After eleven gravitational-wave detections from compact-binary mergers, we are yet to observe the striking general-relativistic phenomenon of orbital precession. Measurements of precession would provide valuable insights into the distribution of black-hole spins, and therefore into astrophysical binary formation mechanisms. Using our recent two-harmonic approximation of precessing-binary signals~\cite{Fairhurst:2019_2harm}, we introduce the ``precession signal-to-noise ratio'', $ρ_p$. We demonstrate that this can be used to clearly identify whether precession was measured in an observation (by comparison with both current detections and simulated signals), and can immediately quantify the measurability of precession in a given signal, which currently requires computationally expensive parameter-estimation studies. $ρ_p$ has numerous potential applications to signal searches, source-property measurements, and population studies. We give one example: assuming one possible astrophysical spin distribution, we predict that precession has a one in $\sim 25$ chance of being observed in any detection.
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…
We present IMRPhenomXPHM, a phenomenological frequency-domain model for the gravitational-wave signal emitted by quasi-circular precessing binary black holes, which incorporates multipoles beyond the dominant quadrupole in the precessing frame. The model is a precessing extension of IMRPhenomXHM (García-Quirós 2020), based on approximate maps between aligned-spin waveform modes in the co-precessing frame and precessing waveform modes in the inertial frame, which is commonly referred to as "twisting up" the non-precessing waveforms. IMRPhenomXPHM includes IMRPhenomXP as a special case, the rest…
The current paradigm for constructing waveforms from precessing compact binaries is to first construct a waveform in a non-inertial, co-precessing binary source frame followed by a time-dependent rotation to map back to the physical, inertial frame. A key insight in the construction of these models is that the co-precessing waveform can be effectively mapped to some equivalent aligned spin waveform. Secondly, the time-dependent rotation implicitly introduces $m$-mode mixing, necessitating an accurate description of higher-order modes in the co-precessing frame. We assess the efficacy of this m…
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…
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…
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) formalis…
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…
When two black holes merge, a tremendous amount of energy is released in the form of gravitational radiation in a short span of time, making such events among the most luminous phenomenon in the universe. Models that predict the peak luminosity of black hole mergers are of interest to the gravitational wave community, with potential applications in tests of general relativity. We present a surrogate model for the peak luminosity that is directly trained on numerical relativity simulations of precessing binary black holes. Using Gaussian process regression, we interpolate the peak luminosity in…
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 …
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-…
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…
In Ref. [1], the properties of the first gravitational wave detected by LIGO, GW150914, were measured by employing an effective-one-body (EOB) model of precessing binary black holes whose underlying dynamics and waveforms were calibrated to numerical-relativity (NR) simulations. Here, we perform the first extensive comparison of such EOBNR model to 70 precessing NR waveforms that span mass ratios from 1 to 5, dimensionless spin magnitudes up to 0.5, generic spin orientations, and length of about 20 orbits. We work in the observer's inertial frame and include all $\ell=2$ modes in the gravitati…
In this work we present IMRPhenomTP, a time domain phenomenological model for the dominant $l=2$, $m=|2|$ modes of coalescing black hole binary systems and its extension to describe general precessing systems within the "twisting up" approximation. The underlying non-precessing model is calibrated to the new release of Numerical Relativity simulations of the SXS Collaboration and its accuracy is comparable to the state-of-the-art non-precessing dominant mode models as IMRPhenomX and SEOBNRv4. The precessing extension allows for flexibility choosing the Euler angles of the time-dependent rotati…
Rapid localization of gravitational-wave events is important for the success of the multi-messenger observations. The forthcoming improvements and constructions of gravitational-wave detectors will enable detecting and localizing compact-binary coalescence events even before mergers, which is called early warning. The performance of early warning can be improved by considering modulation of gravitational wave signal amplitude due to the Earth rotation and the precession of a binary orbital plane caused by the misaligned spins of compact objects. In this paper, for the first time we estimate lo…
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…
The aftermath of binary black hole coalescence is a perturbed remnant whose gravitational radiation rings down, encoding information about the new black hole's recent history and current state.It is expected that this ringdown radiation will be composed primarily of Kerr quasinormal modes, and thereby enable tests of general relativity.Here, the first complete ringdown signal model for nonprecessing binary black hole systems is presented: multipole amplitudes and phases are modeled as functions of initial binary parameters. It is found that using the peak time of the dominant merger multipole …
The properties of compact binaries, such as masses and spins, are imprinted in the gravitational-waves they emit and can be measured using parameterised waveform models. Accurately and efficiently describing the complicated precessional dynamics of the various angular momenta of the system in these waveform models is the object of active investigation. One of the key models extensively used in the analysis of LIGO and Virgo data is the single-precessing-spin waveform model IMRPhenomPv2. In this article we present a new model IMRPhenomPv3 which includes the effects of two independent spins in t…
Extending prior work by Pankow et al, we introduce RIFT, an algorithm to perform Rapid parameter Inference on gravitational wave sources via Iterative Fitting. We demonstrate this approach can correctly recover the parameters of coalescing compact binary systems, using detailed comparisons of RIFT to the well-tested LALInference software library. We provide several examples where the unique speed and flexibility of RIFT enables otherwise intractable or awkward parameter inference analyses, including (a) adopting either costly and novel models for outgoing gravitational waves; and (b) mixed app…
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 present a public catalogue of numerical-relativity binary-black-hole simulations. The catalogue contains datasets from 80 distinct configurations of precessing binary-black-hole systems, with mass ratios up to $m_2/m_1 = 8$, dimensionless spin magnitudes on the larger black hole up to $|\vec{S}_2|/m_2^2 = 0.8$ (the small black hole is non-spinning), and a range of five values of spin misalignment for each mass-ratio/spin combination. We discuss the physical properties of the configurations in our catalogue, and assess the accuracy of the initial configuration of each simulation and of the g…
We present IMRPhenomTPHM, a phenomenological model for the gravitational wave signals emitted by the coalescence of quasi-circular precessing binary black holes systems. The model is based on the "twisting up" approximation, which maps non-precessing signals to precessing ones in terms of a time dependent rotation described by three Euler angles, and which has been utilized in several frequency domain waveform models that have become standard tools in gravitational wave data analysis. Our model is however constructed in the time domain, which allows several improvements over the frequency doma…
In this work we present an extension of the time domain phenomenological model IMRPhenomT for gravitational wave signals from binary black hole coalescences to include subdominant harmonics, specifically the $(l=2, m=\pm 1)$, $(l=3, m=\pm 3)$, $(l=4, m=\pm 4)$ and $(l=5, m=\pm 5)$ spherical harmonics. We also improve our model for the dominant $(l=2, m=\pm 2)$ mode and discuss mode mixing for the $(l=3, m=\pm 2)$ mode. The model is calibrated to numerical relativity solutions of the full Einstein equations up to mass ratio 18, and to numerical solutions of the Teukolsky equations for higher ma…
We report a degeneracy between the gravitational-wave signals from quasi-circular precessing black-hole mergers and those from extremely eccentric mergers, namely head-on collisions. Performing model selection on numerically simulated signals of head-on collisions using models for quasi-circular binaries we find that, for signal-to-noise ratios of 15 and 25, typical of Advanced LIGO observations, head-on mergers with respective total masses of $M\in (125,300)M_\odot$ and $M\in (200,440)M_\odot$ would be identified as precessing quasi-circular intermediate-mass black hole binaries, located at a…
We present the first surrogate model for gravitational waveforms from the coalescence of precessing binary black holes. We call this surrogate model NRSur4d2s. Our methodology significantly extends recently introduced reduced-order and surrogate modeling techniques, and is capable of directly modeling numerical relativity waveforms without introducing phenomenological assumptions or approximations to general relativity. Motivated by GW150914, LIGO's first detection of gravitational waves from merging black holes, the model is built from a set of $276$ numerical relativity (NR) simulations with…
Universal phenomenological relations between spherical harmonic modes in non-precessing eccentric binary black hole merger waveforms
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）；Theoretical AstroPhysics Including Relativity and Cosmology, California Institute of Technology（加州理工学院理论天体物理学（含相对论与宇宙学）部门）；Department of Physics, University of California at Santa Barbara（加州大学圣塔芭芭拉分校物理系）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（印度塔塔基础研究院国际理论科学中心）
The properties of precessing, coalescing binary black holes are presently inferred through comparison with two approximate models of compact binary coalescence. In this work we show these two models often disagree substantially when binaries have modestly large spins ($a\gtrsim 0.4$) and modest mass ratios ($q\gtrsim 2$). We demonstrate these disagreements using standard figures of merit and the parameters inferred for recent detections of binary black holes. By comparing to numerical relativity, we confirm these disagreements reflect systematic errors. We provide concrete examples to demonstr…
Gravitational waves from a binary with a single dynamically significant spin, notably including precessing black hole-neutron star (BH-NS) binaries, let us constrain that binary's properties: the two masses and the dominant black hole spin. Based on a straightforward fourier transform of $h(t)$ enabled by the corotating frame, we show the Fisher matrix for precessing binaries can be well-approximated by an extremely simple semianalytic approximation. This approximation can be easily understood as a weighted average of independent information channels, each associated with one gravitational wav…
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…
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…
A catalog of long, eccentric and precessing binary black hole simulations from ICTS-TIFR
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（理论科学国际中心，塔塔基础研究所）；Institute for Gravitation and the Cosmos, The Pennsylvania State University（引力与宇宙学研究所，宾夕法尼亚州立大学）；Department of Astronomy and Astrophysics, Penn State University（天文学与天体物理学系，宾夕法尼亚州立大学）；Cornell Center for Astrophysics and Planetary Science, Cornell University（天体物理学与行星科学中心，康奈尔大学）；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））；Theoretical Astrophysics 350-17, California Institute of Technology（理论天体物理学 350-17，加州理工学院）
We derive the conservative secular evolution of precessing compact binaries to second post-Newtonian order accuracy, with leading-order spin-orbit, spin-spin and mass quadrupole-monopole contributions included. The emerging closed system of first-order differential equations evolves the pairs of polar and azimuthal angles of the spin and orbital angular momentum vectors together with the periastron angle. In contrast with the instantaneous dynamics, the secular dynamics is autonomous. This secular dynamics reliably characterizes the system over timescales starting from a few times the radial p…
We study the observable pulse profiles that can be generated from precessing pulsars. A novel coordinate system is defined to aid visualization of the observing geometry. Using this system we explore the different families of profiles that can be generated by simple, circularly symmetric beam shapes. An attempt is then made to fit our model to the observations of relativistic binary PSR B1913+16. It is found that while qualitatively similar pulse profiles can be produced, this minimal model is insufficient for an accurate match to the observational data. Consequently, we confirm that the emiss…
We use the open source, community-driven, numerical relativity software, the Einstein Toolkit to study the physics of eccentric, spinning, nonprecessing binary black hole mergers with mass-ratios $q=\{2, 4, 6\}$, individual dimensionless spin parameters $χ_{1z}=\pm0.6$, $χ_{2z}=\pm0.3$, that include higher order gravitational wave modes $\ell\leq4$, except for memory modes. Assuming stellar mass binary black hole mergers that may be detectable by the advanced LIGO detectors, we find that including modes up to $\ell=4$ increases the signal-to-noise of compact binaries between $3.5\%$ to $35\%$,…
We briefly discuss a method to construct a global, analytic, approximate spacetime for precessing, spinning binary black holes. The spacetime construction is broken into three parts: the inner zones are the spacetimes close to each black hole, and are approximated by perturbed Kerr solutions; the near zone is far from the two black holes, and described by the post-Newtonian metric; and finally the wave (far) zone, where retardation effects need to be taken into account, is well modeled by the post-Minkowskian metric. These individual spacetimes are then stitched together using asymptotic match…
We demonstrate the implementation of a sensitive search pipeline for gravitational waves from coalescing binary black holes whose components have spins aligned with the orbital angular momentum. We study the pipeline recovery of simulated gravitational wave signals from aligned-spin binary black holes added to real detector noise, comparing the pipeline performance with aligned-spin filter templates to the same pipeline with non-spinning filter templates. Our results exploit a three-parameter phenomenological waveform family that models the full inspiral-merger-ringdown coalescence and treats …
Ground-based gravitational wave detectors are sensitive to a narrow range of frequencies, effectively taking a snapshot of merging compact-object binary dynamics just before merger. We demonstrate that by adopting analysis parameters that naturally characterize this 'picture', the physical parameters of the system can be extracted more efficiently from the gravitational wave data, and interpreted more easily. We assess the performance of MCMC parameter estimation in this physically intuitive coordinate system, defined by (a) a frame anchored on the binary's spins and orbital angular momentum a…
We present PhenomPNR, a frequency-domain phenomenological model of the gravitational-wave (GW) signal from binary-black-hole mergers that is tuned to numerical relativity (NR) simulations of precessing binaries. In many current waveform models, e.g., the "Phenom" and "EOBNR" families that have been used extensively to analyse LIGO-Virgo GW observations, analytic approximations are used to add precession effects to models of non-precessing (aligned-spin) binaries, and it is only the aligned-spin models that are fully tuned to NR results. In PhenomPNR we incorporate precessing-binary NR results …
Estimates of the source parameters of gravitational-wave (GW) events produced by compact binary mergers rely on theoretical models for the GW signal. We present the first frequency-domain model for inspiral, merger and ringdown of the GW signal from precessing binary-black-hole systems that also includes multipoles beyond the leading-order quadrupole. Our model, {\tt PhenomPv3HM}, is a combination of the higher-multipole non-precessing model {\tt PhenomHM} and the spin-precessing model {\tt PhenomPv3} that includes two-spin precession via a dynamical rotation of the GW multipoles. We validate …
We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass monopole/spin-induced quadrupole interaction terms. In the case of both quasi-circular and eccentric orbits, we search for the presence of chaos (using the method of Lyapunov exponents) for a large variety of initial conditions. For quasi-circular orbits, we find no chaotic behavior for black holes with total mass 10 - 40 solar masses when initially at a separation cor…
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 …
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 $…
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…
Since gravitational and electromagnetic waves from a compact binary coalescence carry independent information about the source, the joint observation is important for understanding the physical mechanisms of the emissions. Rapid detection and source localization of a gravitational wave signal are crucial for the joint observation to be successful. For a signal with a high signal-to-noise ratio, it is even possible to detect it before the merger, which is called early warning. In this letter, we estimate the performances of the early warning for neutron-star black-hole binaries, considering the…
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）
Binary-black-hole orbits precess when the black-hole spins are mis-aligned with the binary's orbital angular momentum. The apparently complicated dynamics can in most cases be described as simple precession of the orbital angular momentum about an approximately fixed total angular momentum. However, the imprint of the precession on the observed gravitational-wave signal is yet more complicated, with a non-trivial time-varying dependence on black-hole dynamics, the binary's orientation and the detector polarization. As a result, it is difficult to predict under which conditions precession effec…
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 precessio…
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 BB…
