The extreme-gravity collisions between black holes allow us to probe the underlying theory of gravity. We apply the theory-agnostic inspiral-merger-ringdown consistency test to an example theory beyond general relativity for the first time. Here we focus on the string-inspired Einstein-dilaton Gauss-Bonnet gravity and modify the inspiral, ringdown, and remnant black hole properties of the gravitational waveform. We found that future multiband observations allow us to constrain the theory stronger than current observations by an order of magnitude. The formalism developed here can easily be applied to other theories.
Gravitational waves from extreme gravity events such as the coalescence of two black holes in a binary system fill our observable universe, bearing with them the underlying theory of gravity driving their process. One compelling alternative theory of gravity -- known as Einstein-dilaton Gauss-Bonnet gravity motivated by string theory -- describes the presence of an additional dilaton scalar field coupled directly to higher orders of the curvature, effectively describing a "fifth force" interaction and the emission of scalar dipole radiation between two scalarized black holes. Most previous stu…
An extreme mass ratio inspiral consists of two parts: adiabatic inspiral and plunge. The plunge trajectory from the innermost stable circular orbit (ISCO) is special (somewhat independent of initial conditions). We write an expression for its solution in closed-form and for the emitted waveform. In particular we extract an expression for the associated black-hole ringdown amplitudes, and evaluate them numerically.
Gravitational waves from the explosive merger of distant black holes are encoded with details regarding the complex extreme-gravity spacetime present at their source. Famously described by the Kerr spacetime metric for rotating black holes in general relativity, what if effects beyond this theory are present? One way to efficiently test this hypothesis is to first obtain a metric which parametrically deviates from the Kerr metric in a model-independent way. Given such a metric, one can then predict the ensuing corrections to both the inspiral and ringdown portions of the gravitational waveform…
The inspiral-merger-ringdown (IMR) consistency test checks the consistency of the final mass and final spin of a binary black hole merger remnant, independently inferred via the inspiral and merger-ringdown parts of the waveform. As binaries are expected to be nearly circularized when entering the frequency band of ground-based detectors, tests of general relativity (GR) currently employ quasicircular waveforms. We quantify the effect of residual orbital eccentricity on the IMR consistency test. We find that eccentricity causes a significant systematic bias in the inferred final mass and spin …
We analyze the problem of parameter estimation for compact binary systems that could be detected by ground-based gravitational wave detectors. So far this problem has only been dealt with for the inspiral and the ringdown phases separately. In this paper, we combine the information from both signals, and we study the improvement in parameter estimation, at a fixed signal-to-noise ratio, by including the ringdown signal without making any assumption on the merger phase. The study is performed for both initial and advanced LIGO and VIRGO detectors.
We investigate the capability of LISA to measure the sky position of equal-mass, nonspinning black hole binaries, combining for the first time the entire inspiral-merger-ringdown signal, the effect of the LISA orbits, and the complete three-channel LISA response. We consider an ensemble of systems near the peak of LISA's sensitivity band, with total rest mass of 2\times10^6 M\odot, a redshift of z = 1, and randomly chosen orientations and sky positions. We find median sky localization errors of approximately \sim3 arcminutes. This is comparable to the field of view of powerful electromagnetic …
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.
Spherical harmonic modes of gravitational waveforms for inspiraling compact binaries in eccentric orbits from post-Newtonian (PN) theory accurate to third post-Newtonian order, and those extracted from numerical relativity (NR) simulations for binary black holes (BBHs) are compared. We combine results from the two approaches (PN and NR) to construct time-domain hybrid waveforms that describe the complete evolution of BBH mergers through inspiral-merger-ringdown (IMR) stages. These hybrids are then used in constructing a fully analytical dominant mode ($\ell$=2, $|m|$=2) eccentric IMR model. A …
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…
Searches for gravitational waves (GWs) from binary black holes using interferometric GW detectors require the construction of template banks for performing matched filtering while analyzing the data. Placement of templates over the parameter space of binaries, as well as coincidence tests of GW triggers from multiple detectors make use of the definition of a metric over the space of gravitational waveforms. Although recent searches have employed waveform templates coherently describing the inspiral, merger and ringdown (IMR) of the coalescence, the metric used in the template banks and coincid…
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,…
This paper presents an algorithm to accelerate the evaluation of inspiral-merger-ringdown waveform models for gravitational wave data analysis. While the idea can also be applied in the time domain, here we focus on the frequency domain, which is most typically used to reduced computational cost in gravitational wave data analysis. Our work extends the idea of multibanding, which has been developed to accelerate frequency domain waveforms, to include the merger and ringdown and spherical harmonics beyond the dominant quadrupole spherical harmonic. The original method is based on a heuristic al…
We numerically solve the Teukolsky equation in the time domain to obtain the gravitational-wave emission of a small mass inspiraling and plunging into the equatorial plane of a Kerr black hole. We account for the dissipation of orbital energy using the Teukolsky frequency-domain gravitational-wave fluxes for circular, equatorial orbits, down to the light-ring. We consider Kerr spins $-0.99 \leq q \leq 0.99$, and compute the inspiral-merger-ringdown (2,2), (2,1), (3,3), (3,2), (4,4), and (5,5) modes. We study the large-spin regime, and find a great simplicity in the merger waveforms, thanks to …
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 fully general relativistic simulations of the quasi-circular inspiral and merger of charged, non-spinning, binary black holes with charge-to-mass ratio $λ\le 0.3$. We discuss the key features that enabled long term and stable evolutions of these binaries. We also present a formalism for computing the angular momentum carried away by electromagnetic waves, and the electromagnetic contribution to black-hole horizon properties. We implement our formalism and present the results for the first time in numerical-relativity simulations. In addition, we compare our full non-linear solutions…
LISA can detect higher harmonics of the ringdown gravitational-wave signal from massive black-hole binary mergers with large signal-to-noise ratio. The most massive black-hole binaries are more likely to have electromagnetic counterparts, and the inspiral will contribute little to their signal-to-noise ratio. Here we address the following question: can we extract the binary parameters and localize the source using LISA observations of the ringdown only? Modulations of the amplitude and phase due to LISA's motion around the Sun can be used to disentangle the source location and orientation when…
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…
The first spectral numerical simulations of 16 orbits, merger, and ringdown of an equal-mass non-spinning binary black hole system are presented. Gravitational waveforms from these simulations have accumulated numerical phase errors through ringdown of ~0.1 radian when measured from the beginning of the simulation, and ~0.02 radian when waveforms are time and phase shifted to agree at the peak amplitude. The waveform seen by an observer at infinity is determined from waveforms computed at finite radii by an extrapolation process accurate to ~0.01 radian in phase. The phase difference between t…
Modeling the merger-ringdown of an eccentric test-mass inspiral into a Kerr black hole using the effective-one-body framework
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））；University of Maryland（马里兰大学）；Niels Bohr Institute（尼尔斯·玻尔研究所）；University of Rhode Island（罗德岛大学）；University of Massachusetts, Dartmouth（马萨诸塞大学达特茅斯分校）
One class of competitive candidates for dark matter is ultralight bosons. If they exist, these bosons may form long-lived bosonic clouds surrounding rotating black holes via superradiant instabilities, acting as sources of gravity and affecting the propagation of gravitational waves around the host black hole. During extreme-mass-ratio inspirals, the bosonic clouds will survive the inspiral phase and can affect the quasinormal-mode frequencies of the perturbed black-hole-bosonic-cloud system. In this work, we compute the shifts of gravitational quasinormal-mode frequencies of a rotating black …
Advanced LIGO's recent observations of gravitational waves (GWs) from merging binary black holes have opened up a unique laboratory to test general relativity (GR) in the highly relativistic regime. One of the tests used to establish the consistency of the first LIGO event with a binary black hole merger predicted by GR was the inspiral-merger-ringdown consistency test. This involves inferring the mass and spin of the remnant black hole from the inspiral (low-frequency) part of the observed signal and checking for the consistency of the inferred parameters with the same estimated from the post…
We present a prescription for computing gravitational waveforms for the inspiral, merger and ringdown of non-spinning eccentric binary black hole systems. The inspiral waveform is computed using the post-Newtonian expansion and the merger waveform is computed by interpolating a small number of quasi-circular NR waveforms. The use of circular merger waveforms is possible because eccentric binaries circularize in the last few cycles before the merger, which we demonstrate up to mass ratio $q = m_1/m_2 = 3$. The complete model is calibrated to 23 numerical relativity (NR) simulations starting ~20…
We estimate the expected signal-to-noise ratios (SNRs) from the three phases (inspiral,merger,ringdown) of coalescing binary black holes (BBHs) for initial and advanced ground-based interferometers (LIGO/VIRGO) and for space-based interferometers (LISA). LIGO/VIRGO can do moderate SNR (a few tens), moderate accuracy studies of BBH coalescences in the mass range of a few to about 2000 solar masses; LISA can do high SNR (of order 10^4) high accuracy studies in the mass range of about 10^5 to 10^8 solar masses. BBHs might well be the first sources detected by LIGO/VIRGO: they are visible to much …
The waveforms from binary black hole mergers include inspiral, merger, and ringdown parts. Usually, the inspiral waveform can be obtained by calibrating from post-Newtonian approximation; The merger and ringdown ones can be gotten from the quasinormal modes with black hole perturbation theory. However, for more general black holes, the calculation of the quasinormal modes is not trivial. In this paper we use the photon sphere to get the quasinormal modes of spinning black holes. Then we connect the ringdown wave with the inspiral part to get full waveforms and compare with the ones from numeri…
We study the inspiral, merger and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and Post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the Post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the Post-Newtonian series to the numerical results is non-monotonic. …
ESIGMAHM: An Eccentric, Spinning inspiral-merger-ringdown waveform model with Higher Modes for the detection and characterization of binary black holes
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…
We first use five non-spinning and two mildly spinning (chi_i \simeq -0.44, +0.44) numerical-relativity waveforms of black-hole binaries and calibrate an effective-one-body (EOB) model for non-precessing spinning binaries, notably its dynamics and the dominant (2,2) gravitational-wave mode. Then, we combine the above results with recent outcomes of small-mass-ratio simulations produced by the Teukolsky equation and build a prototype EOB model for detection purposes, which is capable of generating inspiral-merger-ringdown waveforms for non-precessing spinning black-hole binaries with any mass r…
The gravitational wave observations of colliding black holes have opened a new window into the unexplored extreme gravity sector of physics, where the gravitational fields are immensely strong, non-linear, and dynamical. 10 binary black hole merger events observed so far can be used to test Einstein's theory of general relativity, which has otherwise been proven to agree with observations from several sources in the weak- or static-field regimes. One interesting future possibility is to detect gravitational waves from GW150914-like stellar-mass black hole binaries with both ground-based and sp…
Spinning Effective-to-Backwards One Body ($\texttt{SEBOB}$): combining Effective One-Body inspirals and Backwards One-Body merger-ringdowns for aligned spin black hole binaries
We characterize the expected statistical errors with which the parameters of black-hole binaries can be measured from gravitational-wave (GW) observations of their inspiral, merger and ringdown by a network of second-generation ground-based GW observatories. We simulate a population of black-hole binaries with uniform distribution of component masses in the interval $(3,80)~M_\odot$, distributed uniformly in comoving volume, with isotropic orientations. From signals producing signal-to-noise ratio $\geq 5$ in at least two detectors, we estimate the posterior distributions of the binary paramet…
There is a forbidden region in the parameter space of quasinormal modes of black holes in general relativity. Using both inspiral and ringdown phases of gravitational waves from binary black holes, we propose two methods to test general relativity. We also evaluate how our methods will work when we apply them to Pop III black-hole binaries with typical masses. Adopting the simple mean of the estimated range of the event rate, we have the expected rate of 500 ${\rm yr^{-1}}$. Then, the rates of events with signal-to-noise ratios greater than 20 and greater than 50 are 32 ${\rm yr^{-1}}$ and 2 $…
The ringdown data of both GW150914 and GW190521\_074359 (GW190521r) show evidence supporting the presence of overtone. Previous studies all adopt a fundamental assumption, which were motivated more by convenience than by first principles, that the first overtone and the fundamental mode share a same onset. In this work, for the first time we relax such assumption, and we aim to probe the possible chromatic onsets of these two components within the GW150914 and GW190521r ringdown data. For both events, we bound the onset lags to be $Δt_0\geq 5M_f$ at probabilities of $\geq 94.7\%$, where $M_f$ …
We propose a novel, frequency-domain approach to the analysis of the gravitational-wave ringdown signal of binary black holes and the identification of quasinormal mode frequencies of the remnant. Our approach avoids the issues of spectral leakage that would normally be expected (associated with the abrupt start of the ringdown) by modeling the inspiral and merger parts of the signal using a flexible sum of sine-Gaussian wavelets truncated at the onset of the ringdown. Performing the analysis in the frequency domain allows us to use standard (and by now well-established) Bayesian inference pip…
Detecting gravitational waves from coalescing compact binaries allows us to explore the dynamical, nonlinear regime of general relativity and constrain modifications to it. Some of the gravitational-wave events observed by the LIGO-Virgo Collaboration have sufficiently high signal-to-noise ratio in the merger, allowing us to probe the relaxation of the remnant black hole to its final, stationary state - the so-called black-hole ringdown, which is characterized by a set of quasinormal modes. Can we use the ringdown to constrain deviations from general relativity, as predicted by several of its …
The late inspiral, merger, and ringdown of a black hole-neutron star (BHNS) system can provide information about the neutron-star equation of state (EOS). Candidate EOSs can be approximated by a parametrized piecewise-polytropic EOS above nuclear density, matched to a fixed low-density EOS; and we report results from a large set of BHNS inspiral simulations that systematically vary two parameters. To within the accuracy of the simulations, we find that, apart from the neutron-star mass, a single physical parameter Lambda, describing its deformability, can be extracted from the late inspiral, m…
The interferometric LIGO detectors have recently measured the first direct gravitational-wave signal from what has been interpreted as the inspiral, merger and ringdown of a binary system of black holes. The signal-to-noise ratio of the measured signal is large enough to leave little doubt that it does refer to the inspiral of two massive and ultracompact objects, whose merger yields a rotating black hole. Yet, the quality of the data is such that some room is left for alternative interpretations that do not involve black holes, but other objects that, within classical general relativity, can …
