Multiple approaches are required to study the evolution of black-hole binaries. While the post-Newtonian approximation is sufficient to describe the early inspiral (even from infinitely large orbital separation), only numerical relativity can capture the full complexity of the dynamics near merger. We combine multi-timescale post-Newtonian integrations with numerical-relativity surrogate models, thus mapping the entire history of the binary from its asymptotic configuration at past-time infinity to the post-merger remnant. This approach naturally allows us to assess the impact of the precessional and orbital phase on the properties - mass, spin, and kick - of the merger remnant. These phases introduce a fundamental uncertainty when connecting the two extrema of the binary evolution.
We construct a new global, fully analytic, approximate spacetime which accurately describes the dynamics of non-precessing, spinning black hole binaries during the inspiral phase of the relativistic merger process. This approximate solution of the vacuum Einstein's equations can be obtained by asymptotically matching perturbed Kerr solutions near the two black holes to a post-Newtonian metric valid far from the two black holes. This metric is then matched to a post-Minkowskian metric even farther out in the wave zone. The procedure of asymptotic matching is generalized to be valid on all spati…
We derive explicit expressions for the multi-detector F-statistic metric applied to short-duration non-precessing inspiral signals. This is required for template bank production associated with coherent searches for short-duration non-precessing inspiral signals in gravitational-wave data from a network of detectors. We compare the metric's performance with explicit overlap calculations for all relevant dimensions of parameter space and find the metric accurately predicts the loss of detection statistic above overlaps of 95%. We also show the effect that neglecting the variations of the detect…
Precessing black hole-neutron star (BH-NS) binaries produce a rich gravitational wave signal, encoding the binary's nature and inspiral kinematics. Using the lalinference\_mcmc Markov-chain Monte Carlo parameter estimation code, we use two fiducial examples to illustrate how the geometry and kinematics are encoded into the modulated gravitational wave signal, using coordinates well-adapted to precession. Even for precessing binaries, we show the performance of detailed parameter estimation can be estimated by "effective" estimates: comparisons of a prototype signal with its nearest neighbors, …
It is customary to use a precessing convention, based on Newtonian orbital angular momentum ${\bf L}_{\rm N}$, to model inspiral gravitational waves from generic spinning compact binaries. A key feature of such a precessing convention is its ability to remove all spin precession induced modulations from the orbital phase evolution. However, this convention usually employs a post-Newtonian (PN) accurate precessional equation, appropriate for the PN accurate orbital angular momentum ${\bf L}$, to evolve the ${\bf L}_{\rm N}$-based precessing source frame. This motivated us to develop inspiral wa…
The detection and characterization of gravitational wave signals from compact binary coalescence events relies on accurate waveform templates in the frequency domain. The stationary phase approximation (SPA) can be used to compute closed-form frequency-domain waveforms for non-precessing, quasi-circular binary inspirals. However, until now, no fast frequency-domain waveforms have existed for generic, spin-precessing quasi-circular compact binary inspirals. Templates for these systems have had to be computed via a discrete Fourier transform of finely sampled time-domain waveforms, which is far …
We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with non-precessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime,…
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 wit…
We analyze the inspiral dynamics of equal-mass precessing black-hole binaries using multi-timescale techniques. The orbit-averaged post-Newtonian evolutionary equations admit two constants of motion in the equal-mass limit, namely the magnitude of the total spin $S$ and the effective spin $ξ$. This feature makes the entire dynamics qualitatively different compared to the generic unequal-mass case, where only $ξ$ is constant while the variable $S$ parametrizes the precession dynamics. For fixed individual masses and spin magnitudes, an equal-mass black-hole inspiral is uniquely characterized by…
One of the greatest theoretical challenges in the build-up to the era of second-generation gravitational-wave detectors is the modeling of generic binary waveforms. We introduce an approximation that has the potential to significantly simplify this problem. We show that generic precessing-binary inspiral waveforms (covering a seven-dimensional space of intrinsic parameters) can be mapped to a two-dimensional space of non-precessing binaries, characterized by the mass ratio and a single effective total spin. The mapping consists of a time-dependent rotation of the waveforms into the quadrupole-…
We study the performance of various analytical frequency-domain templates for detection and parameter estimation of gravitational waves from spin-precessing, quasi-circular, compact binary inspirals. We begin by assessing the extent to which non-spinning, spin-aligned, and the new (analytical, frequency-domain, small-spin) double-precessing frequency-domain templates can be used to detect signals from such systems. For effective, dimensionless spin values above $0.2$, the use of non-spinning or spin-aligned templates for detection purposes will result in a loss of up to $30%$ of all events, wh…
In this paper, we derive a set of equations of motions for binaries on eccentric orbits undergoing spin-induced precession that can efficiently be integrated on the radiation-reaction timescale. We find a family of solutions with a computation cost improved by a factor $10$ - $50$ down to $\sim 10$ ms per waveform evaluation compared to waveforms obtained by directly integrating the precession equations, that maintain a mismatch of the order $10^{-4}$ - $10^{-6}$ for waveforms lasting a million orbital cycles and a thousand spin-induced precession cycles. We express it in terms of parameters t…
The coalescence of compact objects is one of the most promising sources of gravitational waves for ground-based interferometric detectors, such as advanced LIGO and Virgo. Generically, com- pact objects in binaries are expected to be spinning with spin angular momenta misaligned with the orbital angular momentum, causing the orbital plane to precess. This precession adds rich structure to the gravitational waves, introducing such complexity that an analytic closed-form description has been unavailable until now. We here construct the first closed-form frequency- domain gravitational waveforms …
We revisit the modeling of the properties of the remnant black hole resulting the merger of a black-hole binary as a function of the parameters of the binary. We provide a set of empirical formulas for the final mass, spin and recoil velocity of the final black hole as a function of the mass ratio and individual spins of the progenitor. In order to determine the fitting coefficients for these formulas, we perform a set of 128 new numerical evolutions of precessing, unequal-mass black-hole binaries, and fit to the resulting remnant mass, spin, and recoil. In order to reduce the complexity of th…
A precessing source frame, constructed using the Newtonian orbital angular momentum ${\bf L_{\rm N}}$, can be invoked to model inspiral gravitational waves from generic spinning compact binaries. An attractive feature of such a precessing convention is its ability to remove all spin precession induced modulations from the orbital phase evolution. However, this convention usually employs a post-Newtonian (PN) accurate precessional equation, appropriate for the PN accurate orbital angular momentum ${\bf L}$, to evolve the ${\bf L_{\rm N}}$-based precessing source frame. This influenced us to dev…
We investigate the non-adiabatic dynamics of spinning black hole binaries by using an analytical Hamiltonian completed with a radiation-reaction force, containing spin couplings, which matches the known rates of energy and angular momentum losses on quasi-circular orbits. We consider both a straightforward post-Newtonian-expanded Hamiltonian (including spin-dependent terms), and a version of the resummed post-Newtonian Hamiltonian defined by the Effective One-Body approach. We focus on the influence of spin terms onto the dynamics and waveforms. We evaluate the energy and angular momentum rele…
Binary black holes which are both eccentric and undergo precession remain unexplored in numerical simulations. We present simulations of such systems which cover about 50 orbits at comparatively high mass ratios 5 and 7. The configurations correspond to the generic motion of a nonspinning body in a Kerr spacetime, and are chosen to study the transition from finite mass-ratio inspirals to point particle motion in Kerr. We develop techniques to extract analogs of the three fundamental frequencies of Kerr geodesics, compare our frequencies to those of Kerr, and show that the differences are consi…
Relativistic spin-orbit and spin-spin couplings has been shown to modify the gravitational waveforms expected from inspiraling binaries with a black hole and a neutron star. As a result inspiral signals may be missed due to significant losses in signal-to-noise ratio, if precession effects are ignored in gravitational-wave searches. We examine the sensitivity of the anticipated loss of signal-to-noise ratio on two factors: the accuracy of the precessing waveforms adopted as the true signals and the expected distributions of spin-orbit tilt angles, given the current understanding of their physi…
We present accurate fits for the remnant properties of generically precessing binary black holes, trained on large banks of numerical-relativity simulations. We use Gaussian process regression to interpolate the remnant mass, spin, and recoil velocity in the 7-dimensional parameter space of precessing black-hole binaries with mass ratios $q\leq2$, and spin magnitudes $χ_1,χ_2\leq0.8$. For precessing systems, our errors in estimating the remnant mass, spin magnitude, and kick magnitude are lower than those of existing fitting formulae by at least an order of magnitude (improvement is also repor…
The dynamics of precessing binary black holes (BBHs) in the post-Newtonian regime has a strong timescale hierarchy: the orbital timescale is very short compared to the spin-precession timescale which, in turn, is much shorter than the radiation-reaction timescale on which the orbit is shrinking due to gravitational-wave emission. We exploit this timescale hierarchy to develop a multi-scale analysis of BBH dynamics elaborating on the analysis of Kesden et al. (2015). We solve the spin-precession equations analytically on the precession time and then implement a quasi-adiabatic approach to evolv…
In a recent investigation of the effects of precession on the anticipated detection of gravitational-wave inspiral signals from compact object binaries with moderate total masses, we found that (i) if precession is ignored, the inspiral detection rate can decrease by almost a factor of 10, and (ii) previously proposed ``mimic'' templates cannot improve the detection rate significantly (by more than a factor of 2). In this paper we propose a new family of templates that can improve the detection rate by factors of 5--6 in cases where precession is most important. Our proposed method for these n…
Post-Newtonian inspiral waveform model for eccentric precessing binaries with higher-order modes and matter effects
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；School of Physics and Astronomy and Institute for Gravitational Wave Astronomy, University of Birmingham（伯明翰大学物理与天文学院及引力波天文研究所）；Department of Physics, University of Maryland, College Park（马里兰大学帕克分校物理系）
We present a new phenomenological gravitational waveform model for the inspiral and coalescence of non-precessing spinning black hole binaries. Our approach is based on a frequency domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near th…
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 inspi…
We introduce \texttt{TEOBResumSP}: an efficient, accurate hybrid scheme for generating gravitational waveforms from spin-precessing compact binaries. The precessing waveforms are generated via the established technique of Euler rotating the non-precessing \texttt{TEOBResumS} waveforms from a precessing frame to an inertial frame. We obtain the Euler angles by solving the post-Newtonian precession equations expanded to second post-Newtonian order. Current version of \texttt{TEOBResumSP} produces precessing waveforms through the inspiral phase up to the onset of the merger. We compare \texttt{TE…
We construct hybrid binary black holes merger waveforms using analytical model waveforms for the early inspiral phase and numerical relativity waveforms for late inspiral to merger and post merger phases. To hybridize analytical and numerical waveforms, we first perform a 3-dimensional rotation to align the instantaneous orbital planes associated with the two waveforms at some fiducial frequency, we then find appropriate phase and time translations that maximize the overlap of the two waveforms in a hybridization interval. We discuss the accuracy and limitations for hybrids constructed by this…
We obtain analytical gravitational waveforms in the frequency-domain for precessing, quasi-circular compact binaries with small spins, applicable, for example, to binary neutron star inspirals. We begin by calculating an analytic solution to the precession equations, obtained by expanding in the dimensionless spin parameters and using multiple-scale analysis to separate timescales. We proceed by analytically computing the Fourier transform of time-domain waveform through the stationary phase approximation. We show that the latter is valid for systems with small spins. Finally, we show that the…
We present a new method for extracting the instantaneous orbital axis only from gravitational wave strains of precessing binary systems observed from a particular observer direction. This method enables us to reconstruct the co-precessing frame waveforms only from observed quantities for the ideal case that the signal-to-noise ratio is high enough to analyze the waveforms directly. Specifically, we do not assume knowledge of the time evolution of the instantaneous orbital axis and the co-precessing waveforms before analyzing the data in our method. We test and measure the accuracy of our metho…
Horizon absorption in eccentric precessing binary black hole inspirals and its importance for gravitational wave data analysis
Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Atmospheric Research and Instrumentation Branch, National Institute for Aerospace Technology (INTA)（国家航空航天技术研究院大气研究与仪器分支）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理学研究所（爱因斯坦研究所））
Parity Violation in Spin-Precessing Binaries: Gravitational Waves from the Inspiral of Black Holes in Dynamical Chern-Simons Gravity
Illinois Center for Advanced Studies of the Universe, Department of Physics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系前沿宇宙学中心）；Dipartimento di Fisica, “Sapienza” Università di Roma & Sezione INFN Roma1（罗马第一大学物理系及INFN罗马第一分部）
We present the IMRPhenomXHM frequency domain phenomenological waveform model for the inspiral, merger and ringdown of quasi-circular non-precessing black hole binaries. The model extends the IMRPhenomXAS waveform model, which describes the dominant quadrupole modes $\ell = |m| = 2$, to the harmonics $(\ell, |m|)=(2,1), (3,3), (3,2), (4,4)$, and includes mode mixing effects for the $(3,2)$ spherical harmonic. IMRPhenomXHM is calibrated against hybrid waveforms, which match an inspiral phase described by the effective-one-body model and post-Newtonian amplitudes for the subdominant harmonics to …
Unified remnant models for aligned-spin, precessing, and eccentric binary black hole mergers
Kavli Institute for Theoretical Physics, University of California Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；Weinberg Institute, University of Texas at Austin（德克萨斯大学奥斯汀分校温伯格研究所）；Department of Physics and Institute for AI & Computational Research, University of Rhode Island（罗德岛大学物理与人工智能及计算研究院）；Department of Physics and Center for Scientific Computing & Data Science Research, University of Massachusetts, Dartmouth（马萨诸塞大学达特茅斯分校物理与科学计算及数据科学研究中心）
Binary systems of two compact objects circularize and spiral toward each other via the emission of gravitational waves. The coupling of the spins of each object with the orbital angular momentum causes the orbital plane to precess, which leads to modulation of the gravitational wave signal. Until now, generating frequency-domain waveforms for fully precessing systems for use in gravitational wave data analysis meant numerically integrating the equations of motion, then Fourier transforming the result, which is very computationally intensive for systems that complete hundreds or thousands of cy…
For black-hole binaries whose spins are (anti-) aligned with respect to the orbital angular momentum of the binary, we compute the frequency domain phasing coefficients including the quadratic-in-spin terms up to the third post-Newtonian (3PN) order, the cubic-in-spin terms at the leading order, 3.5PN, and the spin-orbit effects up to the 4PN order. In addition, we obtain the 2PN spin contributions to the amplitude of the frequency-domain gravitational waveforms for non-precessing binaries, using recently derived expressions for the time-domain polarization amplitudes of binaries with generic …
We present the first estimation of the mass and spin magnitude of Kerr black holes resulting from the coalescence of binary black holes using a deep neural network. The network is trained on a dataset containing 80\% of the full publicly available catalog of numerical simulations of gravitational waves emission by binary black hole systems, including full precession effects for spinning binaries. The network predicts the remnant black holes mass and spin with an error less than 0.04\% and 0.3\% respectively for 90\% of the values in the non-precessing test dataset, it is 0.1\% and 0.3\% respec…
We study precession dynamics of generic binary black holes in eccentric orbits using an effective potential based formalism derived in [M. Kesden et al., PRL {\bf 114}, 081103 (2015)]. This effective potential is used to classify binary black holes into three mutually exclusive spin morphologies. During the inspiral phase, binaries make transitions from one morphology to others. We evolve a population of binary black holes from an initial separation of $1000\mathbf{M}$ to a final separation of $10\mathbf{M}$ using post-Newtonian accurate evolution equations. We find that, given suitable initia…
Only numerical relativity simulations can capture the full complexities of binary black hole mergers. These simulations, however, are prohibitively expensive for direct data analysis applications such as parameter estimation. We present two new fast and accurate surrogate models for the outputs of these simulations: the first model, NRSur7dq4, predicts the gravitational waveform and the second model, \RemnantModel, predicts the properties of the remnant black hole. These models extend previous 7-dimensional, non-eccentric precessing models to higher mass ratios, and have been trained against 1…
Gravitational waves (GWs) emitted by generic black-hole binaries show a rich structure that directly reflects the complex dynamics introduced by the precession of the orbital plane, which poses a real challenge to the development of generic waveform models. Recent progress in modelling these signals relies on an approximate decoupling between the non-precessing secular inspiral and a precession-induced rotation. However, the latter depends in general on all physical parameters of the binary which makes modelling efforts as well as understanding parameter-estimation prospects prohibitively comp…
We compare the science capabilities of different eLISA mission designs, including four-link (two-arm) and six-link (three-arm) configurations with different arm lengths, low-frequency noise sensitivities and mission durations. For each of these configurations we consider a few representative massive black hole formation scenarios. These scenarios are chosen to explore two physical mechanisms that greatly affect eLISA rates, namely (i) black hole seeding, and (ii) the delays between the merger of two galaxies and the merger of the black holes hosted by those galaxies. We assess the eLISA parame…
The inspiral of binary black holes is governed by gravitational radiation reaction at binary separations r < 1000 M, yet it is too computationally expensive to begin numerical-relativity simulations with initial separations r > 10 M. Fortunately, binary evolution between these separations is well described by post-Newtonian equations of motion. We examine how this post-Newtonian evolution affects the distribution of spin orientations at separations r ~ 10 M where numerical-relativity simulations typically begin. Although isotropic spin distributions at r ~ 1000 M remain isotropic at r ~ 10 M, …
We consider the problem of searching for gravitational waves emitted during the inspiral phase of binary systems when the orbital plane precesses due to relativistic spin-orbit coupling. Such effect takes place when the spins of the binary members are misaligned with respect to the orbital angular momentum. As a first step we assess the importance of precession specifically for the first-generation of LIGO detectors. We investigate the extent of the signal-to-noise ratio reduction and, hence, detection rate that occurs when precession effects are not accounted for in the template waveforms. We…
Spin precession is a generic feature of compact binary coalescences, which leaves clear imprints in the gravitational waveforms. Building on previous work, we present an efficient time domain inspiral-merger-ringdown effective-one-body model (EOB) for precessing binary black holes, which incorporates subdominant modes beyond $\ell=2$, and the first EOB frequency domain approximant for precessing binary neutron stars. We validate our model against 99 ``short'' numerical relativity precessing waveforms, where we find median mismatches of $5\times 10^{-3}$, $7 \times 10^{-3}$ at inclinations of $…
The inspiral and merger of two orbiting black holes is among the most promising sources for the first (hopefully imminent) direct detection of gravitational waves (GWs), and measurements of these signals could provide a wealth of information about astrophysics, fundamental physics and cosmology. Detection and measurement require a theoretical description of the GW signals from all possible black-hole-binary configurations, which can include complicated precession effects due to the black-hole spins. Modelling the GW signal from generic precessing binaries is therefore one of the most urgent th…
We calculate the gravitational waveform for spinning, precessing compact binary inspirals through second post-Newtonian order in the amplitude. When spins are collinear with the orbital angular momentum and the orbits are quasi-circular, we further provide explicit expressions for the gravitational-wave polarizations and the decomposition into spin-weighted spherical-harmonic modes. Knowledge of the second post-Newtonian spin terms in the waveform could be used to improve the physical content of analytical templates for data analysis of compact binary inspirals and for more accurate comparison…
The detection of the gravitational waves (GWs) emitted by precessing binaries of spinning compact objects is complicated by the large number of parameters (such as the magnitudes and initial directions of the spins, and the position and orientation of the binary with respect to the detector) that are required to model accurately the precession-induced modulations of the GW signal. In this paper we describe a fast matched-filtering search scheme for precessing binaries, and we adopt the physical template family proposed by Buonanno, Chen, and Vallisneri [Phys.Rev.D 67, 104025 (2003)] for ground…
The construction of a model of the gravitational-wave (GW) signal from generic configurations of spinning-black-hole binaries, through inspiral, merger and ringdown, is one of the most pressing theoretical problems in the build-up to the era of GW astronomy. We present the first such model in the frequency domain, "PhenomP", which captures the basic phenomenology of the seven-dimensional parameter space of binary configurations with only three key physical parameters. Two of these (the binary's mass ratio and an effective total spin parallel to the orbital angular momentum, which determines th…
We present a new frequency-domain phenomenological model of the gravitational-wave signal from the inspiral, merger and ringdown of non-precessing (aligned-spin) black-hole binaries. The model is calibrated to 19 hybrid effective-one-body--numerical-relativity waveforms up to mass ratios of 1:18 and black-hole spins of $|a/m| \sim 0.85$ ($0.98$ for equal-mass systems). The inspiral part of the model consists of an extension of frequency-domain post-Newtonian expressions, using higher-order terms fit to the hybrids. The merger-ringdown is based on a phenomenological ansatz that has been signifi…
Gravitational waves from precessing binary black holes exhibit new features that are absent in non-precessionary systems. All current waveform models take into account only the modulation of the signal due to precession. In this letter, we find that this effect has its own signature, by gravitational emission of a short and transient signal, or burst. The frequency of the burst is comparable to that of the late stage of the inspiral. We show that under certain conditions, this signal is strong enough to be detected by Advanced LIGO. For third-generation detectors like the Einstein telescope, t…
Neutron star-black hole binaries are among the strongest sources of gravitational waves detectable by current observatories. They can also power bright electromagnetic signals (gamma-ray bursts, kilonovae), and may be a significant source of production of r-process nuclei. A misalignment of the black hole spin with respect to the orbital angular momentum leads to precession of that spin and of the orbital plane, and has a significant effect on the properties of the post-merger remnant and of the material ejected by the merger. We present a first set of simulations of precessing neutron star-bl…
Biased parameter inference of eccentric, spin-precessing binary black holes
Cardiff University（卡迪夫大学）；Indian Institute of Technology Madras（马德拉斯印度理工学院）；Penn State University（宾夕法尼亚州立大学）；Tata Institute of Fundamental Research（塔塔基础研究所）
In numerical evolutions of binary black holes (BBH) it is desirable to easily control the orbital eccentricity of the BBH, and the number of orbits completed by the binary through merger. This paper presents fitting formulae that allow to choose initial-data parameters for generic precessing BBH resulting in an orbital eccentricity $\sim 10^{-4}$, and that allow to predict the number of orbits to merger. We further demonstrate how these fits can be used to choose initial-data parameters of desired non-zero eccentricity. For both usage scenarios, no costly exploratory BBH evolutions are necessa…
