Ringdown Gravitational Waves Research Articles

Automated design of digital filters using convolutional neural networks for extracting ringdown gravitational waves

Abstract The observation of gravitational waves is expected to allow new tests of general relativity to be performed. As the gravitational wave signal is hidden by detector noise in observed data, a method to reduce noise is required to analyze the ringdown phase of gravitational wave signals. Recently, some noise reduction methods based on a neural network have been proposed; however, the results of these methods must be considered with caution because the output can contain spurious components. To overcome this limitation, in this study, we developed a neural network– based method to design optimal digital filters for extracting ringdown gravitational wave signals. In this method, no spurious components appear in the output because the digital filters reduce the noise. We conducted simulations with waveforms of gravitational waves from binary black hole coalescence and confirmed that the proposed method designs appropriate filters that reduce detector noise.

Iterative extraction of overtones from black hole ringdown

Abstract Extraction of multiple quasinormal modes (QNMs) from ringdown gravitational waves emitted from a binary black hole coalescence is a touchstone to test whether a remnant black hole is described by the Kerr spacetime in general relativity. However, it is not straightforward to check the consistency between the ringdown signal and the QNM frequencies predicted by the linear perturbation theory. While the longest-lived mode can be extracted in a stable manner, the higher overtones damp more quickly and hence the fitting of overtones tends to end up with the overfit. To improve the extraction of overtones, we propose an iterative procedure consisting of fitting and subtraction of the longest-lived mode of the ringdown waveform in the time domain. Through the analyses of the mock waveform and numerical relativity waveform, we clarify that the iterative procedure allows us to extract the overtones in a more stable manner.

Constraints on quasinormal modes from black hole shadows in regular non-minimal Einstein Yang–Mills gravity

This work deals with scalar quasinormal modes using the higher-order WKB method and black hole shadow in non-minimal Einstein–Yang–Mills theory. To validate the results of quasinormal modes, time domain profiles are also investigated. We find that with an increase in the magnetic charge of the black hole, the ringdown gravitational wave increases non-linearly and the damping rate decreases non-linearly. The presence of a magnetic charge also results in a non-linear decrease in the black hole shadow. For large values of the coupling parameter, the black hole becomes a soliton solution and the corresponding ringdown gravitational wave frequency increases slowly with a decrease in the damping rate. For the soliton solutions, the shadow is also smaller. The constraints on the model parameters calculated using shadow observations of M87* and Sgr A* and an approximate analytical relation between quasinormal modes and shadows at the eikonal limit are discussed.

Ringdown Gravitational Waves from Close Scattering of Two Black Holes.

We have numerically investigated close scattering processes of two black holes (BHs). Our careful analysis shows for the first time a nonmerging ringdown gravitational wave induced by dynamical tidal deformations of individual BHs during their close encounter. The ringdown wave frequencies turn out to agree well with the quasinormal ones of a single BH in perturbation theory, despite its distinctive physical context from the merging case. Our study shows a new type of gravitational waveform and opens up a new exploration of strong gravitational interactions using BH encounters.

Black Hole Spectroscopy by Mode Cleaning.

We formulate a Bayesian framework to analyze ringdown gravitational waves from colliding binary black holes and test the no-hair theorem. The idea hinges on mode cleaning-revealing subdominant oscillation modes by removing dominant ones using newly proposed "rational filters." By incorporating the filter into Bayesian inference, we construct a likelihood function that depends only on the mass and spin of the remnant black hole (no dependence on mode amplitudes and phases) and implement an efficient pipeline to constrain the remnant mass and spin without Markov chain MonteCarlo. We test ringdown models by cleaning combinations of different modes and evaluating the consistency between the residual data and pure noise. The model evidence and Bayes factor are used to demonstrate the presence of a particular mode and to infer the mode starting time. In addition, we design a hybrid approach to estimate the remnant black hole properties exclusively from a single mode using Markov chain MonteCarlo after mode cleaning. We apply the framework to GW150914 and demonstrate more definitive evidence of the first overtone by cleaning the fundamental mode. This new framework provides a powerful tool for black hole spectroscopy in future gravitational-wave events.

Binary neutron star mergers in Einstein-scalar-Gauss-Bonnet gravity

Binary neutron star mergers, which can lead to less massive black holes relative to other known astrophysical channels, have the potential to probe modifications to general relativity that arise at smaller curvature scales compared to more massive compact object binaries. As a representative example of this, here we study binary neutron star mergers in shift-symmetric Einstein-scalar-Gauss-Bonnet gravity using evolutions of the full, nonperturbative evolution equations. We find that the impact on the inspiral is small, even at large values of the modified gravity coupling (as expected, as neutron stars do not have scalar charge in this theory). However, postmerger there can be strong scalar effects, including radiation. When a black hole forms, it develops scalar charge, impacting the ringdown gravitational wave signal. In cases where a longer-lived remnant star persists postmerger, we find that the oscillations of the star source levels of scalar radiation similar to the black hole formation cases. In remnant stars, we further find that at coupling values comparable to the maximum value for which black hole solutions of the same mass exist, there is significant nonlinear enhancement in the scalar field, which if sufficiently large leads to a breakdown in the evolution, seemingly due to loss of hyperbolicity of the underlying equations.

Quasinormal modes of the Kerr-Newman black hole: GW150914 and fundamental physics implications

We develop an analytical ringdown waveform model, including both the fundamental and the overtone quasinormal modes, for charged black holes and show that it is precise enough to analyze current gravitational wave data. Applying this waveform model to GW150914, the charge to mass ratio of the remnant black hole (${\ensuremath{\lambda}}_{f}$) has been constrained with the sole ringdown gravitational wave data for the first time and the 90% upper limit is ${\ensuremath{\lambda}}_{f}\ensuremath{\le}0.38$. Correspondingly, the deviation parameter of the scalar-tensor vector gravity (${\ensuremath{\alpha}}_{\mathrm{s}}$) is limited to be ${\ensuremath{\alpha}}_{\mathrm{s}}\ensuremath{\le}0.17$. Our approach can be directly applied to other binary black hole mergers with loud ringdown radiation.

Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation

Ringdown gravitational waves of compact object binaries observed by ground-based gravitational-wave detectors encapsulate rich information to understand remnant objects after the merger and to test general relativity in the strong field. In this work, we investigate the ringdown gravitational waves in detail to better understand their property, assuming that the remnant objects are black holes. For this purpose, we perform numerical simulations of post-merger phase of binary black holes by using the black hole perturbation scheme with the initial data given under the close-limit approximation, and we generate data of ringdown gravitational waves with smaller numerical errors than that associated with currently available numerical relativity simulations. Based on the analysis of the data, we propose an orthonormalization of the quasinormal mode functions describing the fundamental tone and overtones to model ringdown gravitational waves. Finally, through some demonstrations of the proposed model, we briefly discuss the prospects for ringdown gravitational-wave data analysis including the overtones of quasinormal modes.

Scope Out Multiband Gravitational-Wave Observations of GW190521-Like Binary Black Holes with Space Gravitational Wave Antenna B-DECIGO

The gravitational wave event, GW190521, is the most massive binary black hole merger observed by ground-based gravitational wave observatories LIGO/Virgo to date. While the observed gravitational wave signal is mainly in the merger and ringdown phases, the inspiral gravitational wave signal of the GW190521-like binary will be more visible to space-based detectors in the low-frequency band. In addition, the ringdown gravitational wave signal will be louder in the next generation (3G) of ground-based detectors in the high-frequency band, displaying the great potential of multiband gravitational wave observations. In this paper, we explore the scientific potential of multiband observations of GW190521-like binaries with a milli-Hz gravitational wave observatory: LISA; a deci-Hz observatory: B-DECIGO; and (next generation of) hecto-Hz observatories: aLIGO and ET. In the case of quasicircular evolution, the triple-band observations of LISA, B-DECIGO, and ET will provide parameter estimation errors of the masses and spin amplitudes of component black holes at the level of order of 1–10%. This would allow consistency tests of general relativity in the strong field at an unparalleled precision, particularly with the “B-DECIGO + ET” observation. In the case of eccentric evolution, the multiband signal-to-noise ratio found in “B-DECIGO + ET” observation would be larger than 100 for a five-year observation prior to coalescence, even with high final eccentricities.

P-stars in the gravitational wave era

P-stars are compact relativistic stars made of deconfined up and down quarks in a chromomagnetic condensate proposed by us long time ago. P-stars do not admit a critical mass thereby they are able to overcome the gravitational collapse to black holes. In this work we discuss in greater details our theoretical proposal for P-stars. We point out that our theory for compact relativistic stars stems from our own understanding of the confining quantum vacuum supported by estensive non-perturbative numerical simulations of Quantum ChromoDynamics on the lattice. We compare our proposal with the constraints arising from the recent observations of massive pulsars, the gravitational event GW170817 and the precise determination of the PSR J0030+0451 mass and radius from NICER data. We argue that core-collapsed supernovae could give rise to a P-star instead of a neutron star. In this case we show that the birth of a P-star could solve the supernova explosion problem leading to successful supernova explosions with total energies up to $10^{53}$ erg. We critically compare P-stars with the gravitational wave event GW170817 and the subsequent electromagnetic follow-up, the short Gamma Ray Burst GRB170817A and the kilonova AT2017gfo. We also present an explorative study on gravitational wave emission from coalescing binary P-stars with masses $M_1 \simeq M_2 \simeq 30 \; M_{\odot}$. We attempt a qualitative comparison with the gravitational wave event GW150914. We find that the gravitational wave strain amplitude from massive P-star binaries could mimic the ringdown gravitational wave emission by coalescing black hole binaries. We point out that a clear signature for massive P-stars would be the detection of wobble frequencies in the gravitational wave strain amplitude in the post-merger phase of two coalescing massive compact objects with unequal masses.

Black hole spectroscopy for KAGRA future prospect in O5

Ringdown gravitational waves of compact binary mergers are an important target to test general relativity. The main components of the ringdown waveform after merger are black hole quasinormal modes. In general relativity, all multipolar quasinormal modes of a black hole should give the same values of black hole parameters. Although the observed binary black hole events so far are not significant enough to perform the test with ringdown gravitational waves, it is expected that the test will be achieved in third generation detectors. The Japanese gravitational wave detector KAGRA, called bKAGRA for the current configuration, has started observation, and discussions for the future upgrade plans have also started. In this study, we consider which KAGRA upgrade plan is the best to detect the subdominant quasinormal modes of black holes in the aim of testing general relativity. We use a numerical relativity waveform as injected signals that contains two multipolar modes and analyze each mode by matched filtering. Our results suggest that the plan FDSQZ, which improves the sensitivity of KAGRA for broad frequency range, is the most suitable configuration for black hole spectroscopy.

Black Hole Ringdown: The Importance of Overtones

It is possible to infer the mass and spin of the remnant black hole from binary black hole mergers by comparing the ringdown gravitational wave signal to results from studies of perturbed Kerr spacetimes. Typically these studies are based on the fundamental quasinormal mode of the dominant $\ell=m=2$ harmonic. By modeling the ringdown of accurate numerical relativity simulations, we find that the fundamental mode alone is insufficient to recover the true underlying mass and spin, unless the analysis is started very late in the ringdown. Including higher overtones associated with this $\ell=m=2$ harmonic resolves this issue, and provides an unbiased estimate of the true remnant parameters. Further, including overtones allows for the modeling of the ringdown signal for all times beyond the peak strain amplitude, indicating that the linear quasinormal regime starts much sooner than previously expected. A model for the ringdown beginning at the peak strain amplitude can exploit the higher signal-to-noise ratio in detectors, reducing uncertainties in the extracted remnant quantities. Tests of the no-hair theorem should consider incorporating overtones in the analysis.

Can massless wormholes mimic a Schwarzschild black hole in the strong field lensing?

Recent trend of research indicates that not only massive but also massless (asymptotic Newtonian mass zero) wormholes can reproduce post-merger initial ring-down gravitational waves characteristic of black hole horizon. In the massless case, it is the non-zero charge of other fields, equivalent to what we call here the "Wheelerian mass", that is responsible for mimicking ring-down quasi-normal modes. In this paper, we enquire whether the same Wheelerian mass can reproduce black hole observables also in an altogether different experiment, viz., the strong field lensing. We examine two classes of massless wormholes, one in the Einstein-Maxwell-Dilaton (EMD) theory and the other in the Einstein-Minimally-coupled-Scalar field (EMS) theory. The observables such as the radius of the shadow, image separation and magnification of the corresponding Wheelerian masses are compared with those of a black hole (idealized SgrA* chosen for illustration) assuming that the three types of lenses share the same minimum impact parameter and distance from the observer. It turns out that, while the massless EMS\ wormholes can closely mimic the black hole in terms of strong field lensing observables, the EMD wormholes show considerable differences due to the presence of dilatonic charge. The conclusion is that masslessless alone is enough to closely mimic Schwarzschild black hole strong lensing observables in the EMS theory but not in the other, where extra parameters also influence those observables. The motion of timelike particles is briefly discussed for completeness.

Black hole perturbation under a 2+2 decomposition in the action

Black hole perturbation theory is useful for studying the stability of black holes and calculating ringdown gravitational waves after the collision of two black holes. Most previous calculations were carried out at the level of the field equations instead of the action. In this work, we compute the Einstein-Hilbert action to quadratic order in linear metric perturbations about a spherically symmetric vacuum background in Regge-Wheeler gauge. Using a $2+2$ splitting of spacetime, we expand the metric perturbations into a sum over scalar, vector, and tensor spherical harmonics, and dimensionally reduce the action to two dimensions by integrating over the two sphere. We find that the axial perturbation degree of freedom is described by a two-dimensional massive vector action, and that the polar perturbation degree of freedom is described by a two-dimensional dilaton massive gravity action. Varying the dimensionally reduced actions, we rederive covariant and gauge-invariant master equations for the axial and polar degrees of freedom. Thus, the two-dimensional massive vector and massive gravity actions we derive by dimensionally reducing the perturbed Einstein-Hilbert action describe the dynamics of a well-studied physical system: the metric perturbations of a static black hole. The $2+2$ formalism we present can be generalized to $m+n$-dimensional spacetime splittings, which may be useful in more generic situations, such as expanding metric perturbations in higher dimensional gravity. We provide a self-contained presentation of $m+n$ formalism for vacuum spacetime splittings.

Event Rates of Gravitational Waves from merging Intermediate mass Black Holes: based on a Runaway Path to a SMBH

Based on a dynamical formation model of a supermassive black hole (SMBH), we estimate the expected observational profile of gravitational wave at ground-based detectors, such as KAGRA or advanced LIGO/VIRGO. Noting that the second generation of detectors have enough sensitivity from 10 Hz and up, we are able to detect the ring-down gravitational wave of a BH with the mass M < 2 × 103M⊙. This enables us to check the sequence of BH mergers to SMBHs via intermediate-mass BHs. We estimate the number density of galaxies from the halo formation model and estimate the number of BH mergers from the giant molecular cloud model assuming hierarchical growth of merged cores. At the designed KAGRA (and/or advanced LIGO/VIRGO), we find that the BH merger of its total mass M ∼ 60M⊙ is at the peak of the expected mass distribution. With its signal-to-noise ratio ρ = 10(30), we estimate the event rate R ∼ 200(20) per year in the most optimistic case, and we also find that BH mergers in the range M < 150M⊙ are R > 1 per year for ρ = 10. Thus, if we observe a BH with more than 100M⊙ in future gravitational-wave observations, our model naturally explains its source.

Estimation of starting times of quasinormal modes in ringdown gravitational waves with the Hilbert-Huang transform

It is known that a quasinormal mode (QNM) of a remnant black hole dominates a ringdown gravitational wave (GW) in a binary black hole (BBH) merger. To study properties of the QNMs, it is important to determine the time when the QNMs appear in a GW signal as well as to calculate its frequency and amplitude. In this paper, we propose a new method of estimating the starting time of the QNM and calculating the QNM frequency and amplitude of BBH GWs. We apply it to simulated merger waveforms by numerical relativity and the observed data of GW150914. The results show that the obtained QNM frequencies and time evolutions of amplitudes are consistent with the theoretical values within 1% accuracy for pure waveforms free from detector noise. In addition, it is revealed that there is a correlation between the starting time of the QNM and the spin of the remnant black hole. In the analysis of GW150914, we show that the parameters of the remnant black hole estimated through our method are consistent with those given by LIGO and a reasonable starting time of the QNM is determined.

Black hole ringdown echoes and howls

Recently the possibility of detecting echoes of ringdown gravitational waves from binary black hole mergers was shown. The presence of echoes is expected if the black hole is surrounded by a mirror that reflects gravitational waves near the horizon. Here, we present slightly more sophisticated templates motivated by a waveform which is obtained by solving the linear perturbation equation around a Kerr black hole with a complete reflecting boundary condition in the stationary traveling wave approximation. We estimate that the proposed template can bring about a |$10\%$| improvement in the signal-to-noise ratio.

Ring-down gravitational waves and lensing observables: How far can a wormhole mimic those of a black hole?

It has been argued that the recently detected ring-down gravity waveforms could be indicative only of the presence of light rings in a horizonless object, such as a surgical Schwarzschild wormhole, with the frequencies differing drastically from those of the horizon quasinormal mode frequencies $\omega _{\text{QNM}}$ at late times. While the possibility of such a horizonless alternative is novel by itself, we show by the example of Ellis-Bronnikov wormhole that the differences in $\omega _{\text{QNM}}$ in the eikonal limit (large $l$) need not be drastic. This result will be reached by exploiting the connection between $\omega _{\text{QNM}}$ and the Bozza strong field lensing parameters. We shall also show that the lensing observables of the Ellis-Bronnikov wormhole can also be very close to those of a black hole (say, SgrA$^{\ast }$ hosted by our galaxy) of the same mass. This situation indicates that the ring-down frequencies and lensing observables of the Ellis-Bronnikov wormhole can remarkably mimic those of a black hole. The constraint on wormhole parameter $\gamma $ imposed by experimental accuracy is briefly discussed. We also provide independent arguments supporting the stability of the Ellis-Bronnikov wormhole proven recently.

Gravitational Waves from Merging Intermediate-mass Black Holes. II. Event Rates at Ground-based Detectors

Based on a dynamical formation model of a supermassive black hole (SMBH), we estimate the expected observational profile of gravitational wave at ground-based detectors, such as KAGRA or advanced LIGO/VIRGO. Noting that the second generation of detectors have enough sensitivity from 10 Hz and up (especially with KAGRA owing to its location at less seismic noise), we are able to detect the ring-down gravitational wave of a BH with the mass $M < 2\times 10^3 M_\odot $. This enables us to check the sequence of BH mergers to SMBHs via intermediate-mass BHs. We estimate the number density of galaxies from the halo formation model and estimate the number of BH mergers from the giant molecular cloud model assuming hierarchical growth of merged cores. At the designed KAGRA (and/or advanced LIGO/VIRGO), we find that the BH merger of its total mass $M\sim 60M_\odot$ is at the peak of the expected mass distribution. With its signal-to-noise ratio $\rho=10 (30)$, we estimate the event rate $R \sim 200 (20)$ per year in the most optimistic case, and we also find that BH mergers in the range $M < 150 M_\odot$ are $R>1$ per year for $\rho=10$. Thus, if we observe a BH with more than $100 M_\odot$ in future gravitational-wave observations, our model naturally explains its source.

Gravitational wave quasinormal mode from Population III massive black hole binaries in various models of population synthesis

Focusing on the remnant black holes after merging binary black holes, we show that ringdown gravitational waves of Population III binary black holes mergers can be detected with the rate of $5.9-500~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for various parameters and functions. This rate is estimated for the events with SNR$>8$ for the second generation gravitational wave detectors such as KAGRA. Here, ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Population III star formation rate and the fraction of binaries, respectively. When we consider only the events with SNR$>35$, the event rate becomes $0.046-4.21~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$. This suggest that for remnant black hole's spin $q_f>0.95$ we have the event rate with SNR$>35$ less than $0.037~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$, while it is $3-30~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for the third generation detectors such as Einstein Telescope. If we detect many Population III binary black holes merger, it may be possible to constrain the Population III binary evolution paths not only by the mass distribution but also by the spin distribution.