Towards numerical-relativity informed effective-one-body waveforms for dynamical capture black hole binaries
Tomas Andrade, Juan Trenado, Simone Albanesi, Rossella Gamba, Sebastiano Bernuzzi, Alessandro Nagar, Juan Calderon-Bustillo, Nicolas Sanchis-Gual, Jose A. Font,… 展开作者
Tomas Andrade, Juan Trenado, Simone Albanesi, Rossella Gamba, Sebastiano Bernuzzi, Alessandro Nagar, Juan Calderon-Bustillo, Nicolas Sanchis-Gual, Jose A. Font, William Cook, Boris Daszuta, Francesco Zappa, David Radice
Dynamical captures of black holes may take place in dense stellar media due to the emission of gravitational radiation during a close passage. Detection of such events requires detailed modelling, since their phenomenology qualitatively differs from that of quasi-circular binaries. Very few models can deliver such waveforms, and none includes information from Numerical Relativity (NR) simulations of non quasi-circular coalescences. In this study we present a first step towards a fully NR-informed Effective One Body (EOB) model of dynamical captures. We perform 14 new simulations of single and double encounter mergers, and use this data to inform the merger-ringdown model of the TEOBResumS-Dali approximant. We keep the initial energy approximately fixed to the binary mass, and vary the mass-rescaled, dimensionless angular momentum in the range $(0.6, 1.1)$, the mass ratio in $(1, 2.15)$ and aligned dimensionless spins in $(-0.5, 0.5)$. We find that the model is able to match NR to $97%$, improving previous performances, without the need of modifying the base-line template. Upon NR informing the model, this improves to $99%$ with the exception of one outlier corresponding to a direct plunge. The maximum EOBNR phase difference at merger for the uninformed model is of $0.15$ radians, which is reduced to $0.1$ radians after the NR information is introduced. We outline the steps towards a fully informed EOB model of dynamical captures, and discuss future improvements.
This article studies sufficient accuracy criteria of hybrid post-Newtonian (PN) and numerical relativity (NR) waveforms for parameter estimation of strong binary black-hole sources in second- generation ground-based gravitational-wave detectors. We investigate equal-mass non-spinning binaries with a new 33-orbit NR waveform, as well as unequal-mass binaries with mass ratios 2, 3, 4 and 6. For equal masses, the 33-orbit NR waveform allows us to recover previous results and to extend the analysis toward matching at lower frequencies. For unequal masses, the errors between different PN approximan…
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…
In this paper, we derive a set of equations of motions for binaries on eccentric orbits undergoing spin-induced precession that can efficiently be integrated on the radiation-reaction timescale. We find a family of solutions with a computation cost improved by a factor $10$ - $50$ down to $\sim 10$ ms per waveform evaluation compared to waveforms obtained by directly integrating the precession equations, that maintain a mismatch of the order $10^{-4}$ - $10^{-6}$ for waveforms lasting a million orbital cycles and a thousand spin-induced precession cycles. We express it in terms of parameters t…
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 $ν\equiv m_1 m_2/(m_1+m_2)^2$…
Gravitational waveforms from numerical simulations are a critical tool to test and analytically calibrate the waveform models used to study the properties of merging compact objects. In this paper, we present a series of high-accuracy waveforms produced with the SpEC code for systems involving at least one neutron star. We provide for the first time waveforms with sub-radian accuracy over more than twenty cycles for low-mass black hole-neutron star binaries, including binaries with non-spinning objects, and binaries with rapidly spinning neutron stars that maximize the impact on the gravitatio…
Using our new numerical-relativity code SACRA, long-term simulations for inspiral and merger of black hole (BH)-neutron star (NS) binaries are performed, focusing particularly on gravitational waveforms. As the initial conditions, BH-NS binaries in a quasiequilibrium state are prepared in a modified version of the moving-puncture approach. The BH is modeled by a nonspinning moving puncture and for the NS, a polytropic equation of state with $Γ=2$ and the irrotational velocity field are employed. The mass ratio of the BH to the NS, $Q=M_{\rm BH}/M_{\rm NS}$, is chosen in the range between 1.5 a…
Binary systems of two compact objects circularize and spiral toward each other via the emission of gravitational waves. The coupling of the spins of each object with the orbital angular momentum causes the orbital plane to precess, which leads to modulation of the gravitational wave signal. Until now, generating frequency-domain waveforms for fully precessing systems for use in gravitational wave data analysis meant numerically integrating the equations of motion, then Fourier transforming the result, which is very computationally intensive for systems that complete hundreds or thousands of cy…
The accuracy of the post-Newtonian waveforms, both in standard and Pade form, is determined by computing their matched-filtering overlap integral with a reference waveform obtained from black-hole perturbation theory.
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…
The paper generalizes the structure of gravitational waves from orbiting spinning binaries under leading order spin-orbit coupling, as given in the work by Königsdörffer and Gopakumar [PRD 71, 024039 (2005)] for single-spin and equal-mass binaries, to unequal-mass binaries and arbitrary spin configurations. The orbital motion is taken to be quasi-circular and the fractional mass difference is assumed to be small against one. The emitted gravitational waveforms are given in analytic form.
We construct hybrid binary black holes merger waveforms using analytical model waveforms for the early inspiral phase and numerical relativity waveforms for late inspiral to merger and post merger phases. To hybridize analytical and numerical waveforms, we first perform a 3-dimensional rotation to align the instantaneous orbital planes associated with the two waveforms at some fiducial frequency, we then find appropriate phase and time translations that maximize the overlap of the two waveforms in a hybridization interval. We discuss the accuracy and limitations for hybrids constructed by this…
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 $…
The availability of accurate numerical waveforms is an important requirement for the creation and calibration of reliable waveform models for gravitational wave astrophysics. For black hole-neutron star binaries, very few accurate waveforms are however publicly available. Most recent models are calibrated to a large number of older simulations with good parameter space coverage for low-spin non-precessing binaries but limited accuracy, and a much smaller number of longer, more recent simulations limited to non-spinning black holes. In this paper, we present long, accurate numerical waveforms f…
The rotation of the bodies and the eccentricity of the orbit have significant effects on the emitted gravitational radiation of binary systems. This work focuses on the evaluation of the gravitational wave polarization states for spinning compact binaries. We consider binaries on eccentric orbits and the spin-orbit interaction up to the 1.5 post-Newtonian order in a way which is independent of the parameterization of the orbit. The equations of motion for angular variables are included. The formal expressions of the polarization states are given with the inclusion of higher order corrections t…
Stellar-mass compact binaries in eccentric orbits are almost guaranteed sources of gravitational waves for Laser Interferometer Space Antenna. We present a prescription to compute accurate and efficient gravitational-wave polarizations associated with bound compact binaries of arbitrary eccentricity and mass ratio moving in slowly precessing orbits. We compare our approach with those existing in the literature and present its advantages.
We present an analytical waveform family describing gravitational waves (GWs) from the inspiral, merger and ringdown of non-spinning black-hole binaries including the effect of several non-quadrupole modes [($\ell = 2, m = \pm 1), (\ell = 3, m = \pm 3), (\ell = 4, m = \pm 4)$ apart from $(\ell = 2, m=\pm2)$]. We first construct spin-weighted spherical harmonics modes of hybrid waveforms by matching numerical-relativity simulations (with mass ratio $1-10$) describing the late inspiral, merger and ringdown of the binary with post-Newtonian/effective-one-body waveforms describing the early inspir…
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…
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 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…
This paper presents a post-Newtonian (PN) template family of gravitational waveforms from inspiralling compact binaries with non-precessing spins, where the spin effects are described by a single "reduced-spin" parameter. This template family, which reparametrizes all the spin-dependent PN terms in terms of the leading-order (1.5PN) spin-orbit coupling term \emph{in an approximate way}, has very high overlaps (fitting factor > 0.99) with non-precessing binaries with arbitrary mass ratios and spins. We also show that this template family is "effectual" for the detection of a significant fractio…
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 present further evidence that the second post-Newtonian (pN) approximation to the gravitational waves emitted by inspiraling compact binaries is sufficient for the detection of these systems. This is established by comparing the 2-pN wave forms to signals calculated from black hole perturbation theory. Results are presented for different detector noise curves. We also discuss the validity of this type of analysis.
In this Comment we compute the contributions of the radiation reaction force in the 2.5 post-Newtonian (PN) gravitational wave polarizations for compact binaries in circular orbits. (i) We point out and correct an inconsistency in the derivation of Arun, Blanchet, Iyer, and Qusailah. (ii) We prove that all contributions from radiation reaction in the 2.5PN waveform are actually negligible since they can be absorbed into a modification of the orbital phase at the 5PN order.
The Laser Interferometer Space Antenna (LISA) will observe black hole binaries of stellar origin during their gravitational wave inspiral, months to years before coalescence. Due to the long duration of the signal in the LISA band, a faithful waveform is necessary in order to keep track of the binary phase. This is crucial to extract the signal from the data and to perform an unbiased estimation of the source parameters. We consider Post-Newtonian (PN) waveforms, and analyze the PN order needed to keep the bias caused by the PN approximation negligible relative to the statistical parameter est…
The two independent ``plus" and ``cross" polarization waveforms associated with the gravitational waves emitted by inspiralling, non-spinning, compact binaries are presented, ready for use in the data analysis of signals received by future laser interferometer gravitational-wave detectors such as LIGO and VIRGO. The computation is based on a recently derived expression of the gravitational field at the second-post-Newtonian approximation of general relativity beyond the dominant (Newtonian) quadrupolar field. The use of these theoretical waveforms to make measurements of astrophysical paramete…
We complete the computation of the gravitational waveform amplitude for non-spinning compact binaries to the third and a half post-Newtonian (PN) order in the quasi-circular case. This is done by performing a spin-weighted spherical harmonics decomposition of the amplitude. This computation is achieved using the post-Newtonian-Multipolar-post-Minkowskian formalism. The amplitude modes are written in a PN expanded way as well as a factorized form suitable for EOB template building. Combining this work with previous ones, we provide in the supplemental materials the expressions of the modes incl…
Accurate parameter estimation of gravitational waves from coalescing compact binary sources is a key requirement for gravitational-wave astronomy. Evaluating the posterior probability density function of the binary's parameters (component masses, sky location, distance, etc.) requires computing millions of waveforms. The computational expense of parameter estimation is dominated by waveform generation and scales linearly with the waveform computational cost. Previous work showed that gravitational waveforms from non-spinning compact binary sources are amenable to a truncated singular value dec…
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…
We investigate the effects of using the {\it full} waveform (FWF) over the conventional {\it restricted} waveform (RWF) of the inspiral signal from a coalescing compact binary (CCB) system in extracting the parameters of the source, using a global network of second generation interferometric detectors. We study a hypothetical population of (1.4-10)$M_\odot$ NS-BH binaries (uniformly distributed and oriented in the sky) by employing the full post-Newtonian waveforms, which not only include contributions from various harmonics other than the dominant one (quadrupolar mode) but also the post-Newt…
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…
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…
During binary black hole (BBH) mergers, energy and momenta are carried away from the binary system as gravitational radiation. Access to the radiated energy and momenta allows us to predict the properties of the remnant black hole. We develop a Python package gw_remnant to compute the remnant mass, remnant spin, peak luminosity, and the final kick imparted on the remnant black hole from the gravitational radiation. Using this package, we compute the remnant properties of the final black hole in case of non-spinning BBH mergers with mass ratios ranging from q=2.5 to q=1000 using waveform modes …
The increasing sophistication and accuracy of numerical simulations of compact binaries (especially binary black holes) presents the opportunity to test the regime in which post-Newtonian (PN) predictions for the emitted gravitational waves are accurate. In order to confront numerical results with those of post-Newtonian theory, it is convenient to compare multipolar decompositions of the two waveforms. It is pointed out here that the individual modes can be computed to higher post-Newtonian order by examining the radiative multipole moments of the system, rather than by decomposing the 2.5PN …
Dynamical capture is a possible formation channel for BBH mergers leading to highly eccentric merger dynamics and to gravitational wave (GW) signals that are morphologically different from those of quasi-circular mergers. The future detection of these mergers by ground-based or space-based GW interferometers can provide invaluable insights on astrophysical black holes, but it requires precise predictions and dedicated waveform models for the analysis. We present a state-of-the-art effective-one-body (EOB) model for the multipolar merger-ringdown waveform from dynamical capture black-hole merge…
We propose a new way of analyzing, and analytically representing, the ringdown part of the gravitational wave signal emitted by coalescing black hole binaries.By contrast with the usual {\it linear} decomposition of the multipolar complex waveform $h(t)$ in a sum of quasi-normal modes, our procedure relies on a {\it multiplicative} decomposition of $h(t)$ as the product of the fundamental quasi-normal mode with a remaining time-dependent complex factor whose amplitude and phase are separately fitted. As an illustrative example, we apply our analysis and fitting procedure to the ringdown part o…
We derived a post-Newtonian (PN) inspiral only gravitational waveform for unequal mass, spinning black hole binaries. Towards the end of the inspiral the larger spin dominates over the orbital angular momentum (while the smaller spin is negligible), hence the name Spin-Dominated Waveforms (SDW). Such systems are common sources for future gravitational wave detectors and during the inspiral the largest amplitude waves are emitted exactly in its last part. The SDW waveforms emerge as a double expansion in the PN parameter and the ratio of the orbital angular momentum to the dominant spin.
This paper defines an angular velocity for time-dependent functions on the sphere, and applies it to gravitational waveforms from compact binaries. Because it is geometrically meaningful and has a clear physical motivation, the angular velocity is uniquely useful in helping to solve an important---and largely ignored---problem in models of compact binaries: the inverse problem of deducing the physical parameters of a system from the gravitational waves alone. It is also used to define the corotating frame of the waveform. When decomposed in this frame, the waveform has no rotational dynamics a…
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.
In preparation for future space-borne gravitational-wave (GW) detectors, should the modelling effort focus on high-precision vacuum templates or on the astrophysical environment of the sources? We perform a systematic comparison of the phase contributions caused by 1) known environmental effects in both gaseous and stellar matter backgrounds, or 2) high-order post-Newtonian {(PN)} terms in the evolution of mHz GW sources {during the inspiral stage of massive binaries}. We use the accuracy of currently available analytical waveform models as a benchmark {value, finding} the following trends: th…
We revisit the scenario of small-mass-ratio (q) black-hole binaries; performing new, more accurate, simulations of mass ratios 10:1 and 100:1 for initially nonspinning black holes. We propose fitting functions for the trajectories of the two black holes as a function of time and mass ratio (in the range 1/100 < q < 1/10$) that combine aspects of post-Newtonian trajectories at smaller orbital frequencies and plunging geodesics at larger frequencies. We then use these trajectories to compute waveforms via black hole perturbation theory. Using the advanced LIGO noise curve, we see a match of ~99.…
The accuracy of time-domain solutions of the inhomogeneous Teukolsky equation is improved significantly. Comparing energy fluxes in gravitational waves with highly accurate frequency-domain results for circular equatorial orbits in Schwarzschild and Kerr, we find agreement to within 1% or better, which we believe can be even further improved. We apply our method to orbits for which frequency-domain calculations have a relative disadvantage, specifically high-eccentricity (elliptical and parabolic) "zoom-whirl" orbits, and find the energy fluxes, waveforms, and characteristic strain in gravitat…
Inspiral waveforms of charged compact binaries and observational constraints
University of Chinese Academy of Sciences（中国科学院大学）；Taiji Laboratory for GW Universe, University of Chinese Academy of Sciences（中国科学院大学太极引力波宇宙实验室）；Hunan Normal University（湖南师范大学）；Yangtze University（长江大学）
We calculate analytical gravitational waveforms in the time- and frequency-domain for precessing quasi-circular binaries with spins of arbitrary magnitude, but nearly aligned with the orbital angular momentum. We first derive an analytical solution to the precession equations by expanding in the misalignment angle and using multiple scale analysis to separate timescales. We then use uniform asymptotic expansions to analytically Fourier transform the time-domain waveform, thus extending the stationary-phase approximation, which fails when precession is present. The resulting frequency-domain wa…
We complete the post-Newtonian (PN) prediction at the 3.5PN order for the spin contributions to the gravitational waveforms emitted by inspiraling compact binaries, in the case of quasi-circular, equatorial orbits, where both spins are aligned with the orbital angular momentum. Using results from the multipolar post-Minkowskian wave generation formalism, we extend previous works that derived the dynamics and gravitational-wave energy flux and phasing, by computing the full waveform decomposed in spin-weighted spherical harmonics. This new calculation requires the computation of multipolar mome…
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…
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-…
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,…
We provide ready-to-use time-domain gravitational waveforms for spinning compact binaries with precession effects through 1.5PN order in amplitude and compute their mode decomposition using spin-weighted -2 spherical harmonics. In the presence of precession, the gravitational-wave modes (l,m) contain harmonics originating from combinations of the orbital frequency and precession frequencies. We find that the gravitational radiation from binary systems with large mass asymmetry and large inclination angle can be distributed among several modes. For example, during the last stages of inspiral, f…
We introduce a new paradigm for constructing accurate analytic waveforms (and fluxes) for eccentric compact binaries. Our recipe builds on the standard Post-Newtonian (PN) approach but (i) retains implicit time-derivatives of the phase space variables in the instantaneous part of the noncircular waveform, and then (ii) suitably factorizes and resums this partly PN-implicit waveform using effective-one-body (EOB) procedures. We test our prescription against the exact results obtained by solving the Teukolsky equation with a test-mass source orbiting a Kerr black hole, and compare the use of the…
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 parameters of inspiralling compact binaries can be estimated using matched filtering of gravitational-waveform templates against the output of laser-interferometric gravitational-wave detectors. Using a recently calculated formula, accurate to second post-Newtonian (2PN) order [order $(v/c)^4$, where $v$ is the orbital velocity], for the frequency sweep ($dF/dt$) induced by gravitational radiation damping, we study the statistical errors in the determination of such source parameters as the ``chirp mass'' $\cal M$, reduced mass $μ$, and spin parameters $β$ and $σ$ (related to spin-orbit an…
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…
We compare recently computed waveforms from second-order gravitational self-force (GSF) theory to those generated by a new, GSF-informed, effective one body (EOB) waveform model for (spin-aligned, eccentric) inspiralling black hole binaries with large mass ratios. We focus on quasi-circular, nonspinning, configurations and perform detailed GSF/EOB waveform phasing comparisons, either in the time domain or via the gauge-invariant dimensionless function $Q_ω\equiv ω^2/\dotω$, where $ω$ is the gravitational wave frequency. The inclusion of high-PN test-mass terms within the EOB radiation reaction…
