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 modelling strategy in the strong field regime using Numerical Relativity simulations. We find that this framework allows for the highly accurate construction of $(2,\pm 2)$ modes in our data set, while for higher order modes, especially the $(2,|1|), (3,|2|)$ and $(4,|3|)$ modes, we find rather large mismatches. We also investigate a variant of the approximate map between co-precessing and aligned spin waveforms, where we only identify the slowly varying part of the time domain co-precessing waveforms with the aligned-spin one, but find no significant improvement. Our results indicate that the simple paradigm to construct precessing waveforms does not provide an accurate description of higher order modes in the strong-field regime, and demonstrate the necessity for modelling mode asymmetries and mode-mixing to significantly improve the description of precessing higher order modes.
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 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…
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 construct a closed-form, fully analytical 4-metric that approximately represents the spacetime evolution of non-precessing, spinning black hole binaries from infinite separations up to a few orbits prior to merger. We employ the technique of asymptotic matching to join a perturbed Kerr metric in the neighborhood of each spinning black hole to a near-zone, post-Newtonian metric farther out. The latter is already naturally matched to a far-zone, post-Minkowskian metric that accounts for full temporal retardation. The result is a 4-metric that is approximately valid everywhere in space and in …
Modelling the end point of binary black hole mergers is a cornerstone of modern gravitational-wave astronomy. Extracting multiple quasinormal mode frequencies from the ringdown signal allows the remnant black hole to be studied in unprecedented detail. Previous studies on numerical relativity simulations of aligned-spin binaries have found that it is possible to start the ringdown analysis much earlier than previously thought if overtones (and possibly mirror modes) are included. This increases the signal-to-noise ratio in the ringdown making identification of subdominant modes easier. In this…
Morphology of coalescing BBH waveforms are affected by its spins. Waveform models built for inference of source parameters have several in-built approximations. In current precessing IMRPhenom and SEOBNR waveform models, systems with the same spin magnitude but varying orientation of spins projected on the orbital plane are effectively mapped to the same system (bar an overall phase change) and the asymmetry due to precession between the $+m$ and $-m$ modes is not modelled. In this study, we investigate the validity of these approximations by generating numerical relativity (NR) simulations of…
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）
In this paper we discuss the anatomy of frequency-domain gravitational-wave signals from non-precessing black-hole coalescences with the goal of constructing accurate phenomenological waveform models. We first present new numerical-relativity simulations for mass ratios up to 18 including spins. From a comparison of different post-Newtonian approximants with numerical-relativity data we select the uncalibrated SEOBNRv2 model as the most appropriate for the purpose of constructing hybrid post-Newtonian/numerical-relativity waveforms, and we discuss how we prepare time-domain and frequency-domai…
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 High-Mass-Ratio Challenge in Gravitational Waveform Modelling
School of Physics and Astronomy, Cardiff University（卡迪夫大学物理与天文学院）；Mathematical Sciences & STAG Research Centre, University of Southampton（南安普顿大学数学科学与STAG研究中心）
Previous analytic and numerical calculations suggest that, at each instant, the emission from a precessing black hole binary closely resembles the emission from a nonprecessing analog. In this paper we quantitatively explore the validity and limitations of that correspondence, extracting the radiation from a large collection of roughly two hundred generic black hole binary merger simulations both in the simulation frame and in a corotating frame that tracks precession. To a first approximation, the corotating-frame waveforms resemble nonprecessing analogs, based on similarity over a band-limit…
The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The go…
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）
Gravitational waves from the coalescences of black hole and neutron stars afford us the unique opportunity to determine the sources' properties, such as their masses and spins, with unprecedented accuracy. To do so, however, theoretical models of the emitted signal that are i) extremely accurate and ii) computationally highly efficient are necessary. The inclusion of more detailed physics such as higher-order multipoles and relativistic spin-induced orbital precession increases the complexity and hence also computational cost of waveform models, which presents a severe bottleneck to the parame…
Analysis of GWTC-3 with fully precessing numerical relativity surrogate models
University of Massachusetts, Dartmouth（达特茅斯马萨诸塞大学）；The University of Auckland（奥克兰大学）；OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery（引力波发现ARC卓越中心）；University of Nevada, Las Vegas（内华达大学拉斯维加斯分校）；Nevada Center for Astrophysics（内华达天体物理学中心）；LIGO Laboratory, Massachusetts Institute of Technology（麻省理工学院LIGO实验室）；Massachusetts Institute of Technology（麻省理工学院）；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））
Gravitational-wave signals from black-hole binaries with non-precessing spins are described by four parameters -- each black hole's mass and spin. It has been shown that the dominant spin effects can be modeled by a \emph{single} spin parameter, leading to the development of several \emph{three-parameter} waveform models. Previous studies indicate that these models should be adequate for gravitational-wave detection. In this paper we focus on the systematic biases that would result from using them to estimate binary parameters, and consider a one-parameter family of configurations at one choic…
Accurately modelling the complete gravitational-wave signal from precessing binary black holes through the late inspiral, merger and ringdown remains a challenging problem. The lack of analytic solutions for the precession dynamics of generic double-spin systems, and the high dimensionality of the problem, obfuscate the incorporation of strong-field spin-precession information into semi-analytic waveform models used in gravitational-wave data analysis. Previously, an effective precession spin, $χ_p$, was introduced to reduce the number of spin degrees of freedom. Here, we show that $χ_p$ alone…
National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校国家超级计算应用中心）；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）；Department of Astronomy, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校天文学系）；Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校电气与计算机工程系）
The spin distribution of binary black hole mergers contains key information concerning the formation channels of these objects, and the astrophysical environments where they form, evolve and coalesce. To quantify the suitability of deep learning to characterize the signal manifold of quasi-circular, spinning, non-precessing binary black hole mergers, we introduce a modified version of WaveNet trained with a novel optimization scheme that incorporates general relativistic constraints of the spin properties of astrophysical black holes. The neural network model is trained, validated and tested w…
We present a simple method to track the precession of a black-hole-binary system, using only information from the gravitational-wave (GW) signal. Our method consists of locating the frame from which the magnitude of the $(\ell=2,|m|=2)$ modes is maximized, which we denote the "quadrupole-aligned" frame. We demonstrate the efficacy of this method when applied to waveforms from numerical simulations. In the test case of an equal-mass nonspinning binary, our method locates the direction of the orbital angular momentum to within $(Δθ, Δϕ) = (0.05^{\circ},0.2^{\circ})$. We then apply the method to …
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 …
Fast gravitational waveform models for quasi-circular coalescences of neutron star--black hole binaries
Universitat de les Illes Balears（巴利阿里群岛大学）；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））；Universität Potsdam（波茨坦大学）；CNRS/IN2P3, Laboratoire de Physique Corpusculaire (LPC) UMR6534（法国国家科学研究中心/法国国家核与粒子物理研究所，核物理实验室）；University of Canterbury（坎特伯雷大学）
