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 mass ratios. This work complements the latest generation of traditional frequency domain phenomenological models (IMRPhenomX), and provides new avenues to develop computationally efficient models for gravitational wave signals from generic compact binaries.
Gravitational wave searches to date have largely focused on non-precessing systems. Including precession effects greatly increases the number of templates to be searched over. This leads to a corresponding increase in the computational cost and can increase the false alarm rate of a realistic search. On the other hand, there might be astrophysical systems that are entirely missed by non-precessing searches. In this paper we consider the problem of constructing a template bank using stochastic methods for neutron-star--black-hole binaries allowing for precession, but with the restrictions that …
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…
We investigate the use of particle swarm optimization (PSO) algorithm for detection of gravitational-wave signals from compact binary coalescences. We show that the PSO is fast and effective in searching for gravitational wave signals. The PSO-based aligned-spin coincident multi-detector search recovers appreciably more gravitational-wave signals, for a signal-to-noise ratio (SNR) of 10, the PSO based aligned-spin search recovers approximately 26 $\%$ more events as compared to the template bank searches. The PSO-based aligned-spin coincident search uses 48k matched-filtering operations, and p…
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 present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical-relativity simulations of spinning, non-precessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of 1000M, we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB (2,2) mode can…
Gravitational waveforms which describe the inspiral, merger and ringdown of coalescing binaries are usually constructed by synthesising information from perturbative descriptions, in particular post-Newtonian theory and black-hole perturbation theory, with numerical solutions of the full Einstein equations. In this paper we discuss the "glueing" of numerical and post-Newtonian waveforms to produce hybrid waveforms which include subdominant spherical harmonics ("higher order modes"), and focus in particular on the process of consistently aligning the waveforms, which requires a comparison of bo…
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 …
Intermediate mass ratio inspiral (IMRI) binaries -- containing stellar-mass black holes coalescing into intermediate-mass black holes ($M>100M_{\odot}$) -- are a highly anticipated source of gravitational waves (GWs) for Advanced LIGO/Virgo. Their detection and source characterization would provide a unique probe of strong-field gravity and stellar evolution. Due to the asymmetric component masses and the large primary, these systems generically excite subdominant modes while reducing the importance of the dominant quadrupole mode. Including higher order harmonics can also result in a $10\%-25…
In this paper we present a method for conducting a coherent search for single spin compact binary coalescences in gravitational wave data and compare this search to the existing coincidence method for single spin searches. We propose a method to characterize the regions of the parameter space where the single spin search, both coincident and coherent, will increase detection efficiency over the existing non-precessing search. We also show example results of the coherent search on a stretch of data from LIGO's fourth science run but note that a set of signal based vetoes will be needed before t…
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…
In this paper we present IMRPhenomXAS, a thorough overhaul of the IMRPhenomD [1,2] waveform model, which describes the dominant $l=2, \:| m | = 2$ spherical harmonic mode of non-precessing coalescing black holes in terms of piecewise closed form expressions in the frequency domain. Improvements include in particular the accurate treatment of unequal spin effects, and the inclusion of extreme mass ratio waveforms. IMRPhenomD has previously been extended to approximately include spin precession [3] and subdominant spherical harmonics [4], and with its extensions it has become a standard tool in …
The ringdown is the late part of the post-merger signature emitted during the coalescence of two black holes and comprises of a superposition of quasi-normal-modes. Within general relativity, because of the no-hair theorems, the frequencies and damping times of these modes are entirely determined by the mass and angular momentum of the final Kerr black hole. A detection of multiple ringdown modes would potentially allow us to test the no-hair theorem from observational data. The parameters which determine whether sub-dominant ringdown modes can be detected are primarily the overall signal-to-n…
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…
We consider the ten confidently detected gravitational-wave signals in the GWTC-1 catalog which are consistent with mergers of binary black hole systems, and perform a thorough parameter estimation re-analysis. This is made possible by using computationally efficient waveform models of the current (fourth) generation of the IMRPhenom family of phenomenological waveform models, which consists of the IMRPhenomX frequency-domain modelsand the IMRPhenomT time-domain models. The analysis is performed with both precessing and non-precessing waveform models with and without subdominant spherical harm…
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 $…
Testing general relativity with amplitudes of subdominant gravitational-wave modes
University of California, Berkeley（加州大学伯克利分校）；Northwestern University（西北大学）；Pennsylvania State University（宾夕法尼亚州立大学）；The University of Mississippi（密西西比大学）；King’s College London（伦敦国王学院）；University of Zürich（苏黎世大学）
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…
Recent years have witnessed tremendous progress in numerical relativity and an ever improving performance of ground-based interferometric gravitational wave detectors. In preparation for Advanced LIGO and a new era in gravitational wave astronomy, the numerical relativity and gravitational wave data analysis communities are collaborating to ascertain the most useful role for numerical relativity waveforms in the detection and characterization of binary black hole coalescences. In this paper, we explore the detectability of equal mass, merging black hole binaries with precessing spins and total…
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…
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,…
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 …
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…
NRSur7dq4v2: A multi-domain precessing surrogate model with improved accuracy
University of Massachusetts, Dartmouth（麻省大学达特茅斯分校）；Cornell University（康奈尔大学）；The University of Mississippi（密西西比大学）；California Institute of Technology（加州理工学院）
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…
We generalize the factorized resummation of multipolar waveforms introduced by Damour, Iyer and Nagar to spinning black holes. For a nonspinning test-particle spiraling a Kerr black hole in the equatorial plane, we find that factorized multipolar amplitudes which replace the residual relativistic amplitude f_{l m} with its l-th root, ρ_{l m} = f_{l m}^{1/l}, agree quite well with the numerical amplitudes up to the Kerr-spin value q \leq 0.95 for orbital velocities v \leq 0.4. The numerical amplitudes are computed solving the Teukolsky equation with a spectral code. The agreement for prograde o…
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…
The inspiral and merger of black-hole binary systems are a promising source of gravitational waves. The most effective method to look for a signal with a well understood waveform, such as the binary black hole signal, is matched filtering against a library of model waveforms. Current model waveforms are comprised solely of the dominant radiation mode, the quadrupole mode, although it is known that there can be significant power in the higher-order modes. The binary black hole waveforms produced by numerical relativity are accurate through late inspiral, merger, and ringdown and include the hig…
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…
Searches for gravitational-wave transients from binary black hole coalescences typically rely on one of two approaches: matched filtering with templates and morphology-independent excess power searches. Multiple algorithmic implementations in the analysis of data from the first generation of ground-based gravitational wave interferometers have used different strategies for the suppression of non-Gaussian noise transients, and targeted different regions of the binary black hole parameter space. In this paper we compare the sensitivity of three such algorithms: matched filtering with full coales…
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…
Astrophysical black holes could be nearly extremal (that is, rotating nearly as fast as possible); therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass $m$ and spin $S$ exceeding the Bowen-York limit of $S/m^2=0.93$. We present improved methods that enable us to simulate merging, nearly extremal black holes more robustly an…
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 …
We re-analyse the gravitational-wave event GW190412 with state-of-the-art phenomenological waveform models. This event, which has been associated with a black hole merger, is interesting due to the significant contribution from subdominant harmonics. We use both frequency-domain and time-domain waveform models. The PhenomX waveform models constitute the fourth generation of frequency-domain phenomenological waveforms for black hole binary coalescence; they have more recently been complemented by the time-domain PhenomT models, which open up new strategies to model precession and eccentricity, …
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…
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…
Matched filtering is a popular data analysis framework used to search for gravitational wave signals emitted by compact object binaries. The templates used in matched filtering searches are constructed predominantly from the quadrupolar mode because this mode is the energetically most dominant channel. However, for highly precessing binaries or binaries with moderately large mass ratios, significant power is also carried by higher-order modes. We investigate how the inclusion of higher modes in the templates increases the prospects for detecting gravitational waves. Specifically, we use numeri…
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 …
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 present a Fourier-domain approach to modulations and delays of gravitational wave signals, a problem which arises in two different contexts. For space-based detectors like LISA, the orbital motion of the detector introduces a time-dependency in the response of the detector, consisting of both a modulation and a varying delay. In the context of signals from precessing spinning binary systems, a useful tool for building models of the waveform consists in representing the signal as a time-dependent rotation of a quasi-non-precessing waveform. In both cases, being able to compute transfer funct…
In the first two years of Gravitational Wave (GW) Astronomy, half a dozen compact binary coalescences (CBCs) have been detected. As the sensitivities and bandwidths of the detectors improve and new detectors join the network, many more sources are expected to be detected. The goal will not only be to find as many sources as possible in the data but to understand the dynamics of the sources much more precisely. Standard searches are currently restricted to a smaller parameter space which assumes aligned spins. Construction of a larger and denser parameter space, and optimising the resultant inc…
The recent observation of GW190412, the first high-mass ratio binary black-hole (BBH) merger, by the LIGO-Virgo Collaboration (LVC) provides a unique opportunity to probe the impact of subdominant harmonics and precession effects encoded in a gravitational wave signal. We present refined estimates of source parameters for GW190412 using \texttt{NRSur7dq4}, a recently developed numerical relativity waveform surrogate model that includes all $\ell \leq 4$ spin-weighted spherical harmonic modes as well as the full physical effects of precession. We compare our results with two different variants …
Gravitational-wave signals from compact binary coalescences are most efficiently identified through matched filter searches, which match the data against a pre-generated bank of gravitational-wave templates. Although different techniques for performing the matched filter, as well as generating the template bank, exist, currently all modelled gravitational-wave searches use templates that restrict the component spins to be aligned (or anti-aligned) with the orbital angular momentum. This means that current searches are less sensitive to gravitational-wave signals generated from binaries with ge…
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…
Faster likelihood evaluation enhances the efficiency of gravitational wave signal analysis. We present Mode-by-mode Relative Binning (MRB), a new method designed for obtaining fast and accurate likelihoods for advanced waveform models that include spin-orbit precession effects and multiple radiation harmonics from compact binary coalescence. Leveraging the "twisting-up" procedure of constructing precessing waveform modes from non-precessing ones, the new method mitigates degrade of relative binning accuracy due to interference from superimposed modes. Additionally, we supplement algorithms for…
Using the Reduced Basis approach, we efficiently compress and accurately represent the space of waveforms for non-precessing binary black hole inspirals, which constitutes a four dimensional parameter space (two masses, two spin magnitudes). Compared to the non-spinning case, we find that only a {\it marginal} increase in the (already relatively small) number of reduced basis elements is required to represent any non-precessing waveform to nearly numerical round-off precision. Most parameters selected by the algorithm are near the boundary of the parameter space, leaving the bulk of its volume…
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）
Black-hole ringdown with templates capturing spin precession: A reanalysis of GW190521
Universitá degli Studi di Milano-Bicocca（米兰比可卡大学）；INFN, Sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）；Institute of Astrophysics, FORTH（基础与技术研究基金会天体物理研究所）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）
Gravitational wave observations of the ringdown of the remnant black hole in a binary black hole coalescence provide a unique opportunity of confronting the black hole no-hair theorem in general relativity with observational data. The most robust tests are possible if multiple ringdown modes can be observed. In this paper, using state-of-the-art Bayesian inference methods and the most up-to-date knowledge of binary black hole population parameters and ringdown mode amplitudes, we evaluate the prospects for black hole spectroscopy with current and future ground based gravitational wave detector…
