The production of numerical relativity waveforms that describe quasicircular binary black hole mergers requires high-quality initial data, and an algorithm to iteratively reduce residual eccentricity. To date, these tools remain closed source, or in commercial software that prevents their use in high performance computing platforms. To address these limitations, and to ensure that the broader numerical relativity community has access to these tools, herein we provide all the required elements to produce high-quality numerical relativity simulations in supercomputer platforms, namely: open source parameter files to numerical simulate spinning black hole binaries with asymmetric mass-ratios; open source $\texttt{Python}$ tools to produce high-quality initial data for numerical relativity simulations of spinning black hole binaries on quasi-circular orbits; open source $\texttt{Python}$ tools for eccentricity reduction, both as stand-alone software and deployed in the $\texttt{Einstein Toolkit}$'s software infrastructure. This open source toolkit fills in a critical void in the literature at a time when numerical relativity has an ever increasing role in the study and interpretation of gravitational wave sources. As part of our community building efforts, and to streamline and accelerate the use of these resources, we provide tutorials that describe, step by step, how to obtain and use these open source numerical relativity tools.
The relevance of orbital eccentricity in the detection of gravitational radiation from (steady state) binary stars is emphasized. Computationnally effective fast and accurate)tools for constructing gravitational wave templates from binary stars with any orbital eccentricity are introduced, including tight estimation criteria of the pertinent truncation and approximation errors.
Post-Newtonian theory-inspired framework for characterizing eccentricity in gravitational 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））；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（塔塔基础研究院国际理论科学中心）
Large-Eccentricity Asymptotics and Fast Analytic Approximation for Fourier modes of Post-Newtonian Eccentric Waveforms
Instituto de Física Téorica UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Beijing Normal University（北京师范大学）；Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院）
Although the gravitational waves observed by advanced LIGO and Virgo are consistent with compact binaries in a quasi-circular inspiral prior to coalescence, eccentric inspirals are also expected to occur in Nature. Due to their complexity, we currently lack ready-to-use, analytic waveforms in the Fourier domain valid for sufficiently high eccentricity, and such models are crucial to coherently extract weak signals from the noise. We here take the first steps to derive and properly validate an analytic waveform model in the Fourier domain that is valid for inspirals of arbitrary orbital eccentr…
While current gravitational wave observations with ground based detectors have been consistent with compact binaries in quasi-circular orbits, eccentric binaries may be detectable by ground-based and space-based instruments in the near future. Eccentricity significantly complicates the gravitational wave signal, and we currently lack fast and accurate models that are valid in the moderate to large eccentricity range. In a previous paper, we built a Fourier domain, eccentric waveform model at leading order in the post-Newtonian approximation, i.e. as an expansion in small velocities and weak fi…
Measuring Eccentricity and Addressing Waveform Systematics in GW231123
Center for Gravitational Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校引力物理中心）；Center for Computational Relativity and Gravitation, Rochester Institute of Technology（罗切斯特理工学院计算相对论与引力中心）
Orbital eccentricity is a key signature of dynamical binary black hole formation. The gravitational waves from a coalescing binary contain information about its orbital eccentricity, which may be measured if the binary retains sufficient eccentricity near merger. Dedicated waveforms are required to measure eccentricity. Several models have been put forward, and show good agreement with numerical relativity at the level of a few percent or better. However, there are multiple ways to define eccentricity for inspiralling systems, and different models internally use different definitions of eccent…
In this paper, we estimate the eccentricity of the 10 BBHs in GWTC-1 by using the inspiral-only BBH waveform template EccentricFD. Firstly, we test our method with simulated eccentric BBHs. Afterwards we apply the method to the real BBH gravitational wave data. We find that the BBHs in GWTC-1 except GW151226, GW170608 and GW170729 admit very small eccentricity. Their upper limits on eccentricity range from 0.033 to 0.084 with 90% credible interval at the reference frequency 10 Hz. For GW151226, GW170608 and GW170729, the upper limits are higher than 0.1. The relatively large eccentricity of GW…
The detection of gravitational-wave signals from coalescing eccentric binary black holes would yield unprecedented information about the formation and evolution of compact binaries in specific scenarios, such as dynamical formation in dense stellar clusters and three-body interactions. The gravitational-wave searches by the ground-based interferometers, LIGO and Virgo, rely on analytical waveform models for binaries on quasicircular orbits. Eccentric merger waveform models are less developed, and only few numerical simulations of eccentric mergers are publicly available, but several eccentric …
While most binary inspirals are expected to have circularized before they enter the LIGO/Virgo frequency band, a small fraction of those binaries could have non-negligible orbital eccentricity depending on their formation channel. Hence, it is important to accurately model eccentricity effects in waveform models used to detect those binaries, infer their properties, and shed light on their astrophysical environment. We develop a multipolar effective-one-body (EOB) eccentric waveform model for compact binaries whose components have spins aligned or anti-aligned with the orbital angular momentum…
The inspiral and merger of supermassive black hole binary systems with high orbital eccentricity are among the promising sources of the advanced gravitational wave observatories. In this paper we derive analytic ready-to-use first post-Newtonian eccentric waveform in Fourier domain with the use of Hansen coefficients. Introducing generic perturbations of celestial mechanics we have generalized the Hansen expansion to the first post-Newtonian order which are then used to express the waveforms. Taking into account the high eccentricity of the orbit leads to the appearance of secular terms in the…
Compact binary systems with black holes are the primary sources of interferometric advanced gravitational wave detectors. Astrophysical models suggest finite possibility of binary systems with appreciable non-zero eccentricity in the dense stellar environment like globular clusters and galactic nuclei. While most of the compact binary measurements have not shown appreciable eccentricity, constrains on the eccentricity have been placed on few detected events. With increasing sensitivity of the gravitational wave detectors, the eccentric binaries are plausible sources in the gravitational wave w…
Revisiting the Coprecessing Frame in the Presence of Orbital Eccentricity
California Institute of Technology（加州理工学院）；LIGO Laboratory, California Institute of Technology（LIGO实验室，加州理工学院）；Department of Physics & Astronomy, Amherst College（阿默斯特学院物理与天文系）；Cornell Center for Astrophysics and Planetary Science, Cornell University（康奈尔大学天体物理学与行星科学中心）
The origin and formation of stellar-mass binary black holes remains an open question that can be addressed by precise measurements of the binary and orbital parameters from their gravitational-wave signal. Such binaries are expected to circularize due to the emission of gravitational waves as they approach merger. However, depending on their formation channel, some binaries could have a non-negligible eccentricity when entering the frequency band of current gravitational-wave detectors. In order to measure eccentricity in an observed gravitational-wave signal, accurate waveform models that des…
Binary black hole systems are among the most important sources for gravitational wave detection. And also they are good objects for theoretical research for general relativity. Gravitational waveform template is important to data analysis. Effective-one-body-numerical-relativity (EOBNR) model has played an essential role in the LIGO data analysis. For future space-based gravitational wave detection, many binary systems will admit somewhat orbit eccentricity. At the same time the eccentric binary is also an interesting topic for theoretical study in general relativity. In this paper we construc…
Effective-one-body waveforms for extreme-mass-ratio binaries: Consistency with second-order gravitational self-force quasicircular results and extension to nonprecessing spins and eccentricity
We build two families of inspiral waveforms for precessing binaries on eccentric orbits in the Fourier domain. To achieve this, we use a small eccentricity expansion of the waveform amplitudes in order to separate the periastron precession timescale from the orbital timescale, and use a shifted uniform asymptotics transformation to compute the Fourier transform in the presence of spin-induced precession. We show that the resulting waveforms can yield a median faithfulness above 0.993 when compared to an equivalent time domain waveform with an initial eccentricity of $e_0 \approx 0.3$. We also …
The detection of ~50 coalescing compact binaries with the Advanced LIGO and Virgo detectors has allowed us to test general relativity, constrain merger rates, and look for evidence of tidal effects, compact object spins, higher waveform modes, and black hole ringdowns. An effect that has not yet been confidently detected is binary eccentricity, which might be present in a small fraction of binaries formed dynamically. Here we discuss general limits on eccentricity that can, in-principle, be placed on all types of compact object binaries by a detector operating at the design sensitivity of Adva…
Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this proves to be a real eccentricity, it could affect the fine details of the subsequent numerical evolutions and the predicted gravitational waveforms.
Parameter estimation for the GWTC-4.0 catalog with phenomenological waveform models that include orbital eccentricity and an updated description of spin precession
Universitat de les Illes Balears（巴利阿里群岛大学）；Institut de Ciències de l’Espai (ICE, CSIC)（空间科学研究所）
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 $35\%$,…
Testing the nature of GW200105 by probing the frequency evolution of eccentricity
Inter-University Centre for Astronomy and Astrophysics（大学天文与天体物理中心）；Department of Physics, Vivekananda Satavarshiki Mahavidyalaya (affiliated to Vidyasagar University)（维韦卡南达萨塔瓦尔希基学院物理系（隶属维迪亚萨加尔大学））
The rotation of the bodies and the eccentricity of the orbit have significant effects on the emitted gravitational radiation of binary systems. This work focuses on the evaluation of the gravitational wave polarization states for spinning compact binaries. We consider binaries on eccentric orbits and the spin-orbit interaction up to the 1.5 post-Newtonian order in a way which is independent of the parameterization of the orbit. The equations of motion for angular variables are included. The formal expressions of the polarization states are given with the inclusion of higher order corrections t…
Eccentric and unbound compact binaries in the LIGO-Virgo-KAGRA catalog: parameter estimation and waveform systematics with SEOBNRv6EHM
University of Nottingham（诺丁汉大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（阿尔伯特·爱因斯坦研究所））；University of Maryland（马里兰大学）
The origin of black hole mergers discovered by the LIGO and Virgo gravitational-wave observatories is currently unknown. GW190521 is the heaviest black hole merger detected so far. Its observed high mass and possible spin-induced orbital precession could arise from the binary having formed following a close encounter. An observational signature of close encounters is eccentric binary orbit; however, this feature is currently difficult to identify due to the lack of suitable gravitational waveforms. No eccentric merger has been previously found. Here we report 611 numerical relativity simulatio…
The Cost of Circularity: Quantifying Eccentricity-Induced Biases in Binary Black Hole Inference
University of Wisconsin–Milwaukee（威斯康星大学密尔沃基分校）；The Pennsylvania State University（宾夕法尼亚州立大学）；University of California, Berkeley（加州大学伯克利分校）；University of Florida（佛罗里达大学）
Building upon recent work, we present an improved effective-one-body (EOB) model for spin-aligned, coalescing, black hole binaries with generic orbital configurations, i.e. quasi-circular, eccentric or hyperbolic orbits. The model relies on the idea of incorporating general Newtonian prefactors, instead of the usual quasi-circular ones, in both radiation reaction and waveform. The major advance with respect to previous work is that the quasi-circular limit of the model is now correctly informed by numerical relativity (NR) quasi-circular simulation. This provides EOB/NR unfaithfulness for the …
Toward a complete understanding of the properties of GW190521
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；California Institute of Technology（加州理工学院）；LIGO Laboratory（LIGO实验室）；Rochester Institute of Technology（罗切斯特理工学院）
One of the promising sources of gravitational radiation is a binary system composed of compact stars. It is an important question how the rotation of the bodies and the eccentricity of the orbit affect the detectable signal. Here we present a method to evaluate the gravitational wave polarization states for inspiralling compact binaries with comparable mass. We consider eccentric orbits and the spin-orbit contribution in the case of one spinning object up to 1.5 post-Newtonian order. For circular orbits our results are in agreement with existing calculations.
We integrate the third and a half post-Newtonian equations of motion for a fully generic binary black hole system, allowing both for non-circular orbits, and for one or both of the black holes to spin, in any orientation. Using the second post-Newtonian order expression beyond the leading order quadrupole formula, we study the gravitational waveforms produced from such systems. Our results are validated by comparing to Taylor T4 in the aligned-spin circular cases, and the additional effects and modulations introduced by the eccentricity and the spins are analyzed. We use the framework to evalu…
Gravitational waves emitted by inner binaries in hierarchical triple systems are interesting astrophysical candidates for space-based detectors like the Laser Interferometer Space Antenna, LISA. In the presence of a third body, such as a supermassive black hole, an inner binary consisting of intermediate mass black holes can undergo oscillations in eccentricity and inclination angle due to the Kozai-Lidov mechanism. In this work, we construct analytic gravitational waveforms in the Fourier domain, taking into account the Kozai-Lidov effect at Newtonian (leading) order. Using multiple-scale ana…
Compact binaries that emit gravitational waves in the sensitivity band of ground-based detectors can have non-negligible eccentricities just prior to merger, depending on the formation scenario. We develop a purely analytic, frequency-domain model for gravitational waves emitted by compact binaries on orbits with small eccentricity, which reduces to the quasi-circular post-Newtonian approximant TaylorF2 at zero eccentricity and to the post-circular approximation of Yunes et al. (2009) at small eccentricity. Our model uses a spectral approximation to the (post-Newtonian) Kepler problem to model…
We lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waveforms produced by eccentric, inspiraling compact binaries in a post-circular or small-eccentricity approximation. The time-dependent, "plus" and "cross" polarizations are expanded in Bessel functions, which are then self-consistently re-expanded in a power series about zero initial eccentricity to eighth order. The stationary phase approximation is then employed to obtain explicit analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify …
We construct an inspiral-merger-ringdown eccentric gravitational-wave (GW) model for binary black holes with non-precessing spins within the effective-one-body formalism. This waveform model, SEOBNRv4EHM, extends the accurate quasi-circular SEOBNRv4HM model to eccentric binaries by including recently computed eccentric corrections up to 2PN order in the gravitational waveform modes, notably the $(l,|m|)=(2,2),(2,1),(3,3),(4,4),(5,5)$ multipoles. The waveform model reproduces the zero eccentricity limit with an accuracy comparable to the underlying quasi-circular model, with the unfaithfulness …
The space-based detector LISA may observe gravitational waves from the early inspiral of stellar-mass black hole binaries, some of which could have significant eccentricity. Current gravitational waveform templates are only valid for small orbital velocities (i.e., in a post-Newtonian expansion) and small initial eccentricity $e_0$ ("post-circular" expansion). We conventionally define $e_0$ as the eccentricity corresponding to an orbital frequency of $5 \text{ mHz}$, and we study the convergence properties of frequency-domain inspiral templates that are accurate up to 2PN and order $e_0^6$ in …
Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data cl…
The possible formation of stellar-mass binary black holes through dynamical interactions in dense stellar environments predicts the existence of binaries with non-negligible eccentricity in the frequency band of ground-based gravitational wave detectors; the detection of binary black hole mergers with measurable orbital eccentricity would validate the existence of this formation channel. Waveform templates currently used in the matched-filter gravitational-wave searches of LIGO-Virgo data neglect effects of eccentricity which is expected to reduce their efficiency to detect eccentric binary bl…
Several scenarios have been proposed in which the orbits of binary black holes enter the band of a gravitational wave detector with significant eccentricity. To avoid missing these signals or biasing parameter estimation it is important that we consider waveform models that account for eccentricity. The ingredients needed to compute post-Newtonian (PN) waveforms produced by spinning black holes inspiralling on quasi-eccentric orbits have been available for almost two decades at 2 PN order, and this work has recently been extended to 2.5 PN order. However, the computational cost of directly imp…
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 …
