Extracting linear and nonlinear quasinormal modes from black hole merger simulations
Mark Ho-Yeuk Cheung, Emanuele Berti, Vishal Baibhav, Roberto Cotesta
备注：
39 pages, 22 figures, 2 tables. Interactive plots and code usage examples available at https://mhycheung.github.io/jaxqualin/. Eq. (20) and Fig. 10 are updated in this version
In general relativity, when two black holes merge they produce a rotating (Kerr) black hole remnant. According to perturbation theory, the remnant emits "ringdown" radiation: a superposition of exponentials with characteristic complex frequencies that depend only on the remnant's mass and spin. While the goal of the black hole spectroscopy program is to measure the quasinormal mode frequencies, a knowledge of their amplitudes and phases is equally important to determine which modes are detectable, and possibly to perform additional consistency checks. Unlike the complex frequencies, the amplitudes and phases depend on the properties of the binary progenitors, such as the binary mass ratio and component spins. In this paper we develop a fitting algorithm designed to reliably identify the modes present in numerical simulations and to extract their amplitudes and phases. We apply the algorithm to over 500 binary black hole simulations from the public SXS numerical relativity simulation catalog, and we present fitting formulas for the resulting mode amplitudes and phases as functions of the properties of the progenitors. Crucially, our algorithm allows for the extraction of not only prograde fundamental modes and overtones, but also retrograde modes and second-order modes. We unveil interesting relations for the amplitude ratios of different modes. The fitting code and interactive versions of some of the plots are publicly available. The results presented in this paper can be updated as more and better simulations become available.
We present results obtained by scattering a scalar field off the curved background of a coalescing binary black hole system. A massless scalar field is evolved on a set of fixed backgrounds, each provided by a spatial hypersurface generated numerically during a binary black hole merger. We show that the scalar field scattered from the merger region exhibits quasinormal ringing once a common apparent horizon surrounds the two black holes. This occurs earlier than the onset of the perturbative regime as measured by the start of the quasinormal ringing in the gravitational waveforms. We also use …
Quasinormal modes describe the return to equilibrium of a perturbed system, in particular the ringdown phase of a black hole merger. But as globally-defined quantities, the quasinormal spectrum can be highly sensitive to global structure, including distant small perturbations to the potential. In what sense are quasinormal modes a property of the resulting black hole? We explore this question for the linearized perturbation equation with two potentials having disjoint bounded support. We give a composition law for the Wronskian that determines the quasinormal frequencies of the combined system…
Recent population synthesis simulations of Pop III stars suggest that the event rate of coalescence of $\sim 30M_\odot$--$30M_\odot$ binary black holes can be high enough for the detection by the second generation gravitational wave detectors. The frequencies of chirp signal as well as quasinormal modes are near the best sensitivity of these detectors so that it would be possible to confirm Einstein's general relativity. Using the WKB method, we suggest that for the typical value of spin parameter $a/M\sim 0.7$ from numerical relativity results of the coalescence of binary black holes, the str…
We study perturbations of black holes absorbing dark energy. Due to the accretion of dark energy, the black hole mass changes. We observe distinct perturbation behaviors for absorption of different forms of dark energy into the black holes. This provides the possibility of extracting information whether dark energy lies above or below the cosmological constant boundary $w=-1$. In particular, we find in the late time tail analysis that, differently from the other dark energy models, the accretion of phantom energy exhibits a growing mode in the perturbation tail. The instability behavior found …
Universal relations independently of the equation of state (EOS) for neutron star matter are valuable, if they exist, for extracting the neutron star properties, which generally depend on the EOS. In this study, we newly derive the universal relations predicting the gravitational wave frequencies for the fundamental ($f$), the 1st pressure ($p_1$), and the 1st spacetime ($w_1$) modes and the damping rate for the $f$- and $w_1$-modes as a function of the dimensionless tidal deformability. In particular, with the universal relations for the $f$-modes one can predict the frequencies and damping r…
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,…
It is expected that all astrophysical black holes in equilibrium are well described by the Kerr solution. Moreover, any black hole far away from equilibrium, such as one initially formed in a compact binary merger or by the collapse of a massive star, will eventually reach a final equilibrium Kerr state. At sufficiently late times in this process of reaching equilibrium, we expect that the black hole is modeled as a perturbation around the final state. The emitted gravitational waves will then be damped sinusoids with frequencies and damping times given by the quasinormal mode spectrum of the …
Recent numerical relativity simulations of mergers of binary black holes suggest that the maximum final value of $a/M$ is $\sim 0.95$ for the coalescence of two equal mass black holes with aligned spins of the same magnitude $a/M=0.994$ which is close to the upper limit $a/M=0.998$ of accretion spin-up shown by Thorne. Using the WKB method, we suggest that if quasinormal modes with $a/M \sim 0.95$ are detected by the second generation gravitational wave detectors, we could confirm the strong gravity space-time based on Einstein's general relativity up to $1.33M$ which is only $\sim 1.014$ time…
We propose two frequency-domain filters to analyze ringdown signals of binary black hole mergers. The first rational filter is constructed based on a set of (arbitrary) quasi-normal modes (QNMs) of the remnant black holes, whereas the second full filter comes from the transmissivity of the remnant black holes. The two filters can remove corresponding QNMs from original time-domain ringdowns, while changing early inspiral signals in a trivial way - merely a time and phase shift. After filtering out dominant QNMs, we can visualize the existence of various subdominant effects. For example, by app…
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…
The existence of the ergoregion of the Kerr space-time has not been confirmed observationally yet. We show that the confirmation would be possible by observing the quasinormal mode in gravitational waves. As an example, using the recent population synthesis results of Pop III binary black holes, we find that the peak of the final merger mass ($M_f$) is about $50~\rm M_{\odot}$, while the fraction of the final spin $q_f = a_f/M_f > 0.7$ needed for the confirmation of a part of ergoregion is $\sim 77\%$. To confirm the frequency of the quasinormal mode, ${\rm SNR} > 35$ is needed. The standard m…
Black hole spectroscopy with gravitational waves is an important tool to measure the mass and spin of astrophysical black holes and to test their Kerr nature. Next-generation ground- and space-based detectors will observe binary black hole mergers with large signal-to-noise ratios and perform spectroscopy routinely. It was recently shown that small perturbations due, e.g., to environmental effects (the "flea") to the effective potential governing gravitational-wave generation and propagation in black hole exteriors (the "elephant") can lead to arbitrarily large changes in the black hole's quas…
The gravitational consequence of local Lorentz violation (LV) should show itself in derivation of the characteristic quasinormal ringing of black hole mergers from their general relativity case. In this paper, we study quasinormal modes (QNMs) of the scalar and electromagnetic field perturbations to Einstein aether black holes. We find that quasinormal ringing of the first kind aether black hole is similar to that of another Lorentz violation model---the QED-extension limit of standard model extension. These similarities between completely different backgrounds may imply that LV in gravity sec…
The behavior of hairy black hole solutions, obtained by the gravitational decoupling (GD) method, is investigated under scalar perturbations. The quasinormal mode frequencies of such solutions are regulated by GD hair. The numerically generated wave solutions are derived for a range of values for the GD hairy black hole parameters, with higher-frequency modes very sensitive to them. The results are confronted with the corresponding ones for the Schwarzschild solution, whose deviations from it demonstrate a unique physical identification of GD hairy black holes. The method here presented compri…
After a long wait, gravitational wave astronomy has finally begun. Binary black hole mergers are being detected by LIGO and Virgo, and theorists are starting to receive a wealth of data to be analized. At this point we can at long last begin to test alternative theories of gravity and different models of compact objects. One powerful tool to do this is the perturbative analysis of background spacetimes. The objective of this brief review is to introduce the notion and analysis of black hole quasinormal modes, starting from the linear perturbation theory and including a brief discussion of nume…
The location of the cutoff in the gravitational-wave spectrum of black hole-neutron star mergers is correlated strongly with the neutron-star radius for the case that the neutron star is disrupted by the black hole during the merger. However, the modulation which appears in the spectrum due to the mode mixing makes it difficult to measure the cutoff frequency if gravitational waves are observed from inclined direction or the binary is precessing. In this letter, we show that the cutoff frequency can be measured even in such situations with a method we have recently proposed to reconstruct the …
In the study of perturbations around black hole configurations, whether an external source can influence the perturbation behavior is an interesting topic to investigate. When the source acts as an initial pulse, it is intuitively acceptable that the existing quasinormal frequencies will remain unchanged. However, the confirmation of such an intuition is not trivial for the rotating black hole, since the eigenvalues in the radial and angular parts of the master equations are coupled. We show that for the rotating black holes, a moderate source term in the master equation in the Laplace s-domai…
Quasinormal modes of a two-parameter family of Lorentzian wormhole spacetimes, which arise as solutions in a specific scalar-tensor theory associated with braneworld gravity, are obtained using standard numerical methods. Being solutions in a scalar-tensor theory, these wormholes can exist with matter satisfying the Weak Energy Condition. If one posits that the end-state of stellar-mass binary black hole mergers, of the type observed in GW150914, can be these wormholes, then we show how their properties can be measured from their distinct signatures in the gravitational waves emitted by them a…
Three-dimensional simulations for the merger of binary neutron stars (BNSs) are performed in the framework of full general relativity. We pay particular attention to the black hole (BH) formation case and to the resulting mass of the surrounding disk for exploring possibility for formation of the central engine of short-duration gamma-ray bursts. Hybrid equations of state (EOSs) are adopted mimicking realistic, stiff nuclear EOSs, for which the maximum allowed gravitational mass of cold and spherical neutron stars (NSs), M_sph, is larger than 2M_sun. For the simulations, we focus on BNSs of th…
Gravitational waves carry energy, angular momentum, and linear momentum. In generic binary black hole mergers, the loss of linear momentum imparts a recoil velocity, or a "kick", to the remnant black hole. We exploit recent advances in gravitational waveform and remnant black hole modeling to extract information about the kick from the gravitational wave signal. Kick measurements such as these are astrophysically valuable, enabling independent constraints on the rate of second-generation mergers. Further, we show that kicks must be factored into future ringdown tests of general relativity with…
Quasinormal modes of perturbed black holes have recently gained much interest because of their tight relations with the gravitational wave signals emitted during the post-merger phase of a binary black hole coalescence. One of the intriguing features of these modes is that they respect the no-hair theorem, and hence, they can be used to test black hole space-times and the underlying gravitational theory. In this paper, we exhibit three different aspects of how black hole quasinormal modes could be altered in theories beyond Einstein general relativity. These aspects are the direct alterations …
Exceptional Points in Quasinormal Spectra of Hairy Black Holes
College of Physics, Sichuan University（四川大学物理学院）；School of Data Science, Shanghai University of Finance and Economics Zhejiang College（上海财经大学浙江学院数据科学学院）
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 frequencie…
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 ($λ_f$) has been constrained with the sole ringdown gravitational wave data for the first time and the $90\%$ upper limit is $λ_f\leq 0.38$. Correspondingly, the deviation parameter of the scalar-tensor vector gravity ($α_{\rm s}$) is limited to be $α_{\rm s}\leq 0.17$. Our approach can…
Closed photon orbits around isolated black holes are related to important aspects of black hole physics, such as strong lensing, absorption cross section of null particles and the way that black holes relax through quasinormal ringing. When two black holes are present -- such as during the inspiral and merger events of interest for gravitational-wave detectors -- the concept of closed photon orbits still exists, but its properties are basically unknown. With these applications in mind, we study here the closed photon orbits of two different static black hole binaries. The first one is the Maju…
Ringdown of a postinnermost stable circular orbit of a rapidly spinning black hole: Mass ratio dependence of higher harmonic quasinormal mode excitation
The Quasinormal modes (QNMs) for gravitational and electromagnetic perturbations are calculated in a Scalar-Tensor-Vector (Modified Gravity) spacetime, which was initially proposed to obtain correct dynamics of galaxies and galaxy clusters without the need for dark matter. It is found that for the increasing model parameter $α$, both the real and imaginary parts of the QNMs decrease compared to those for a standard Schwarzschild black hole. On the other hand, when taking into account the $1/(1+α)$ mass re-scaling factor present in MOG, Im($ω$) matches almost identically that of GR, while Re($ω…
Squeezed Quasinormal Modes from Nonlinear Gravitational Effects
Nordita, Stockholm University and KTH Royal Institute of Technology（诺尔迪塔，斯德哥尔摩大学与皇家理工学院）；Tata Institute of Fundamental Research Hyderabad（泰姬玛哈巴德基础研究所）；Department of Physics, Stockholm University（斯德哥尔摩大学物理系）；Department of Physics and Origins Project, Arizona State University（亚利桑那州立大学物理系与起源项目）；T. D. Lee Institute（李政道研究所）；Wilczek Quantum Center, Department of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院费曼量子中心）；Center for Theoretical Physics, Massachusetts Institute of Technology（麻省理工学院理论物理中心）
The advent of gravitational wave observation starts a new era of precision tests of gravitational theory. Estimations of black holes mergers should come from any well established gravitational theories, provided that the theory has not been ruled out by observations. In this paper we consider the low energy limit of heterotic string theory where the associated rotating and charged black holes are described by the Kerr-Sen solution. We investigate the approximate final spins and quasinormal modes of the black hole resulting from the merger process.
Structure at the horizon scale of black holes would give rise to echoes of the gravitational wave signal associated with the post-merger ringdown phase in binary coalescences. We study the waveform of echoes in static and stationary, traversable wormholes in which perturbations are governed by a symmetric effective potential. We argue that echoes are dominated by the wormhole quasinormal frequency nearest to the fundamental black hole frequency that controls the primary signal. We put forward an accurate method to construct the echoes waveform(s) from the primary signal and the quasinormal fre…
In this paper, we explore the signatures of non-rotating and rotating black hole mergers in the matter-free modified gravity. First, we solve the unstable circular null orbits and the innermost stable circular timelike orbits via the geodesic motion. The characteristic quantities of these orbits are systematically analyzed by varying the black hole spin and the scalar field parameter of the gravity. Then based on it, we study the ringdown modes from the light ring/quasinormal modes correspondence. The final spins of the merged black holes are also estimated with the Buonanno-Kidder-Lehner reci…
Optimal extraction of information from gravitational-wave observations of binary black-hole coalescences requires detailed knowledge of the waveforms. Current approaches for representing waveform information are based on spin-weighted spherical harmonic decomposition. Higher-order harmonic modes carrying a few percent of the total power output near merger can supply information critical to determining intrinsic and extrinsic parameters of the binary. One obstacle to constructing a full multi-mode template of merger waveforms is the apparently complicated behavior of some of these modes; instea…
The local Lorentz violation (LV) in gravity sector should show itself in derivation of the characteristic quasinormal modes (QNMs) of black hole mergers from their general relativity case. In this paper, I study QNMs of the gravitational field perturbations to Einstein-aether black holes and, at first compare them to those in Schwarzschild black hole, and then some other known LV gravity theories. By comparing to Schwarzschild black hole, the first kind aether black holes have larger damping rate and the second ones have lower damping rate. And they all have smaller real oscillation frequency …
Ultralight bosons are a class of hypothetical particles that could potentially solve critical problems in fields ranging from cosmology to astrophysics and fundamental physics. If ultralight bosons exist, they form clouds around spinning black holes with sizes comparable to their particle Compton wavelength through superradiance, a well-understood classical wave amplification process that has been studied for decades. After these clouds form, they dissipate and emit continuous gravitational waves through the annihilation of ultralight bosons into gravitons. These gravitons could be detected wi…
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…
