A new family of restricted post-Newtonian-accurate waveforms, termed TaylorEt approximants, was recently proposed for searching gravitational wave (GW) signals from inspiraling non-spinning compact binaries having arbitrary mass-ratios. We perform detailed fitting factor (FF) studies to probe if the TaylorEt (3.5PN) signals for non-spinning comparable mass compact binaries can be effectually and faithfully searched with TaylorT1, TaylorT4, and TaylorF2 (3.5PN) templates in LIGO, Advanced LIGO, and Virgo interferometers. We observe that a good fraction of the templates, which by choice are from TaylorT1, TaylorT4, and TaylorF2 (3.5PN) families, have FF <~ 0.97 and substantial biases for the estimated total-mass against the fiducial TaylorEt (3.5PN) signals for equal-mass systems. Both these observations can bear on the detectability of a signal. TaylorEt (3.5PN) signals with mass-ratios of a third or a quarter yield high FFs against those same template banks, but at the expense of inviting large systematic errors in the estimated values of their total mass and symmetric mass-ratio. In general, the aforementioned templates are found to be increasingly {\it unfaithful} with respect to a TaylorEt signal as one increases the total mass of the inspiraling system. We also observe that the amount of bias in the estimated mass varies with the (noise power spectral density of the) detector. This can be of some concern for multi-detector searches, which check for consistency in the estimated masses of concurrent triggers in their data. (Abridged)
Recently, a new class of restricted gravitational wave search templates, termed the TaylorEt template was proposed for the search of inspiralling compact binaries. The TaylorEt approximant is different from the usual time-domain post-Newtonian approximants in that it employs the orbital binding energy rather than the orbital frequency or the closely related parameter "x". We perform detailed studies to probe the fitting factors of TaylorEt at 3.5pN for nonspinning comparable mass compact binaries vis-a-vis the TaylorT1, TaylorT4, and TaylorF2 at 3.5pN approximants in LIGO, Advanced LIGO and Vi…
We compare the phase evolution of equal-mass nonspinning black-hole binaries from numerical relativity (NR) simulations with post-Newtonian (PN) results obtained from three PN approximants: the TaylorT1 and T4 approximants, for which NR-PN comparisons have already been performed in the literature, and the recently proposed approximant TaylorEt. The accumulated phase disagreement between NR and PN results over the frequency range $Mω= 0.0455$ to $Mω= 0.1$ is greater for TaylorEt than either T1 or T4, but has the attractive property of decreasing monotonically as the PN order is increased.
Extreme mass ratio inspirals (EMRIs), the inspirals of compact objects into supermassive black holes, are important gravitational wave sources for the Laser Interferometer Space Antenna (LISA). We study the performance of various post-Newtonian (PN) template families relative to the high precision numerical waveforms in the context of EMRI parameter estimation with LISA. Expressions for the time domain waveforms TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt are derived up to 22PN order, i.e $\mathcal{O}(v^{44})$ ($v$ is the characteristic velocity of the binary) beyond the Newtonian term…
We probe the ability of various types of post-Newtonian(PN)-accurate circular templates to capture inspiral gravitational-wave (GW) signals from compact binaries having tiny orbital eccentricities. The GW signals are constructed by adapting the phasing formalism, available in T. Damour, A. Gopakumar, and B. R. Iyer, [Phys. Rev. D 70, 064028 (2004)], employing the orbital energy and the time-eccentricity to describe the orbital evolution. Using the fitting factor estimates, relevant for the initial LIGO, we show that circular templates, based on the adiabatic TaylorT1, complete adiabatic Taylor…
Frequency-domain filters for time-windowed gravitational waves from inspiralling compact binaries are constructed which combine the excellent performance of our previously developed time-domain P-approximants with the analytic convenience of the stationary phase approximation without a serious loss in event rate. These Fourier-domain representations incorporate the ``edge oscillations'' due to the (assumed) abrupt shut-off of the time-domain signal caused by the relativistic plunge at the last stable orbit. These new analytic approximations, the SPP-approximants, are not only `effectual' for d…
In the adiabatic post-Newtonian (PN) approximation, the phase evolution of gravitational waves (GWs) from inspiralling compact binaries in quasicircular orbits is computed by equating the change in binding energy with the GW flux. This energy balance equation can be solved in different ways, which result in multiple approximants of the PN waveforms. Due to the poor convergence of the PN expansion, these approximants tend to differ from each other during the late inspiral. Which of these approximants should be chosen as templates for detection and parameter estimation of GWs from inspiraling co…
The two-body dynamics in general relativity has been solved perturbatively using the post-Newtonian (PN) approximation. The evolution of the orbital phase and the emitted gravitational radiation are now known to a rather high order up to O(v^8), v being the characteristic velocity of the binary. The orbital evolution, however, cannot be specified uniquely due to the inherent freedom in the choice of parameter used in the PN expansion as well as the method pursued in solving the relevant differential equations. The goal of this paper is to determine the (dis)agreement between different PN wavef…
The order of the post-Newtonian expansion needed, to extract in a reliable and accurate manner the fully general relativistic gravitational wave signal from inspiralling compact binaries, is explored. A class of approximate wave forms, called P-approximants, is constructed based on the following two inputs: (a) The introduction of two new energy-type and flux-type functions e(v) and f(v), respectively, (b) the systematic use of Pade approximation for constructing successive approximants of e(v) and f(v). The new P-approximants are not only more effectual (larger overlaps) and more faithful (sm…
(Abridged): The standard adiabatic approximation to phasing of gravitational waves from inspiralling compact binaries uses the post-Newtonian expansions of the binding energy and gravitational wave flux both truncated at the same relative post-Newtonian order. Motivated by the eventual need to go beyond the adiabatic approximation we must view the problem as the dynamics of the binary under conservative post-Newtonian forces and gravitational radiation damping. From the viewpoint of the dynamics of the binary, the standard approximation at leading order is equivalent to retaining the 0PN and 2…
We compare the performances of the templates defined by three different types of approaches: traditional post-Newtonian templates (Taylor-approximants), ``resummed'' post-Newtonian templates assuming the adiabatic approximation and stopping before the plunge (P-approximants), and further ``resummed'' post-Newtonian templates going beyond the adiabatic approximation and incorporating the plunge with its transition from the inspiral (Effective-one-body approximants). The signal to noise ratio is significantly enhanced (mainly because of the inclusion of the plunge signal) by using these new effe…
Inspiraling compact binaries with non-negligible orbital eccentricities are plausible gravitational wave (GW) sources for the upcoming network of GW observatories. In this paper, we present two prescriptions to compute post-Newtonian (PN) accurate inspiral templates for such binaries. First, we adapt and extend the post-circular scheme of Yunes {\it et al.} [Phys. Rev. D 80, 084001 (2009)] to obtain a Fourier-domain inspiral approximant that incorporates the effects of PN-accurate orbital eccentricity evolution. This results in a fully analytic frequency-domain inspiral waveform with Newtonian…
Compact binaries inspiralling along quasi-circular orbits are the most plausible gravitational wave (GW) sources for the operational, planned and proposed laser interferometers. We provide new class of restricted post-Newtonian accurate GW templates for non-spinning compact binaries inspiralling along PN accurate quasi-circular orbits. Arguments based on data analysis, theoretical and astrophysical considerations are invoked to show why these time-domain Taylor approximants should be interesting to various GW data analysis communities.
Constraining initial orbital eccentricity of inspiral-dominated gravitational-wave events with an analytic approximant
The Chinese University of Hong Kong（香港中文大学）；Tata Institute of Fundamental Research（塔塔基础研究所）；Nikhef—National Institute for Subatomic Physics（NIKHEF-国家亚原子物理研究所）；KU Leuven（荷语鲁汶大学）；The Inter-University Centre for Astronomy and Astrophysics（大学间天文学与天体物理学中心）
Compact binaries inspiralling along eccentric orbits are plausible gravitational wave (GW) sources for the ground-based laser interferometers. We explore the losses in the event rates incurred when searching for GWs from compact binaries inspiralling along post-Newtonian accurate eccentric orbits with certain obvious non-optimal search templates. For the present analysis, GW signals having 2.5 post-Newtonian accurate orbital evolution are modeled following the phasing formalism, presented in [T. Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D \textbf{70}, 064028 (2004)]. We demonstrate that…
Current tests of General Relativity are performed using approximations which neglect a key feature of complete solution of Einstein's theory: higher-order modes. Our analysis will reassess these tests, including these higher-order mode effects. We have chosen to perform inspiral-merger-ringdown consistency tests on the gravitational transients detected by LIGO and Virgo during the observing run O2. We use an approximant which includes all higher modes with $\ell \le 4$ (NRSur7dq2) and then, for the most interesting cases, we repeat the tests involving fits on Numerical Relativity simulations.
Observations of transient gravitational wave (GW) events with non-negligible orbital eccentricity can be highly rewarding from astrophysical considerations. Ready-to-use fully analytic frequency domain inspiral GW templates are crucial ingredients to construct eccentric inspiral-merger-ringdown waveform families, required for the detection of such GW events. It turns out that a fully analytic, post-Newtonian (PN) accurate frequency domain inspiral template family, which uses certain post-circular approximation, may only be suitable to model events with initial eccentricities $e_0 \leq 0.2$.We …
When a gravitational wave is detected by Advanced LIGO/Virgo, sophisticated parameter estimation (PE) pipelines spring into action. These pipelines leverage approximants to generate large numbers of theoretical gravitational waveform predictions to characterize the detected signal. One of the most accurate and physically comprehensive classes of approximants in wide use is the "Spinning Effective One Body--Numerical Relativity" (SEOBNR) family. Waveform generation with these approximants can be computationally expensive, which has limited their usefulness in multiple data analysis contexts. In…
We introduce \texttt{TEOBResumSP}: an efficient, accurate hybrid scheme for generating gravitational waveforms from spin-precessing compact binaries. The precessing waveforms are generated via the established technique of Euler rotating the non-precessing \texttt{TEOBResumS} waveforms from a precessing frame to an inertial frame. We obtain the Euler angles by solving the post-Newtonian precession equations expanded to second post-Newtonian order. Current version of \texttt{TEOBResumSP} produces precessing waveforms through the inspiral phase up to the onset of the merger. We compare \texttt{TE…
We study the astrophysical impact of inaccurate and incomplete modeling of the gravitational waveforms from compact binary coalescences (CBCs). We do so by the matched filtering of complete inspiral-merger-ringdown (IMR) signals with a bank of inspiral-phase templates modeled after the 3.5 post-Newtonian TaylorT1 approximant. The rationale for the choice of the templates is threefold: (1) The inspiral phase of the Phenomenological signals, which are an example of complete IMR signals, is modeled on the same TaylorT1 approximant. (2) In the low-mass limit, where the merger and ringdown phases l…
[abridged] Although gravitational radiation causes inspiralling compact binaries to circularize, a variety of astrophysical scenarios suggest that binaries might have small but nonnegligible orbital eccentricities when they enter the low-frequency bands of ground and space-based gravitational-wave detectors. If not accounted for, even a small orbital eccentricity can cause a potentially significant systematic error in the mass parameters of an inspiralling binary. Gravitational-wave search templates typically rely on the quasi-circular approximation, which provides relatively simple expression…
To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB)model. The typical numerical phasing errors over the $\simeq 22$ GW cycles are $Δϕ\simeq \pm 0.24$ rad. By calibrating only one parameter (representing…
The prior knowledge of the gravitational waveform from compact binary systems makes matched filtering an attractive detection strategy. This detection method involves the filtering of the detector output with a set of theoretical waveforms or templates. One of the most important factors in this strategy is knowing how many templates are needed in order to reduce the loss of possible signals. In this study we calculate the number of templates and computational power needed for a one-step search for gravitational waves from inspiralling binary systems. We build on previous works by firstly expan…
Post-Newtonian expansions of the binding energy and gravitational wave flux truncated at the {\it same relative} post-Newtonian order form the basis of the {\it standard adiabatic} approximation to the phasing of gravitational waves from inspiralling compact binaries. Viewed in terms of the dynamics of the binary, the standard approximation is equivalent to neglecting certain conservative post-Newtonian terms in the acceleration. In an earlier work, we had proposed a new {\it complete adiabatic} approximant constructed from the energy and flux functions. At the leading order it employs the 2PN…
We develop a waveform model to describe the inspiral, merger and ringdown of binary systems with comparable and intermediate mass-ratios. This model incorporates first-order conservative self-force corrections to the energy and angular momentum, which are valid in the strong-field regime [1]. We model the radiative part of the self-force by deriving second-order radiative corrections to the energy flux. These corrections are obtained by minimizing the phase discrepancy between our self-force model and the effective one body model [2, 3] for a variety of mass-ratios. We show that our model perf…
We present $\texttt{ENIGMA}$, a time domain, inspiral-merger-ringdown waveform model that describes non-spinning binary black holes systems that evolve on moderately eccentric orbits. The inspiral evolution is described using a consistent combination of post-Newtonian theory, self-force and black hole perturbation theory. Assuming eccentric binaries that circularize prior to coalescence, we smoothly match the eccentric inspiral with a stand-alone, quasi-circular merger, which is constructed using machine learning algorithms that are trained with quasi-circular numerical relativity waveforms. W…
We continue the program of constructing, within the Effective-One-Body (EOB) approach, high accuracy, faithful analytic waveforms describing the gravitational wave signal emitted by inspiralling and coalescing binary black holes (BHs). We present the comparable-mass version of a new, resummed 3PN-accurate EOB quadrupolar waveform recently introduced in the small-mass-ratio limit. We compare the phase and the amplitude of this waveform to the recently published results of a high-accuracy numerical relativity (NR) simulation of 15 orbits of an inspiralling equal-mass binary BHs system performed …
By post-Newtonian (PN) expanding the well-known, factorized and resummed, effective-one-body energy flux for circularized binaries we show that: (i) because of the presence of the resummed tail factor, the 4.5PN-accurate tails-of-tails-of-tails contribution to the energy flux recently computed by Marchand et al. [Class. Q. Grav. 33 (2016) 244003] is actually contained in the resummed expression; this is also the case of the the next-to-leading-order tail-induced spin-orbit term of Marsat et al. [Class. Q. Grav. 31 (2014) 025023]; (ii) in performing this expansion, we also obtain, for the first…
We present the first numerical-relativity simulation of a compact-object binary whose gravitational waveform is long enough to cover the entire frequency band of advanced gravitational-wave detectors, such as LIGO, Virgo and KAGRA, for mass ratio 7 and total mass as low as $45.5\,M_\odot$. We find that effective-one-body models, either uncalibrated or calibrated against substantially shorter numerical-relativity waveforms at smaller mass ratios, reproduce our new waveform remarkably well, with a negligible loss in detection rate due to modeling error. In contrast, post-Newtonian inspiral wavef…
Building upon several recent advances in the development of effective-one-body models for spin-aligned eccentric binaries with individual masses $(m_1,m_2)$ we introduce a new EOB waveform model that aims at describing inspiralling binaries in the large mass-ratio regime, $m_1\gg m_2$. The model exploits the current state-of-the-art TEOBResumS-Dali model for eccentric binaries, but the standard EOB potentials $(A,\bar{D},Q)$, informed by Numerical Relativity (NR) simulations, are replaced with the corresponding functions that are linear in the symmetric mass ratio $ν\equiv m_1 m_2/(m_1+m_2)^2$…
Motivated by the possibility of observing gravitational waves from merging black holes whose spins are nearly extremal (i.e., 1 in dimensionless units), we present numerical waveforms from simulations of merging black holes with the highest spins simulated to date: (1) a 25.5-orbit inspiral, merger, and ringdown of two holes with equal masses and spins of magnitude 0.97 aligned with the orbital angular momentum; and (2) a previously reported 12.5-orbit inspiral, merger, and ringdown of two holes with equal masses and spins of magnitude 0.95 anti-aligned with the orbital angular momentum. First…
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 combined observation of gravitational and electromagnetic waves from the coalescence of two neutron stars marks the beginning of multi-messenger astronomy with gravitational waves (GWs). The development of accurate gravitational waveform models is a crucial prerequisite to extract information about the properties of the binary system that generated a detected GW signal. In binary neutron star systems (BNS), tidal effects also need to be incorporated in the modeling for an accurate waveform representation. Building on previous work [Phys.Rev.D96 121501], we explore the performance of inspir…
An accurate knowledge of the coalescing binary gravitational waveform is crucial for experimental searches as the ones performed by the LIGO-Virgo collaboration. Following an earlier paper by the same authors we refine the construction of analytical phenomenological waveforms describing the signal sourced by generically spinning binary systems. The gap between the initial inspiral part of the waveform, described by spin-Taylor approximants, and its final ring-down part, described by damped exponentials, is bridged by a phenomenological phase calibrated by comparison with the dominant spherical…
The quest for gravitational waves from coalescing binaries is customarily performed by the LIGO-Virgo collaboration via matched filtering, which requires a detailed knowledge of the signal. Complete analytical coalescence waveforms are currently available only for the non-precessing binary systems. In this paper we introduce complete phenomenological waveforms for the dominant quadrupolar mode of generically spinning systems. These waveforms are constructed by bridging the gap between the analytically known inspiral phase, described by spin Taylor (T4) approximants in the restricted waveform a…
We compare results from numerical simulations of spinning binaries in the "orbital hangup" case, where the binary completes at least nine orbits before merger, with post-Newtonian results using the approximants TaylorT1, T4 and Et. We find that, over the ten cycles before the gravitational-wave frequency reaches $Mω= 0.1$, the accumulated phase disagreement between NR and 2.5PN results is less than three radians, and is less than 2.5 radians when using 3.5PN results. The amplitude disagreement between NR and restricted PN results increases with the black holes' spin, from about 6% in the equal…
We introduce a new method for modelling the gravitational wave flux function of a test-mass particle inspiralling into an intermediate mass Schwarzschild black hole which is based on Chebyshev polynomials of the first kind. It is believed that these Intermediate Mass Ratio Inspiral events (IMRI) are expected to be seen in both the ground and space based detectors. Starting with the post-Newtonian expansion from Black Hole Perturbation Theory, we introduce a new Chebyshev approximation to the flux function, which due to a process called Chebyshev economization gives a model with faster converge…
Gravitational waves radiated by the coalescence of compact-object binaries containing a neutron star and a black hole are one of the most interesting sources for the ground-based gravitational-wave observatories Advanced LIGO and Advanced Virgo. Advanced LIGO will be sensitive to the inspiral of a $1.4\, M_\odot$ neutron star into a $10\,M_\odot$ black hole to a maximum distance of $\sim 900$ Mpc. Achieving this sensitivity and extracting the physics imprinted in observed signals requires accurate modeling of the binary to construct template waveforms. In a NSBH binary, the black hole may have…
This article presents a study of the sufficient accuracy of post-Newtonian and numerical relativity waveforms for the most demanding usage case: parameter estimation of strong sources in advanced gravitational wave detectors. For black hole binaries, these detectors require accurate waveform models which can be constructed by fusing an analytical post-Newtonian inspiral waveform with a numerical relativity merger-ringdown waveform. We perform a comprehensive analysis of errors that enter such "hybrid waveforms". We find that the post-Newtonian waveform must be aligned with the numerical relati…
We derive fourth post-Newtonian (4PN) contributions to the Keplerian-type parametric solution associated with the conservative dynamics of eccentric, non-spinning compact binaries. The solution has been computed while ignoring certain zero-average, oscillatory terms arising due to 4PN tail effects. We provide explicit expressions for the parametric solution and various orbital elements in terms of the conserved energy, angular momentum and symmetric mass ratio. Canonical perturbation theory (along with the technique of Pade approximant) is used to incorporate the 4PN nonlocal-in-time tail effe…
Accurate gravitational-wave (GW) signal models exist for black hole binary (BBH) and neutron-star binary (BNS) systems, which are consistent with all of the published GW observations to date. Detections of a third class of compact-binary systems, neutron-star black hole (NSBH) binaries, have not yet been confirmed, but are eagerly awaited in the near future. For NSBH systems, GW models do not exist across the viable parameter space of signals. In this work we present the frequency-domain phenomenological model, PhenomNSBH, for GWs produced by NSBH systems with mass ratios from equal-mass up to…
Combining new gravitational waveforms derived by long-term (14--16 orbits) numerical-relativity simulations with waveforms by an effective-one-body (EOB) formalism for coalescing binary neutron stars, we construct hybrid waveforms and estimate the measurability for the dimensionless tidal deformability of the neutron stars, $Λ$, by advanced gravitational-wave detectors. We focus on the equal-mass case with the total mass $2.7M_\odot$. We find that for an event at a hypothetical effective distance of $D_{\rm eff}=200$ Mpc, the distinguishable difference in the dimensionless tidal deformability …
We prove that merging supermassive black holes (SMBHs) typically have neither equal masses, nor is their mass ratio too extreme. The majority of such mergers fall into the mass ratio range of 1:30 to 1:3, implying a spin flip during the inspiral. We also present a simple expression for the final spin $χ_{f}$ of the emerging SMBH, as function of the mass ratio, initial spin magnitudes, and orientation of the spins with respect to the orbital plane and each other. This formula approximates well more cumbersome expressions obtained from the fit with numerical simulations. By integrating over all …
[Abridged] We introduce an improved version of the Eccentric, Non-spinning, Inspiral-Gaussian-process Merger Approximant (ENIGMA) waveform model. We find that this ready-to-use model can: (i) produce physically consistent signals when sampling over 1M samples chosen over the $m_{\{1,\,2\}}\in[5M_{\odot},\,50M_{\odot}]$ parameter space, and the entire range of binary inclination angles; (ii) produce waveforms within 0.04 seconds from an initial gravitational wave frequency $f_{\textrm{GW}} =15\,\textrm{Hz}$ and at a sample rate of 8192 Hz; and (iii) reproduce the physics of quasi-circular merge…
University of Coimbra（科英布拉大学）；Universidade de Aveiro（阿威罗大学）；Centre for Research and Development in Mathematics and Applications（数学与应用研究发展中心）；Universidade do Minho（米尼奥大学）；Centro de Física das Universidades do Minho e do Porto（米尼奥大学与波尔图大学物理中心）；LIP（葡萄牙高能物理实验室）；Universitat de València（瓦伦西亚大学）；Observatori Astronòmic, Universitat de València（瓦伦西亚大学天文台）
We demonstrate the application of the YOLOv5 model, a general purpose convolution-based single-shot object detection model, in the task of detecting binary neutron star (BNS) coalescence events from gravitational-wave data of current generation interferometer detectors. We also present a thorough explanation of the synthetic data generation and preparation tasks based on approximant waveform models used for the model training, validation and testing steps. Using this approach, we achieve mean average precision ($\text{mAP}_{[0.50]}$) values of 0.945 for a single class validation dataset and as…
