioannou/gw170729hm_datarelease

Gravitational-wave detectors have begun to observe coalescences of heavy black holes at a consistent pace for the past few years. Accurate models of gravitational waveforms are essential for unbiased and precise estimation of source parameters. Recently developed surrogate models based on high-accuracy numerical relativity (NR) simulations are ideal for constraining physical parameters of heavy black hole merger events. In this paper, we first demonstrate the viability of these multi-modal surrogates as reliable parameter estimation tools. We show that NR surrogates can extract additional information from GW data that is inaccessible to traditional models, by analyzing a set of synthetic signals with the NR surrogate and other approximants. We also consider the case of two of the earliest binary black holes detected by the LIGO observatories: GW150914 and GW170104. We reanalyze their data with fully-precessing NR-surrogate templates 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. We estimate the sources of both events to be 20-25% further away than was previously estimated. Our analyses also constrain their orbital orientation more tightly around face-on or face-off configurations than before. Additionally, for GW150914 we constrain the effective inspiral spin 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 also motivates that NR surrogates be extended to cover more of the binary black hole parameter space., Comment: 20 pages, 14 figures; Updated to published version

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., Comment: 8 pages, 7 figures, final published version

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 $\Delta \phi = 180^{\circ}$ have higher FFs ($\Delta \phi$ is the angle between the components of the black hole spins in the plane orthogonal to the orbital angular momentum) as compared to their $\Delta \phi =0^{\circ}$ and generic counterparts. This implies that we will have a slight observation bias towards $\Delta \phi=180^{\circ}$ 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 $\Delta \phi = 180^{\circ}$ resonant binaries. The symmetric mass ratio can be estimated with errors below $15\%$. The effective spin parameter $\chi_{\rm eff}$ is measured with maximum absolute error of 0.13. The in-plane spin parameter $\chi_p$ 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., Comment: 27 pages, 15 figures. Abstract shortened due to word limit

Black hole-torus systems from compact binary mergers are possible engines for gamma-ray bursts (GRBs). During the early evolution of the post-merger remnant, the state of the torus is determined by a combination of neutrino cooling and magnetically-driven heating processes, so realistic models must include both effects. In this paper, we study the post-merger evolution of a magnetized black hole-neutron star binary system using the Spectral Einstein Code (SpEC) from an initial post-merger state provided by previous numerical relativity simulations. We use a finite-temperature nuclear equation of state and incorporate neutrino effects in a leakage approximation. To achieve the needed accuracy, we introduce improvements to SpEC's implementation of general-relativistic magnetohydrodynamics (MHD), including the use of cubed-sphere multipatch grids and an improved method for dealing with supersonic accretion flows where primitive variable recovery is difficult. We find that a seed magnetic field triggers a sustained source of heating, but its thermal effects are largely cancelled by the accretion and spreading of the torus from MHD-related angular momentum transport. The neutrino luminosity peaks at the start of the simulation, and then drops significantly over the first 20\,ms but in roughly the same way for magnetized and nonmagnetized disks. The heating rate and disk's luminosity decrease much more slowly thereafter. These features of the evolution are insensitive to grid structure and resolution, formulation of the MHD equations, and seed field strength, although turbulent effects are not fully converged, Comment: 17 pages, 18 figures

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., Comment: 30 pages, 22 figures; submitted to PRD

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., Comment: 10 pages, 5 figures; Added report number

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., Comment: 27 pages, 15 figures

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 $e_0^{\rm GW151226}\leq0.1$., Comment: 31 pages, 19 figures, 3 appendices. Submitted to Phys Rev D. v2: direct comparison to eccentric numerical relativity simulations, not used for calibration of the model, included. References added. Accepted to Phys Rev D

The coalescence of a neutron star with a black hole is a primary science target of ground-based gravitational wave detectors. Constraining or measuring the neutron star spin directly from gravitational wave observations requires knowledge of the dependence of the emission properties of these systems on the neutron star spin. This paper lays foundations for this task, by developing a numerical method to construct initial data for black hole--neutron star binaries with arbitrary spin on the neutron star. We demonstrate the robustness of the code by constructing initial-data sets in large regions of the parameter space. In addition to varying the neutron star spin-magnitude and spin-direction, we also explore neutron star compactness, mass-ratio, black hole spin, and black hole spin-direction. Specifically, we are able to construct initial data sets with neutron stars spinning near centrifugal break-up, and with black hole spins as large as $S_{\rm BH}/M_{\rm BH}^2=0.99$., Comment: 25 pages, 12 figures

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., Comment: 11 pages, 3 figures, submitted to Classical and Quantum Gravity

We present a new approach for the Cauchy-characteristic extraction of gravitational radiation strain, news function, and the flux of the energy-momentum, supermomentum and angular momentum associated with the Bondi-Metzner-Sachs asymptotic symmetries. In Cauchy-characteristic extraction, a characteristic evolution code takes numerical data on an inner worldtube supplied by a Cauchy evolution code, and propagates it outwards to obtain the space-time metric in a neighborhood of null infinity. The metric is first determined in a scrambled form in terms of coordinates determined by the Cauchy formalism. In prior treatments, the waveform is first extracted from this metric and then transformed into an asymptotic inertial coordinate system. This procedure provides the physically proper description of the waveform and the radiated energy but it does not generalize to determine the flux of angular momentum or supermomentum. Here we formulate and implement a new approach which transforms the full metric into an asymptotic inertial frame and provides a uniform treatment of all the radiation fluxes associated with the asymptotic symmetries. Computations are performed and calibrated using the Spectral Einstein Code (SpEC)., Comment: 30 pages, 17 figures

We present results on the inspiral, merger, and post-merger evolution of a neutron star - neutron star (NSNS) system. Our results are obtained using the hybrid pseudospectral-finite volume Spectral Einstein Code (SpEC). To test our numerical methods, we evolve an equal-mass system for $\approx 22$ orbits before merger. This waveform is the longest waveform obtained from fully general-relativistic simulations for NSNSs to date. Such long (and accurate) numerical waveforms are required to further improve semi-analytical models used in gravitational wave data analysis, for example the effective one body models. We discuss in detail the improvements to SpEC's ability to simulate NSNS mergers, in particular mesh refined grids to better resolve the merger and post-merger phases. We provide a set of consistency checks and compare our results to NSNS merger simulations with the independent BAM code. We find agreement between them, which increases confidence in results obtained with either code. This work paves the way for future studies using long waveforms and more complex microphysical descriptions of neutron star matter in SpEC., Comment: 23 pages, 15 figures, published version

Extracting the unique information on ultradense nuclear matter from the gravitational waves emitted by merging, neutron-star binaries requires robust theoretical models of the signal. We develop a novel effective-one-body waveform model that includes, for the first time, dynamic (instead of only adiabatic) tides of the neutron star, as well as the merger signal for neutron-star--black-hole binaries. We demonstrate the importance of the dynamic tides by comparing our model against new numerical-relativity simulations of nonspinning neutron-star--black-hole binaries spanning more than 24 gravitational-wave cycles, and to other existing numerical simulations for double neutron-star systems. Furthermore, we derive an effective description that makes explicit the dependence of matter effects on two key parameters: tidal deformability and fundamental oscillation frequency.

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., Comment: 24 pages, 15 figures, minor changes

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., Comment: 22 pages, 9 figures

Gravitational waves from binary neutron star (BNS) and black hole/neutron star (BHNS) inspirals are primary sources for detection by the Advanced Laser Interferometer Gravitational-Wave Observatory. The tidal forces acting on the neutron stars induce changes in the phase evolution of the gravitational waveform, and these changes can be used to constrain the nuclear equation of state. Current methods of generating BNS and BHNS waveforms rely on either computationally challenging full 3D hydrodynamical simulations or approximate analytic solutions. We introduce a new method for computing inspiral waveforms for BNS/BHNS systems by adding the post-Newtonian (PN) tidal effects to full numerical simulations of binary black holes (BBHs), effectively replacing the nontidal terms in the PN expansion with BBH results. Comparing a waveform generated with this method against a full hydrodynamical simulation of a BNS inspiral yields a phase difference of $<1$ radian over $\sim 15$ orbits. The numerical phase accuracy required of BNS simulations to measure the accuracy of the method we present here is estimated as a function of the tidal deformability parameter ${\lambda}$., Comment: 7 pages, 3 figures; updated acknowledgements; published PRD version

We present a code to construct initial data for binary neutron star systems in which the stars are rotating. Our code, based on a formalism developed by Tichy, allows for arbitrary rotation axes of the neutron stars and is able to achieve rotation rates near rotational breakup. We compute the neutron star angular momentum through quasi-local angular momentum integrals. When constructing irrotational binary neutron stars, we find a very small residual dimensionless spin of $\sim 2\times 10^{-4}$. Evolutions of rotating neutron star binaries show that the magnitude of the stars' angular momentum is conserved, and that the spin- and orbit-precession of the stars is well described by post-Newtonian approximation. We demonstrate that orbital eccentricity of the binary neutron stars can be controlled to $\sim 0.1\%$. The neutron stars show quasi-normal mode oscillations at an amplitude which increases with the rotation rate of the stars., Comment: 20 pages, 22 figures

Coalescing binaries of neutron stars (NS) and black holes (BH) are one of the most important sources of gravitational waves for the upcoming network of ground based detectors. Detection and extraction of astrophysical information from gravitational-wave signals requires accurate waveform models. The Effective-One-Body and other phenomenological models interpolate between analytic results and $10-30$ orbit numerical relativity (NR) merger simulations. In this paper we study the accuracy of these models using new NR simulations that span $36-88$ orbits, with mass-ratios and black hole spins $(q,\chi_{BH}) = (7, \pm 0.4), (7, \pm 0.6)$, and $(5, -0.9)$. We find that: (i) the recently published SEOBNRv1 and SEOBNRv2 models of the Effective-One-Body family disagree with each other (mismatches of a few percent) for black hole spins $\geq 0.5$ or $\leq -0.3$, with waveform mismatch accumulating during early inspiral; (ii) comparison with numerical waveforms indicate that this disagreement is due to phasing errors of SEOBNRv1, with SEOBNRv2 in good agreement with all of our simulations; (iii) Phenomenological waveforms disagree with SEOBNRv2 over most of the NSBH binary parameter space; (iv) comparison with NR waveforms shows that most of the model's dephasing accumulates near the frequency interval where it switches to a phenomenological phasing prescription; and finally (v) both SEOBNR and post-Newtonian (PN) models are effectual for NSBH systems, but PN waveforms will give a significant bias in parameter recovery. Our results suggest that future gravitational-wave detection searches and parameter estimation efforts targeted at NSBH systems with $q\lesssim 7$ and $\chi_\mathrm{BH} \approx [-0.9, +0.6]$ will benefit from using SEOBNRv2 templates. For larger black hole spins and/or binary mass-ratios, we recommend the models be further investigated as suitable NR simulations become available., Comment: 20 pages, 18 figures

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., Comment: 28 pages, 13 figures, 1 table

Simulating a binary black hole (BBH) 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 non-spinning BBH 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 {\em 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 ${}_{-2}Y_{\ell m}$ waveform modes resolved by the NR code up to $\ell=8.$ We compare our surrogate model to Effective One Body waveforms from $50$-$300 M_\odot$ for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases)., Comment: Updated to published version, which includes a section comparing the surrogate and effective-one-body models. The surrogate is publicly available for download at http://www.black-holes.org/surrogates/ . 6 pages, 6 figures

We present gauge invariant spectral Cauchy characteristic extraction. We compare gravitational waveforms extracted from a head-on black hole merger simulated in two different gauges by two different codes. We show rapid convergence, demonstrating both gauge invariance of the extraction algorithm and consistency between the legacy Pitt null code and the much faster Spectral Einstein Code (SpEC).

We present the first numerical-relativity simulation of a compact-object binary whose gravitational waveform is long enough to cover the entire frequency band of advanced gravitational-wave detectors, such as LIGO, Virgo and KAGRA, for mass ratio 7 and total mass as low as $45.5\,M_\odot$. We find that effective-one-body models, either uncalibrated or calibrated against substantially shorter numerical-relativity waveforms at smaller mass ratios, reproduce our new waveform remarkably well, with a negligible loss in detection rate due to modeling error. In contrast, post-Newtonian inspiral waveforms and existing calibrated phenomenological inspiral-merger-ringdown waveforms display greater disagreement with our new simulation. The disagreement varies substantially depending on the specific post-Newtonian approximant used.

We present a first simulation of the post-merger evolution of a black hole-neutron star binary in full general relativity using an energy-integrated general relativistic truncated moment formalism for neutrino transport. We describe our implementation of the moment formalism and important tests of our code, before studying the formation phase of a disk after a black hole-neutron star merger. We use as initial data an existing general relativistic simulation of the merger of a neutron star of 1.4 solar mass with a black hole of 7 solar mass and dimensionless spin a/M=0.8. Comparing with a simpler leakage scheme for the treatment of the neutrinos, we find noticeable differences in the neutron to proton ratio in and around the disk, and in the neutrino luminosity. We find that the electron neutrino luminosity is much lower in the transport simulations, and that the remnant is less neutron-rich. The spatial distribution of the neutrinos is significantly affected by relativistic effects. Over the short timescale evolved, we do not observe purely neutrino-driven outflows. However, a small amount of material (3e-4Msun) is ejected in the polar region during the circularization of the disk. Most of that material is ejected early in the formation of the disk, and is fairly neutron rich. Through r-process nucleosynthesis, that material should produce high-opacity lanthanides in the polar region, and could thus affect the lightcurve of radioactively powered electromagnetic transients. We also show that by the end of the simulation, while the bulk of the disk is neutron-rich, its outer layers have a higher electron fraction. As that material would be the first to be unbound by disk outflows on longer timescales, the changes in Ye experienced during the formation of the disk could have an impact on the nucleosynthesis outputs from neutrino-driven and viscously-driven outflows. [Abridged], Comment: 29 pages, 25 figures

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.

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)., Comment: 18 pages, 18 figures

The spin angular momentum $S$ of an isolated Kerr black hole is bounded by the surface area $A$ of its apparent horizon: $8\pi S \le A$, with equality for extremal black holes. In this paper, we explore the extremality of individual and common apparent horizons for merging, rapidly spinning binary black holes. We consider simulations of merging black holes with equal masses $M$ and initial spin angular momenta aligned with the orbital angular momentum, including new simulations with spin magnitudes up to $S/M^2 = 0.994$. We measure the area and (using approximate Killing vectors) the spin on the individual and common apparent horizons, finding that the inequality $8\pi S < A$ is satisfied in all cases but is very close to equality on the common apparent horizon at the instant it first appears. We also introduce a gauge-invariant lower bound on the extremality by computing the smallest value that Booth and Fairhurst's extremality parameter can take for any scaling. Using this lower bound, we conclude that the common horizons are at least moderately close to extremal just after they appear. Finally, following Lovelace et al. (2008), we construct quasiequilibrium binary-black-hole initial data with "overspun" marginally trapped surfaces with $8\pi S > A$ and for which our lower bound on their Booth-Fairhurst extremality exceeds unity. These superextremal surfaces are always surrounded by marginally outer trapped surfaces (i.e., by apparent horizons) with $8\pi S

We present a spectral algorithm for solving the full nonlinear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate spectral characteristic evolution as a technical precursor to Cauchy Characteristic Extraction (CCE), a rigorous method for obtaining gauge-invariant gravitational waveforms from existing and future astrophysical simulations. We demonstrate the new algorithm's stability, convergence, and agreement with existing evolution methods. We explain how an innovative spectral approach enables a two orders of magnitude improvement in computational efficiency., Comment: 28 pages, 9 figures

As a network of advanced-era gravitational wave detectors is nearing its design sensitivity, efficient and accurate waveform modeling becomes more and more relevant. Understanding of the nature of the signal being sought can have an order unity effect on the event rates seen in these instruments. The paper provides a description of key elements of the Spectral Einstein Code ({\tt SpEC}), with details of our spectral adaptive mesh refinement (AMR) algorithm that has been optimized for binary black hole (BBH) evolutions. We expect that the gravitational waveform catalog produced by our code will have a central importance in both the detection and parameter estimation of gravitational waves in these instruments., Comment: 39 pages, 16 figures, invited review paper

Dynamical instabilities in protoneutron stars may produce gravitational waves whose observation could shed light on the physics of core-collapse supernovae. When born with sufficient differential rotation, these stars are susceptible to a shear instability (the "low-T/|W| instability"), but such rotation can also amplify magnetic fields to strengths where they have a considerable impact on the dynamics of the stellar matter. Using a new magnetohydrodynamics module for the Spectral Einstein Code, we have simulated a differentially-rotating neutron star in full 3D to study the effects of magnetic fields on this instability. Though strong toroidal fields were predicted to suppress the low-T/|W| instability, we find that they do so only in a small range of field strengths. Below 4e13 G, poloidal seed fields do not wind up fast enough to have an effect before the instability saturates, while above 5e14 G, magnetic instabilities can actually amplify a global quadrupole mode (this threshold may be even lower in reality, as small-scale magnetic instabilities remain difficult to resolve numerically). Thus, the prospects for observing gravitational waves from such systems are not in fact diminished over most of the magnetic parameter space. Additionally, we report that the detailed development of the low-T/|W| instability, including its growth rate, depends strongly on the particular numerical methods used. The high-order methods we employ suggest that growth might be considerably slower than found in some previous simulations., Comment: REVTeX 4.1, 21 pages, 18 figures, submitting to Physical Review D

We present a first exploration of the results of neutron star-black hole mergers using black hole masses in the most likely range of $7M_\odot-10M_\odot$, a neutrino leakage scheme, and a modeling of the neutron star material through a finite-temperature nuclear-theory based equation of state. In the range of black hole spins in which the neutron star is tidally disrupted ($\chi_{\rm BH}\gtrsim 0.7$), we show that the merger consistently produces large amounts of cool ($T\lesssim 1\,{\rm MeV}$), unbound, neutron-rich material ($M_{\rm ej}\sim 0.05M_\odot-0.20M_\odot$). A comparable amount of bound matter is initially divided between a hot disk ($T_{\rm max}\sim 15\,{\rm MeV}$) with typical neutrino luminosity $L_\nu\sim 10^{53}\,{\rm erg/s}$, and a cooler tidal tail. After a short period of rapid protonization of the disk lasting $\sim 10\,{\rm ms}$, the accretion disk cools down under the combined effects of the fall-back of cool material from the tail, continued accretion of the hottest material onto the black hole, and neutrino emission. As the temperature decreases, the disk progressively becomes more neutron-rich, with dimmer neutrino emission. This cooling process should stop once the viscous heating in the disk (not included in our simulations) balances the cooling. These mergers of neutron star-black hole binaries with black hole masses $M_{\rm BH}\sim 7M_\odot-10M_\odot$ and black hole spins high enough for the neutron star to disrupt provide promising candidates for the production of short gamma-ray bursts, of bright infrared post-merger signals due to the radioactive decay of unbound material, and of large amounts of r-process nuclei., Comment: 20 pages, 19 figures

Many relevant applications in gravitational wave physics share a significant common problem: the seven-dimensional parameter space of gravitational waveforms from precessing compact binary inspirals and coalescences is large enough to prohibit covering the space of waveforms with sufficient density. We find that by using the reduced basis method together with a parametrization of waveforms based on their phase and precession, we can construct ultra-compact yet high-accuracy representations of this large space. As a demonstration, we show that less than $100$ judiciously chosen precessing inspiral waveforms are needed for $200$ cycles, mass ratios from $1$ to $10$ and spin magnitudes $\le 0.9$. In fact, using only the first $10$ reduced basis waveforms yields a maximum mismatch of $0.016$ over the whole range of considered parameters. We test whether the parameters selected from the inspiral regime result in an accurate reduced basis when including merger and ringdown; we find that this is indeed the case in the context of a non-precessing effective-one-body model. This evidence suggests that as few as $\sim 100$ numerical simulations of binary black hole coalescences may accurately represent the seven-dimensional parameter space of precession waveforms for the considered ranges., Comment: 5 pages, 3 figures. The parameters selected for the basis of precessing waveforms can be found in the source files

This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational procedures that make it possible to explore the never before studied properties of solutions to Einstein's equation on manifolds with arbitrary toplogical structures. A new covariant, first-order symmetric-hyperbolic representation of Einstein's equation is developed for this purpose, along with the needed boundary conditions at the interfaces between adjoining cubic regions. Numerical tests are presented that demonstrate the long-term numerical stability of this method for evolutions of a complicated, time-dependent solution of Einstein's equation coupled to a complex scalar field on a manifold with spatial topology S^3. The accuracy of these numerical test solutions is evaluated by performing convergence studies and by comparing the full non-linear numerical results to the analytical perturbation solutions, which are also derived here., Comment: 20 pages, 12 figures, 1 table; v2 minor revisions to agree with published version

Gravitational waves emitted by black-hole binary systems have the highest signal-to-noise ratio in LIGO and Virgo detectors when black-hole spins are aligned with the orbital angular momentum and extremal. For such systems, we extend the effective-one-body inspiral-merger-ringdown waveforms to generic mass ratios and spins calibrating them to 38 numerical-relativity nonprecessing waveforms produced by the SXS Collaboration. The numerical-relativity simulations span mass ratios from 1 to 8, spin magnitudes up to 98% of extremality, and last for 40 to 60 gravitational-wave cycles. When the total mass of the binary is between 20Msun and 200Msun, the effective-one-body nonprecessing (dominant mode) waveforms have overlaps above 99% (using the advanced-LIGO design noise spectral density) with all of the 38 nonprecessing numerical waveforms, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling. Moreover, without further calibration, we show that the precessing effective-one-body (dominant mode) waveforms have overlaps above 97% with two very long, strongly precessing numerical-relativity waveforms, when maximizing only on the initial phase and time., Comment: 5 pages, 4 figures

The detection of gravitational waves and the extraction of physical information from them requires the prediction of accurate waveforms to be used in template banks. For that purpose, the accuracy of effective-one-body (EOB) waveforms has been improved over the last years by calibrating them to numerical-relativity (NR) waveforms. So far, the calibration has employed a handful of NR waveforms with a total length of ~30 cycles, the length being limited by the computational cost of NR simulations. Here we address the outstanding problem of the stability of the EOB calibration with respect to the length of NR waveforms. Performing calibration studies against NR waveforms of nonspinning black-hole binaries with mass ratios 1, 1.5, 5, and 8, and with a total length of ~60 cycles, we find that EOB waveforms calibrated against either 30 or 60 cycles will be indistinguishable by the advanced detectors LIGO and Virgo when the signal-to-noise ratio (SNR) is below 110. When extrapolating to a very large number of cycles, using very conservative assumptions, we can conclude that state-of-the-art nonspinning EOB waveforms of any length are sufficiently accurate for parameter estimation with advanced detectors when the SNR is below 20, the mass ratio is below 5 and total mass is above 20 Msun. The results are not conclusive for the entire parameter space because of current NR errors., Comment: 5 pages, 3 figures

Gravitational waves (GW) from coalescing stellar-mass black hole binaries (BBH) 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 BBH are constructed from intermediary analytical waveform models which are calibrated against numerical relativity simulations and which can be aluated 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 non-spinning 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 non-spinning 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., Comment: 16 pages, 21 figures

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 $\Psi_4$ 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-$\Psi_4$ waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-$\Psi_4$ 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., Comment: 26 pages, 20 figures

At the beginning of binary black hole simulations, there is a pulse of spurious radiation (or junk radiation) resulting from the initial data not matching astrophysical quasi-equilibrium inspiral exactly. One traditionally waits for the junk radiation to exit the computational domain before taking physical readings, at the expense of throwing away a segment of the evolution, and with the hope that junk radiation exits cleanly. We argue that this hope does not necessarily pan out as junk radiation could excite long-lived constraint violation. Another complication with the initial data is that it contains orbital eccentricity that needs to be removed, usually by evolving the early part of the inspiral multiple times with gradually improved input parameters. We show that this procedure is also adversely impacted by junk radiation. In this paper, we do not attempt to eliminate junk radiation directly, but instead tackle the much simpler problem of ameliorating its long-lasting effects. We report on the success of a method that achieves this goal by combining the removal of junk radiation and eccentricity into a single "joint-elimination" procedure. This approach has the following benefits: (1) We do not have to contend with the influence of junk radiation on eccentricity measurements for later iterations of the eccentricity reduction procedure. (2) We re-enforce constraints periodically by invoking the initial data solver, removing the constraint violation excited by junk radiation previously. (3) The wasted simulation segment associated with the junk radiation's evolution is absorbed into the eccentricity reduction iterations. Furthermore, (1) and (2) together allow us to carry out our joint-elimination procedure at low resolution, even when the subsequent "production run" is intended as a high resolution simulation., Comment: 13 pages, 14 figures

We compute the periastron advance using the effective-one-body formalism for binary black holes moving on quasi-circular orbits and having spins collinear with the orbital angular momentum. We compare the predictions with the periastron advance recently computed in accurate numerical-relativity simulations and find remarkable agreement for a wide range of spins and mass ratios. These results do not use any numerical-relativity calibration of the effective-one-body model, and stem from two key ingredients in the effective-one-body Hamiltonian: (i) the mapping of the two-body dynamics of spinning particles onto the dynamics of an effective spinning particle in a (deformed) Kerr spacetime, fully symmetrized with respect to the two-body masses and spins, and (ii) the resummation, in the test-particle limit, of all post-Newtonian (PN) corrections linear in the spin of the particle. In fact, even when only the leading spin PN corrections are included in the effective-one-body spinning Hamiltonian but all the test-particle corrections linear in the spin of the particle are resummed we find very good agreement with the numerical results (within the numerical error for equal-mass binaries and discrepancies of at most 1% for larger mass ratios). Furthermore, we specialize to the extreme mass-ratio limit and derive, using the equations of motion in the gravitational skeleton approach, analytical expressions for the periastron advance, the meridional Lense-Thirring precession and spin precession frequency in the case of a spinning particle on a nearly circular equatorial orbit in Kerr spacetime, including also terms quadratic in the spin., Comment: minor changes to match published version

We study the general relativistic periastron advance in spinning black hole binaries on quasi-circular orbits, with spins aligned or anti-aligned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result, and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the periastron advance of a non-spinning particle orbiting a Kerr black hole of mass M and spin S = -0.5 M^2, down to separations of order 9M. Comparing the predictions of our improved perturbative expansion with the exact results from numerical simulations of equal-mass and equal-spin binaries, we find a remarkable agreement over a wide range of spins and orbital separations., Comment: 18 pages, 12 figures; matches version to appear in Phys. Rev. D

We present the first direct comparison of numerical simulations of neutron star-black hole and black hole-black hole mergers in full general relativity. We focus on a configuration with non spinning objects and within the most likely range of mass ratio for neutron star-black hole systems (q=6). In this region of the parameter space, the neutron star is not tidally disrupted prior to merger, and we show that the two types of mergers appear remarkably similar. The effect of the presence of a neutron star on the gravitational wave signal is not only undetectable by the next generation of gravitational wave detectors, but also too small to be measured in the numerical simulations: even the plunge, merger and ringdown signals appear in perfect agreement for both types of binaries. The characteristics of the post-merger remnants are equally similar, with the masses of the final black holes agreeing within dM< 5 10^{-4}M_BH and their spins within da< 10^{-3}M_BH. The rate of periastron advance in the mixed binary agrees with previously published binary black hole results, and we use the inspiral waveforms to place constraints on the accuracy of our numerical simulations independent of algorithmic choices made for each type of binary. Overall, our results indicate that non-disrupting neutron star-black hole mergers are exceptionally well modeled by black hole-black hole mergers, and that given the absence of mass ejection, accretion disk formation, or differences in the gravitational wave signals, only electromagnetic precursors could prove the presence of a neutron star in low-spin systems of total mass ~10Msun, at least until the advent of gravitational wave detectors with a sensitivity comparable to that of the proposed Einstein Telescope., Comment: 13 pages, 9 figures

We describe a general procedure to generate spinning, precessing waveforms that include inspiral, merger and ringdown stages in the effective-one-body (EOB) approach. The procedure uses a precessing frame in which precession-induced amplitude and phase modulations are minimized, and an inertial frame, aligned with the spin of the final black hole, in which we carry out the matching of the inspiral-plunge to merger-ringdown waveforms. As a first application, we build spinning, precessing EOB waveforms for the gravitational modes l=2 such that in the nonprecessing limit those waveforms agree with the EOB waveforms recently calibrated to numerical-relativity waveforms. Without recalibrating the EOB model, we then compare EOB and post-Newtonian precessing waveforms to two numerical-relativity waveforms produced by the Caltech-Cornell-CITA collaboration. The numerical waveforms are strongly precessing and have 35 and 65 gravitational-wave cycles. We find a remarkable agreement between EOB and numerical-relativity precessing waveforms and spins' evolutions. The phase difference is ~ 0.2 rad at merger, while the mismatches, computed using the advanced-LIGO noise spectral density, are below 2% when maximizing only on the time and phase at coalescence and on the polarization angle., Comment: 17 pages, 10 figures

The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ~100-200 solar masses, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios <= 4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters., Comment: 51 pages, 10 figures; published version

The behavior of merging black holes (including the emitted gravitational waves and the properties of the remnant) can currently be computed only by numerical simulations. This paper introduces ten numerical relativity simulations of binary black holes with equal masses and equal spins aligned or anti-aligned with the orbital angular momentum. The initial spin magnitudes have $|\chi_i| \lesssim 0.95$ and are more concentrated in the aligned direction because of the greater astrophysical interest of this case. We combine this data with five previously reported simulations of the same configuration, but with different spin magnitudes, including the highest spin simulated to date, $\chi_i \approx 0.97$. This data set is sufficiently accurate to enable us to offer improved analytic fitting formulae for the final spin and for the energy radiated by gravitational waves as a function of initial spin. The improved fitting formulae can help to improve our understanding of the properties of binary black hole merger remnants and can be used to enhance future approximate waveforms for gravitational wave searches, such as Effective-One-Body waveforms., Comment: 13 pages, 10 figures

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., Comment: 6 pages; text clarified; additional results added