Ringdown Signal Research Articles

Precise Reflectance/Transmittance Measurements of Highly Reflective Optics with Saturated Cavity Ring-Down Signals

In this paper, a data processing approach was developed to accurately extract the ring-down time and amplitude of the saturated cavity ring-down (CRD) signal; both were utilized to determine simultaneously the high reflectance and residual transmittance of highly reflective (HR) mirrors with a dual-channel CRD configuration. The influence of saturation was eliminated by deleting the beginning saturated data points of the saturated CRD signal and fitting the remaining non-saturated CRD signal to a single-exponential function. By comparing the reflectance/transmittance measurement results of HR samples obtained via data processing of saturated CRD signals and via single-exponentially fitting non-saturated CRD signals with utilization of neutral density filter(s) to eliminate saturation, it was found that the reflectances obtained with both methods were in excellent agreement, while the residual transmittance obtained with the saturated CRD signal was more accurate than that obtained with the neutral-density-filter-attenuated non-saturated CRD signal. The proposed data processing method eliminated the need to use the neutral density filters, therefore avoiding the adding of the optical density error to the uncertainty of residual transmittance measurement and improving the measurement accuracy. The proposed data processing method also extended the dynamic range of the dual-channel CRD scheme for simultaneous measurement of reflectance, transmittance and optical loss.

Gravitational Wave Ringdown Analysis Using the F -statistic

After the final stage of the merger of two black holes (BHs), the ringdown signal takes an important role in providing information about the gravitational dynamics in strong field. We introduce a novel time-domain (TD) approach, predicated on the F -statistic, for ringdown analysis. This method diverges from traditional TD techniques in that its parameter space remains constant irrespective of the number of modes incorporated. This feature is achieved by reconfiguring the likelihood and analytically maximizing over the extrinsic parameters that encompass the amplitudes and reference phases of all modes. Consequently, when performing the ringdown analysis under the assumption that the ringdown signal is detected by the Einstein Telescope, the parameter estimation computation time is shortened by at most 5 orders of magnitude compared to the traditional TD method. We further establish that traditional TD methods become difficult when including multiple overtone modes due to close oscillation frequencies and damping times across different overtone modes. Encouragingly, this issue is effectively addressed by our new TD technique. The accessibility of this new TD method extends to a broad spectrum of research and offers flexibility for various topics within BH spectroscopy applicable to both current and future gravitational wave detectors.

Close Range and High-Resolution Detection of Vibration by Ultrasonic Wave Using Silicon-on-Nothing PMUTs.

This article presents a novel method for close-range, high-resolution ultrasonic time-of-flight (ToF) ranging using piezoelectric micromachined ultrasonic transducers (PMUTs) operating below the device resonance in air. The proposed method involves cross correlation techniques to accurately detect the reflected echo signals despite the presence of ringdown signal interference. For the experiments, a high fill-factor array of silicon-on-nothing (SON) PMUTs was used to enhance the signal-to-noise ratio (SNR). A thorough investigation was conducted to determine the optimal driving frequency for below-resonance ToF ranging, to improve resolution and minimize detection errors. The results of the experiments showed that the system was able to accurately measure sub- μ m vibrations of a metal plate placed 13 mm away from the PMUT array. The system exhibited the ability to detect target object vibrations with a peak-to-peak displacement under 6 μ m and sub- μ m floor noise. Moreover, the maximum detectable vibration frequency reached up to 1 kHz. This study highlights the potential of the proposed ToF ranging method in noncontact vibration monitoring applications across various fields, such as robotics and predictive maintenance.

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.

Multi-method piecewise low-frequency identification

Inter-area frequency modes of electromechanical oscillations are decisive factors that influence the performance of electrical power systems. However, the accurate estimation of these frequencies remains a challenge due to the non-linear behavior of the response system following a disturbance and the strong coupling among the frequencies. This work describes a curve fitting and electromechanical frequency estimation algorithm, called Multi-method Piecewise Identification (MPI), based on a combination of the Matrix Pencil Method (MPM), the Prony method, and Subspace Identification (SSI), choosing the best approximation of an interval basis according to the model accuracy index (MAI) and the mean square error (MSE). The advantages and limitations of MPI were analyzed by computational analyses that were carried out with Python-based code that estimates the low frequencies for several ringdown signals, including oscillating signals from Australian and Brazilian systems that arise after large disturbances. To ensure robustness to random and noisy conditions, the method was tested with a synthetic signal with Gaussian white noise and time-variant frequencies, and compared to the methods mentioned above, the Hilbert–Huang Transform (HHT), and Eigensystem Realization Algorithm (ERA). The MPI has shown robust results and is capable of obtaining a better fitting for the signal than the other methods.

Measuring source properties and quasinormal mode frequencies of heavy massive black-hole binaries with LISA

The Laser Interferometer Space Antenna (LISA) will be launched in the mid-2030s. It promises to observe the coalescence of massive black-hole (BH) binaries with signal-to-noise ratios (SNRs) reaching thousands. Crucially, it will detect some of these binaries with high SNR in both the inspiral and the merger-ringdown stages. Such signals are ideal for tests of general relativity (GR) using information from the whole waveform. Here, we consider astrophysically motivated binary systems at the high-mass end of the population observable by LISA and simulate their signals using the newly developed multipolar effective-one-body model: pSEOBNRv5HM. The merger-ringdown signal in this model depends on the binary properties (masses and spins) and also on parameters that describe fractional deviations from the GR quasinormal mode (complex) frequencies of the remnant BH. Performing full Bayesian analyses, we assess to which accuracy LISA will be able to constrain deviations from GR in the ringdown signal when using information from the whole signal. We find that these deviations can typically be constrained to within 10% and in the best cases to within 1%. We also show that with this model we can measure the binary masses and spins with great accuracy even for very massive BH systems with low SNR in the inspiral. In particular, individual source-frame masses can typically be constrained to within 10% and as precisely as 1%, and individual spins can typically be constrained to within 0.1 and, in the best cases, to within 0.001. We also probe the accuracy of the SEOBNRv5HM waveform family by performing synthetic injections of GR numerical-relativity waveforms. Using a novel method that we develop here to quantify the impact of systematic errors, we show that, already for sources with SNR O(100), we would measure erroneous deviations from GR due to waveform model inaccuracies. One of the main sources of error is the mismodeling of the relative alignment between harmonics. These results confirm the need for improving waveform models to perform tests of GR with binary BHs observed at high SNR by LISA. Published by the American Physical Society 2024

Search for Gravitational-wave Transients Associated with Magnetar Bursts in Advanced LIGO and Advanced Virgo Data from the Third Observing Run

Gravitational waves are expected to be produced from neutron star oscillations associated with magnetar giant flares and short bursts. We present the results of a search for short-duration (milliseconds to seconds) and long-duration (∼100 s) transient gravitational waves from 13 magnetar short bursts observed during Advanced LIGO, Advanced Virgo, and KAGRA’s third observation run. These 13 bursts come from two magnetars, SGR 1935+2154 and Swift J1818.0−1607. We also include three other electromagnetic burst events detected by Fermi-GBM which were identified as likely coming from one or more magnetars, but they have no association with a known magnetar. No magnetar giant flares were detected during the analysis period. We find no evidence of gravitational waves associated with any of these 16 bursts. We place upper limits on the rss of the integrated incident gravitational-wave strain that reach 3.6 × 10−23 /Hz at 100 Hz for the short-duration search and 1.1 × 10−22 /Hz at 450 Hz for the long-duration search. For a ringdown signal at 1590 Hz targeted by the short-duration search the limit is set to 2.3 × 10−22 /Hz . Using the estimated distance to each magnetar, we derive upper limits on the emitted gravitational-wave energy of 1.5 × 1044 erg (1.0 × 1044 erg) for SGR 1935+2154 and 9.4 × 1043 erg (1.3 × 1044 erg) for Swift J1818.0−1607, for the short-duration (long-duration) search. Assuming isotropic emission of electromagnetic radiation of the burst fluences, we constrain the ratio of gravitational-wave energy to electromagnetic energy for bursts from SGR 1935+2154 with the available fluence information. The lowest of these ratios is 4.5 × 103.

From regular black holes to horizonless objects: quasi-normal modes, instabilities and spectroscopy

We study gravitational and test-field perturbations for the two possible families of spherically symmetric black-hole mimickers that smoothly interpolate between regular black holes and horizonless compact objects accordingly to the value of a regularization parameter.One family can be described by the Bardeen-like metrics, and the other by the Simpson-Visser metric.We compute the spectrum of quasi-normal modes (QNMs) of these spacetimes enlightening a common misunderstanding regarding this computation present in the recent literature.In both families, we observe long-living modes for values of the regularization parameter corresponding to ultracompact, horizonless configurations. Such modes appear to be associated with the presence of a stable photon sphere and are indicative of potential non-linear instabilities.In general, the QNM spectra of both families display deviations from the standard spectrum of GR singular BHs.In order to address the future detectability of such deviations in the gravitational-wave ringdown signal, we perform a preliminary study, finding that third generation ground-based detectors might be sensible to macroscopic values of the regularization parameter.

FPGA-based pulsed laser with high modulation depth from Mach-Zehnder electro-optic modulator and its application

Mach-Zehnder electro-optic modulator as the essential component of high-speed modulation in the optical fiber communication and sensing system, its stability control of operating bias-point plays a key role in determining the transmission signal quality. Based on the output characteristic principle of Mach-Zehnder electro-optic modulator, researches on its bias-point drifting for causing the reduction mechanism of modulation depth and extinction ratio are analyzed. Switching its internal state machine from FPGA is proposed to automatically adjust the bias voltage in real time realizing the operating bias-point control of Mach-Zehnder electro-optic modulator, which is studied through the theoretical investigation. A pulsed laser with the temperature sensing system of fiber Bragg grating ring-down cavity based on FPGA is established experimentally to demonstrate its effectiveness. The experimental results show the modulation depth and the extinction ratio of pulsed laser are improved by 40.45% and 32.85 dB, respectively. Output characteristic curve of the sensing system is optimized, which includes the phenomenon of initial curve rise of ring-down signals and the distortion of ring-down waveform are eliminated. The good linearity, repeatability, stability and accuracy of sensing system are investigated at the continuous variation temperature from −30℃ to 30℃.

Parameter estimation for Einstein-dilaton-Gauss-Bonnet gravity with ringdown signals* *Supported by the National Key R & D Program of China (2022YFC2204602), and the Natural Science Foundation of China (11925503)

Future space-based gravitational-wave detectors will detect gravitational waves with high sensitivity in the millihertz frequency band, providing more opportunities to test theories of gravity than ground-based detectors. The study of quasinormal modes (QNMs) and their application in gravity theory testing have been an important aspect in the field of gravitational physics. In this study, we investigate the capability of future space-based gravitational wave detectors, such as LISA, TaiJi, and TianQin, to constrain the dimensionless deviating parameter for Einstein-dilaton-Gauss-Bonnet (EdGB) gravity with ringdown signals from the merger of binary black holes. The ringdown signal is modeled by the two strongest QNMs in EdGB gravity. Considering time-delay interferometry, we calculate the signal-to-noise ratio of different space-based detectors for ringdown signals to analyze their capabilities. The Fisher information matrix is employed to analyze the accuracy of parameter estimation, with particular focus on the dimensionless deviating parameter for EdGB gravity. The impact of the parameters of gravitational wave sources on the estimation accuracy of the dimensionless deviating parameter is also studied. We find that the constraint ability of EdGB gravity is limited because the uncertainty of the dimensionless deviating parameter increases with a decrease in the dimensionless deviating parameter. LISA and TaiJi offer more advantages in constraining the dimensionless deviating parameter to a more accurate level for massive black holes, whereas TianQin is more suited to less massive black holes. The Bayesian inference method is used to perform parameter estimation on simulated data, which verifies the reliability of the conclusion.

Modern methods for identification of atoms, molecules, and aerosols in various objects

The study is aimed at developing highly sensitive methods of laser analytical spectroscopy. The physical mechanisms of forming useful signals (selective ionization signal and cavity ring-down signal) were identified that provided registration of parameters of atomic and aerosol systems in the intensive pulsed laser field. High-sensitive laser methods of laser resonance ionization spectroscopy in vacuum, laser-enhanced ionization spectrometry in flame, and cavity ringdown laser absorption spectroscopy (CRLAS) are used for the determination of ultra-small concentrations of atoms in different phase states of the substance. Samples of aqueous standard solutions and solid metals of s (Li, K, Na, Ca, Cs), p (Al, In), d (Cr, Mn, Fe, Co, Ni, Cu, Ag, Au, Pt, Zn, Hg), f (Yb) elements, aluminum alloys, especially pure solvents, crystals (NH4F, NaF), semi-conductor materials (GaAs, Si) and various aerosols of salts (NaCl, CsCl, NaI, NaF, KCl AgNO3), chemicals, organic dyes, alloys, soils and rocks were studied. The new mechanisms of getting free particles are revealed and new methods increasing the efficiency of atomization, selective ionization and excitation of atoms in systems «flame», «rod – flame», in atomizer «graphite – furnace» are proposed. The particle size distribution of aerosols formed under the impact of high-power laser radiation on the surface of a solid sample has been studied. The dependence of the absolute concentration of aerosol particles on their size has been determined. Aerosol extinction coefficients and extinction efficiency have been measured using intracavity laser spectroscopy. For the first time new parameters of aerosols are revealed by physical and chemical properties of aerosol plumes from solid surfaces and aerosols of salt of metals and organic aerosols. Methods of additives and calibration curve were used to examine the effects of the matrix on the analytical signal of the studied atoms.

Measuring the ringdown scalar polarization of gravitational waves in Einstein-scalar-Gauss-Bonnet gravity

We model the scalar waves produced during the ringdown stage of binary black hole coalescence in Einstein scalar Gauss-Bonnet (EsGB) gravity, using numerical relativity simulations of the theory in the decoupling limit. Through a conformal coupling of the scalar field to the metric in the matter-field action, we show that the gravitational waves in this theory can have a scalar polarization. We model the scalar quasi-normal modes of the ringdown signal in EsGB gravity, and quantify the extent to which current and future gravitational wave detectors could observe the spectrum of scalar radiation emitted during the ringdown phase of binary black hole coalescence. We find that within the limits of the theory's coupling parameters set by current theoretical and observational constraints, the scalar ringdown signal from black hole remnants in the $10^1 - 10^3 \, M_{\odot}$ mass range is expected to be well below the detectability threshold with the current network of gravitational-wave detectors (LIGO-Virgo-KAGRA), but is potentially measurable with next-generation detectors such as the Einstein Telescope.

Using rational filters to uncover the first ringdown overtone in GW150914

There have been debates in the literature about the existence of the first overtone in the ringdown of GW150914. We develop a novel Bayesian framework to reanalyze the data of this event, by incorporating a new technique, the ``rational filter'' that can clean particular modes from the ringdown signal. We examine the existence of the first overtone in GW150914 from multiple novel perspectives. First, we confirm that the estimates of the remnant black hole mass and spin are more consistent with those obtained from the full inspiral-merger-ringdown signal when including the first overtone at an early stage of the ringdown (right after the inferred signal peak); such improvement fades away at later times. Second, we formulate a new way to compare the ringdown models with and without the first overtone by calculating the Bayes factor at different times during the ringdown. We obtain a Bayes factor of 600 at the time when the signal amplitude reaches its peak. The Bayes factor decreases sharply when moving away from the peak time and eventually oscillates around a small value when the overtone signal is expected to have decayed. Third, we clean the fundamental mode from the ringdown of GW150914 and estimate the amplitudes of the modes using the filtered data with Markov chain Monte Carlo (MCMC). The inferred amplitude of the fundamental mode is $\ensuremath{\sim}0$ whereas the amplitude of the first overtone remains almost unchanged, implying that the filtered data is consistent with a first-overtone-only template. Similarly, if we remove the first overtone from the GW150914 data, the filtered data are consistent with a fundamental-mode-only template. Finally, after removing the fundamental mode, we use MCMC to infer the remnant black hole mass and spin from the first overtone alone. We find the posteriors are still informative and consistent with those inferred from the fundamental mode. The conclusions are also verified through simulations in Gaussian noise using a GW150914-like numerical relativity waveform.

The Extreme Learning Machine for the Extraction of Mono-Exponential Decay Time

The mono-exponential decay has been used to describe various physical phenomena such as cavity ring-down signal, fluorescence decay, etc. In this paper, a neural network method of extreme learning machine (ELM) is adopted to efficiently extract decay time. The theoretical extraction precision, accuracy, and computation cost are all preliminarily analyzed and quantitatively compared with the traditional Levenberg-Marquardt (LM) algorithm. The training set and the testing set for the ELM are built based on our experimental system parameters. After dataset training, the ELM model for mono-exponential decay extraction is obtained. In the dataset testing, this model gives almost the same results with the LM algorithm. The relative deviation of precision is only about ±1 nanosecond. This ELM model can also be directly used in experimental cavity ring-down system. Comparing with the LM algorithm, the relative deviations are less than ±2 nanoseconds when the decay time is in the range of 0.98 μs∼2.20 μs. The ELM method for mono-exponential decay extraction has high efficiency and fine robustness. It has the potential for the applications in cavity ring-down spectroscopy, fluorescence decay analysis, and nuclear radioactive technique, etc.

Strong Coupling of aGd3+Multilevel Spin System to an On-Chip Superconducting Resonator

We report the realization of a strong coupling between a Gd$^{3+}$ spin ensemble hosted in a scheelite (CaWO$_4$) single crystal and the resonant mode of a coplanar stripline superconducting cavity leading to a large separation of spin-photon states of 146 MHz. The interaction is well described by the Dicke model and the crystal-field Hamiltonian of the multilevel spin system. We observe a change of the crystal-field parameters due to the presence of photons in the cavity that generates a significant perturbation of the crystal ground state. Using finite-element calculations, we numerically estimate the cavity sensing volume as well as the average spin-photon coupling strength of $g_0\approx$ 620 Hz. Lastly, the dynamics of the spin-cavity states are explored via pulsed measurements by recording the cavity ring-down signal as a function of pulse length and amplitude. The results indicate a potential method to initialize this multilevel system in its ground state via an active cooling process.

Black-hole ringdown as a probe of higher-curvature gravity theories

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 contenders? Here, we address this question by using an inspiral-merger-ringdown waveform model in the effective-one-body formalism, augmented with a parametrization of the ringdown based on an expansion in the final black hole's spin. We give a prescription on how to include in this waveform model, the quasinormal mode frequencies calculated on a theory-by-theory basis. In particular, we focus on theories that modify general relativity by higher-order curvature corrections, namely, Einstein-dilaton-Gauss-Bonnet, dynamical Chern-Simons theories, and cubic- and quartic-order effective-field-theories of general relativity. We use this parametrized waveform model to measure the ringdown properties of the two loudest ringdown signals observed so far, GW150914 and GW200129. We find that while the Einstein-dilaton-Gauss-Bonnet theory cannot be constrained with these events, we can place upper bounds on the fundamental lengthscale of cubic- (${\ensuremath{\ell}}_{\text{cEFT}}\ensuremath{\le}38.2\text{ }\text{ }\mathrm{km}$) and quartic-order (${\ensuremath{\ell}}_{\text{qEFT}}\ensuremath{\le}51.3\text{ }\text{ }\mathrm{km}$) effective-field-theories of general relativity, and of dynamical Chern-Simons gravity (${\ensuremath{\ell}}_{\text{dCS}}\ensuremath{\le}38.7\text{ }\text{ }\mathrm{km}$). The latter result is a concrete example of a theory presently unconstrained by inspiral-only analyses which, however, can be constrained by merger-ringdown studies with current gravitational-wave data.

Quasinormal modes of Schwarzschild black holes on the real axis

We study the scattering of gravitational waves by a Schwarzschild black hole and its perturbed siblings to investigate influences of proposed spectral instability of quasinormal modes on the ringdown signal. Our results indicate that information of dominant ringdown signals, which are ascribed to the fundamental (i.e., least damping) quasinormal mode of unperturbed Schwarzschild black holes, is imprinted in the phase shift defined from the transmission amplitude (1/A_{in} in our notation). This approximately parallels the fact that the resonance of quantum systems is imprinted in the phase shift of the S-matrix. The phase shift around the oscillation frequency of the fundamental mode is modified only perturbatively even if the quasinormal-mode spectrum is destabilized by a perturbative bump at a distant location, signifying the stability of the ringdown signal. At the same time, the phase shift at low frequencies is modulated substantially reflecting the late-time excitation of echo signals associated with the quasinormal-mode spectrum after destabilization.

Exploring supernova gravitational waves with machine learning

ABSTRACT Core-collapse supernovae (CCSNe) emit powerful gravitational waves (GWs). Since GWs emitted by a source contain information about the source, observing GWs from CCSNe may allow us to learn more about CCSNs. We study if it is possible to infer the iron core mass from the bounce and early ring-down GW signal. We generate GW signals for a range of stellar models using numerical simulations and apply machine learning to train and classify the signals. We consider an idealized favorable scenario. First, we use rapidly rotating models, which produce stronger GWs than slowly rotating models. Secondly, we limit ourselves to models with four different masses, which simplifies the selection process. We show that the classification accuracy does not exceed $\sim \! 70{{\ \mathrm{ per \, cent}}}$, signifying that even in this optimistic scenario, the information contained in the bounce, and early ring-down GW signal is not sufficient to precisely probe the iron core mass. This suggests that it may be necessary to incorporate additional information such as the GWs from later post-bounce evolution and neutrino observations to accurately measure the iron core mass.

Novel Ringdown Amplitude-Phase Consistency Test.

The ringdown signal emitted during a binary black hole coalescence can be modeled as a linear superposition of the characteristic damped modes of the remnant black hole that get excited during the merger phase. While checking the consistency of the measured frequencies and damping times against theKerr BH spectrum predicted by general relativity (GR) is a cornerstone of strong-field tests of gravity, the consistency of measured excitation amplitudes and phases have been largely left unexplored. For a nonprecessing, quasicircular binary black hole merger, we find that GR predicts a narrow region in the space of mode amplitude ratio and phase difference, independently of the spin of the binary components. Using this unexpected result, we develop a new null test of strong-field gravity which demands that the measured amplitudes and phases of different ringdown modes should lie within this narrow region predicted by GR. We call this the amplitude-phase consistency test and introduce a procedure for performing it using information from the ringdown signal. Lastly, we apply this test to the GW190521 event, using the multimodal ringdown parameters inferred by Capano etal. [arXiv:2105.05238]. While ringdown measurements errors for this event are large, we show that GW190521 is consistent with the amplitude-phase consistency test. Our test is particularly well suited for accommodating multiple loud ringdown detections as those expected in the near future, and can be used complementarily to standard black-hole spectroscopy as a proxy for modified gravity, compact objects other than black holes, binary precession and eccentricity.

Gravitational waveform model based on photon motion for spinning black holes

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 numerical relativity. We find that they match with each other very well. In principle this method can be extended to some general compact objects. As an example, the ringdown waveforms from parametrized axisymmetric black holes are obtained. We also use this method to get the ringdown signals of the accelerating final black hole; this is due to gravitational recoil during the merger. Even for the extreme cases, the acceleration due to the recoil cannot produce detectable effects.