Ringdown Signal Research Articles

Coupling analysis of high Q resonators in add-drop configuration through cavity ringdown spectroscopy

An original method able to fully characterize high-Q resonators in an add-drop configuration has been implemented. The method is based on the study of two cavity ringdown (CRD) signals, which are produced at the transmission and drop ports by wavelength sweeping a resonance in a time interval comparable with the photon cavity lifetime. All the resonator parameters can be assessed with a single set of simultaneous measurements. We first developed a model describing the two CRD output signals and a fitting program able to deduce the key parameters from the measured profiles. We successfully validated the model with an experiment based on a fiber ring resonator of known characteristics. Finally, we characterized a high-Q, home-made, MgF2 whispering gallery mode disk resonator in the add-drop configuration, assessing its intrinsic and coupling parameters.

How well can ultracompact bodies imitate black hole ringdowns?

The ongoing observations of merging black holes by the instruments of the fledging gravitational wave astronomy has opened the way for testing the general relativistic Kerr black hole metric and, at the same time, for probing the existence of more speculative horizonless ultracompact objects. In this paper we quantify the difference that these two classes of objects may exhibit in the post-merger ringdown signal. By considering rotating systems in general relativity and assuming an eikonal limit and a third-order Hartle-Thorne slow rotation approximation, we provide the first calculation of the early ringdown frequency and damping time as a function of the body's multipolar structure. Using the example of a gravastar, we show that the main ringdown signal may differ as much as a few percent with respect to that of a Kerr black hole, a deviation that could be probed by near future Advanced LIGO/Virgo searches.

Foundations of an effective-one-body model for coalescing binaries on eccentric orbits

We develop the foundations of an effective-one-body (EOB) model for eccentric binary coalescences that includes the conservative dynamics, radiation reaction, and gravitational waveform modes from the inspiral and the merger-ringdown signals. We use the same approach as is commonly employed in black-hole perturbation theory by introducing a relativistic parameterization of the dynamics that is defined by the orbital geometry and consists of a set of phase variables and quantities that evolve only due to gravitational radiation reaction. Specializing to nonspinning binaries, we derive the EOB evolution equations and compute the binary's radiative multipole moments that determine the gravitational waves through a decomposition into the fundamental frequencies of the motion. The major differences between our treatment and the quasi-Keplerian approach often used in post-Newtonian (PN) calculations are that the orbital parameters describe strong-field dynamics, and that expressing the multipole moments in terms of the frequencies simplifies the calculations and also results in an unambiguous orbit-averaging operation. While our description of the conservative dynamics is fully relativistic, we limit explicit derivations in the radiative sector to 1.5PN order for simplicity. This already enables us to establish methods for computing both instantaneous and hereditary contributions to the gravitational radiation in EOB coordinates that have straightforward extensions to higher PN order. The weak-field, small eccentricity limit of our results for the orbit-averaged fluxes of energy and angular momentum agrees with known PN results when expressed in terms of gauge-invariant quantities. We further address considerations for the numerical implementation of the model and the completion of the waveforms to include the merger and ringdown signals, and provide illustrative results.

Challenges for testing the no-hair theorem with current and planned gravitational-wave detectors

General relativity's no-hair theorem states that isolated astrophysical black holes are described by only two numbers: mass and spin. As a consequence, there are strict relationships between the frequency and damping time of the different modes of a perturbed Kerr black hole. Testing the no-hair theorem has been a longstanding goal of gravitational-wave astronomy. The recent detection of gravitational waves from black hole mergers would seem to make such tests imminent. We investigate how constraints on black hole ringdown parameters scale with the loudness of the ringdown signal---subject to the constraint that the post-merger remnant must be allowed to settle into a perturbative, Kerr-like state. In particular, we require that---for a given detector---the gravitational waveform predicted by numerical relativity is indistinguishable from an exponentially damped sine after time $t^\text{cut}$. By requiring the post-merger remnant to settle into such a perturbative state, we find that confidence intervals for ringdown parameters do not necessarily shrink with louder signals. In at least some cases, more sensitive measurements probe later times without necessarily providing tighter constraints on ringdown frequencies and damping times. Preliminary investigations are unable to explain this result in terms of a numerical relativity artifact.

Algorithm for the estimation of electromechanical modes via modal decomposition techniques

This paper proposes an algorithm for the application of mode decomposition techniques based on ringdown signals to estimate electromechanical modes in electrical power systems. The estimation of the electromechanical modes is done by defining parameters for the application of modal estimation technique successive times, followed by routines of identification and analysis of the results. Results are obtained by using the techniques LS-ESPRIT, TLS-ESPRIT and WTLS-ESPRIT. The simulations were performed for a distribution network in the presence of a group of three synchronous generators.

Validating the effective-one-body model of spinning, precessing binary black holes against numerical relativity

In Ref. [1], the properties of the first gravitational wave detected by LIGO, GW150914, were measured by employing an effective-one-body (EOB) model of precessing binary black holes whose underlying dynamics and waveforms were calibrated to numerical-relativity (NR) simulations. Here, we perform the first extensive comparison of such EOBNR model to 70 precessing NR waveforms that span mass ratios from 1 to 5, dimensionless spin magnitudes up to 0.5, generic spin orientations, and length of about 20 orbits. We work in the observer's inertial frame and include all $\ell=2$ modes in the gravitational-wave polarizations. We introduce new prescriptions for the EOB ringdown signal concerning its spectrum and time of onset. For total masses between 10Msun and 200Msun, we find that precessing EOBNR waveforms have unfaithfulness within about 3% to NR waveforms when considering the Advanced-LIGO design noise curve. This result is obtained without recalibration of the inspiral-plunge of the underlying nonprecessing EOBNR model. The unfaithfulness is computed with maximization over time and phase of arrival, sky location and polarization of the EOBNR waveform and it is averaged over sky location and polarization of the NR signal. We also present comparisons between NR and EOBNR waveforms in a frame that tracks the orbital precession.

Simultaneous measurements of s- and p-polarization reflectivity with a cavity ring-down technique employing no polarization optics

The cavity ring-down (CRD) technique is adopted for simultaneously measuring s- and p-polarization reflectivity of highly reflective coatings without employing any polarization optics. As the s- and p-polarized light trapped in the ring-down cavity decay independently, with a randomly polarized light source the ring-down signal recorded by a photodetector presents a double-exponential waveform consisting of ring-down signals of both s- and p-polarized light. The s- and p-polarization reflectivity values of a test mirror are therefore simultaneously determined by fitting the recorded ring-down signal with a double-exponential function. The determined s- and p-polarization reflectivity of 30° and 45° angle of incidence mirrors are in good agreement with the reflectivity values measured with the conventional CRD technique employing a polarizer for polarization control.

Power system low frequency oscillation mode estimation using wide area measurement systems

Oscillations in power systems are triggered by a wide variety of events. The system damps most of the oscillations, but a few undamped oscillations may remain which may lead to system collapse. Therefore low frequency oscillations inspection is necessary in the context of recent power system operation and control. Ringdown portion of the signal provides rich information of the low frequency oscillatory modes which has been taken into analysis. This paper provides a practical case study in which seven signal processing based techniques i.e. Prony Analysis (PA), Fast Fourier Transform (FFT), S-Transform (ST), Wigner-Ville Distribution (WVD), Estimation of Signal Parameters by Rotational Invariance Technique (ESPRIT), Hilbert-Huang Transform (HHT) and Matrix Pencil Method (MPM) were presented for estimating the low frequency modes in a given ringdown signal. Preprocessing of the signal is done by detrending. The application of the signal processing techniques is illustrated using actual wide area measurement systems (WAMS) data collected from four different Phasor Measurement Unit (PMU) i.e. Dadri, Vindyachal, Kanpur and Moga which are located near the recent disturbance event at the Northern Grid of India. Simulation results show that the seven signal processing technique (FFT, PA, ST, WVD, ESPRIT, HHT and MPM) estimates two common oscillatory frequency modes (0.2, 0.5) from the raw signal. Thus, these seven techniques provide satisfactory performance in determining small frequency modes of the signal without losing its valuable property. Also a comparative study of the seven signal processing techniques has been carried out in order to find the best one. It was found that FFT and ESPRIT gives exact frequency modes as compared to other techniques, so they are recommended for estimation of low frequency modes. Further investigations were also carried out to estimate low frequency oscillatory mode with another case study of Eastern Interconnect Phasor Project (EIPP) data with the seven signal processing techniques (FFT, PA, ST, WVD, ESPRIT, HHT and MPM). It was found from the simulation results of EIPP data that two low frequency oscillatory mode (0.51Hz, 0.2Hz) exist.

Did GW150914 produce a rotating gravastar?

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 be equally massive and compact, namely, gravastars. We here consider the hypothesis that the merging objects were indeed gravastars and explore whether the merged object could therefore be not a black hole but a rotating gravastar. After comparing the real and imaginary parts of the ringdown signal of GW150914 with the corresponding quantities for a variety of gravastars, and notwithstanding the very limited knowledge of the perturbative response of rotating gravastars, we conclude it is not possible to model the measured ringdown of GW150914 as due to a rotating gravastar.

Is the Gravitational-Wave Ringdown a Probe of the Event Horizon?

It is commonly believed that the ringdown signal from a binary coalescence provides a conclusive proof for the formation of an event horizon after the merger. This expectation is based on the assumption that the ringdown waveform at intermediate times is dominated by the quasinormal modes of the final object. We point out that this assumption should be taken with great care, and that very compact objects with a light ring will display a similar ringdown stage, even when their quasinormal-mode spectrum is completely different from that of a black hole. In other words, universal ringdown waveforms indicate the presence of light rings, rather than of horizons. Only precision observations of the late-time ringdown signal, where the differences in the quasinormal-mode spectrum eventually show up, can be used to rule out exotic alternatives to black holes and to test quantum effects at the horizon scale.

Adaptive imaging processing for reducing ultrasonic ringdown interference pattern

In the oil and gas industry, ultrasonic imaging tools are actively used in stress identification and fracture detection. Pulse-echo transducers measure the properties of the echoes reflected from the formation, and the signal peak amplitude and travel time are typically displayed as a circumferential image of the borehole wall. A well-known problem is that the pulse-echo transducers have internal ringdown which constantly modulates formation echoes. As a result, the acquired image is often dominated by a “wood-grain” interference pattern which degrades image quality. Traditional ringdown reduction methods try to remove the ringdown effect by estimating the ringdown waveform. However, the ringdown signal varies versus borehole conditions, which make it inadequate for traditional methods to efficiently reduce the image interference pattern. In this paper, we proposed an image processing method which significantly reduces the interference pattern. This new image processing method does not require any ringdown waveforms. It adaptively estimates the ringdown modulation template and after that constructs the interference amplitude pattern. Examples shows promising results and have proven the propose method is more efficient than traditional ringdown reduction methods on the ringdown interference pattern reduction.

Open-path cavity ring-down spectroscopy for trace gas measurements in ambient air.

The present work used a near-infrared methane cavity ring-down spectroscopy (CRDS) sensor to examine performance and limitations of open-path CRDS for atmospheric measurements. A simple purge-enclosure was developed to maintain high mirror reflectivity and allowed >100 hours of operation with mirror reflectivity above 0.99996. We characterized effects of aerosols on ring-down decay signals and found the dominant effect to be fluctuations by large super-micron particles. Simple software filtering approaches were developed to combat these fluctuations allowing noise-equivalent sensitivity of ~6x10-10 cm-1HJ Hz-1/2 within a factor of ~3 of closed-path systems (based on stability of the absorption baseline). Sensor measurements were validated against known methane concentrations in a closed-path configuration, while open-path validation was performed by side-by-side comparison with a commercial closed-path system.

Transient Dynamics of a Superconducting Nonlinear Oscillator

We investigate the transient dynamics of a lumped-element oscillator based on a dc superconducting quantum interference device (SQUID). The SQUID is shunted with a capacitor forming a nonlinear oscillator with resonance frequency in the range of several GHz. The resonance frequency is varied by tuning the Josephson inductance of the SQUID with on-chip flux lines. We report measurements of decaying oscillations in the time domain following a brief excitation with a microwave pulse. The nonlinearity of the SQUID oscillator is probed by observing the ringdown response for different excitation amplitudes while the SQUID potential is varied by adjusting the flux bias. Simulations are performed on a model circuit by numerically solving the corresponding Langevin equations incorporating the SQUID potential at the experimental temperature and using parameters obtained from separate measurements characterizing the SQUID oscillator. Simulations are in good agreement with the experimental observations of the ringdowns as a function of applied magnetic flux and pulse amplitude. We observe a crossover between the occurrence of ringdowns close to resonance and adiabatic following at larger detuning from the resonance. We also discuss the occurrence of phase jumps at large amplitude drive. Finally, we briefly outline prospects for a readout scheme for superconducting flux qubits based on the discrimination between ringdown signals for different levels of magnetic flux coupled to the SQUID.

Autonomous system for in Situ Assay of Antibiotic Activity on Bacterial Biofilms Using Viscosity and Density Sensing Quartz Tuning Forks

Piezoelectric quartz tuning forks (QTF) were used for viscosity and density measurements. Compact autonomous system, based on the modulated excitation signal technique, providing the QTF excitation, measurement of the ring-down oscillations and signal processing was built and calibrated. It was used for in situ determination of the antibiotic activity od ciprofloxacin on the biofilm formation in real time. The effect of the antibiotic concentration and the time at which it was introduced to the culture were shown.

Estimation of Electromechanical Oscillation Parameters Using an Extended Kalman Filter

Estimation of electromechanical modes of a power system has attracted attention in the past few decades because it can provide vital information about the stability of the system. In this paper, a new state-space model is proposed for online detection of parameters of a ringdown signal using an extended Kalman filter (EKF). The proposed model can estimate both constant and time-varying parameters. Furthermore, stability analysis of the proposed model is performed to demonstrate the convergence of the parameters. Simulation results confirm the desirable performance of the proposed method for ringdown parameter estimation.

Measuring Intermediate-Mass Black-Hole Binaries with Advanced Gravitational Wave Detectors.

We perform a systematic study to explore the accuracy with which the parameters of intermediate-mass black-hole binary systems can be measured from their gravitational wave (GW) signatures using second-generation GW detectors. We make use of the most recent reduced-order models containing inspiral, merger, and ringdown signals of aligned-spin effective-one-body waveforms to significantly speed up the calculations. We explore the phenomenology of the measurement accuracies for binaries with total masses between 50M(⊙) and 500M(⊙) and mass ratios between 0.1 and 1. We find that (i) at total masses below ∼200M(⊙), where the signal-to-noise ratio is dominated by the inspiral portion of the signal, the chirp mass parameter can be accurately measured; (ii) at higher masses, the information content is dominated by the ringdown, and total mass is measured more accurately; (iii) the mass of the lower-mass companion is poorly estimated, especially at high total mass and more extreme mass ratios; and (iv) spin cannot be accurately measured for our injection set with nonspinning components. Most importantly, we find that for binaries with nonspinning components at all values of the mass ratio in the considered range and at a network signal-to-noise ratio of 15, analyzed with spin-aligned templates, the presence of an intermediate-mass black hole with mass >100M(⊙) can be confirmed with 95% confidence in any binary that includes a component with a mass of 130M(⊙) or greater.

Estimation of interarea electromechanical modes during ambient operation of the power systems using the RDT–ITD method

Abstract An accurate awareness of the properties of the interarea electromechanical oscillation modes is essential for the secure operation of the power systems. Previously, the Ibrahim time domain (ITD) method has been applied to estimate the interarea oscillation modes using ring-down signals caused by major disturbances (such as three phase faults). In this paper, through the combination of the random decrement technique (RDT) and the ITD method, the RDT–ITD method is proposed to estimate the interarea modes during ambient operation of the power systems, using random responses caused by random changes of the loads. The estimated parameters include the frequencies, damping ratios and mode shapes. Considering the fact that both the ambient excitations and the measurement noise are stochastic in nature, Monte Carlo simulations were conducted to evaluate the performances of the RDT–ITD method in a statistical way. Simulation results in the 16 machine nonlinear power system model, as well as comparison results with the RDT-Prony method, the NExT-ERA method and the Subspace method realized by N4SID (Numerical algorithm for Subspace State Space System Identification) show that the RDT–ITD method is promising in estimating the interarea modes during ambient operation conditions. The RDT–ITD method was also validated using real PMU measurements from Sichuan power grid of China.

Environmental Effects for Gravitational-wave Astrophysics

The upcoming detection of gravitational waves by terrestrial interferometers will usher in the era of gravitational-wave astronomy. This will be particularly true when space-based detectors will come of age and measure the mass and spin of massive black holes with exquisite precision and up to very high redshifts, thus allowing for better understanding of the symbiotic evolution of black holes with galaxies, and for high-precision tests of General Relativity in strong-field, highly dynamical regimes. Such ambitious goals require that astrophysical environmental pollution of gravitational-wave signals be constrained to negligible levels, so that neither detection nor estimation of the source parameters are significantly affected. Here, we consider the main sources for space-based detectors - the inspiral, merger and ringdown of massive black-hole binaries and extreme mass-ratio inspirals - and account for various effects on their gravitational waveforms, including electromagnetic fields, cosmological evolution, accretion disks, dark matter, “firewalls” and possible deviations from General Relativity. We discover that the black-hole quasinormal modes are sharply different in the presence of matter, but the ringdown signal observed by interferometers is typically unaffected. The effect of accretion disks and dark matter depends critically on their geometry and density profile, but is negligible for most sources, except for few special extreme mass-ratio inspirals. Electromagnetic fields and cosmological effects are always negligible. We finally explore the implications of our findings for proposed tests of General Relativity with gravitational waves, and conclude that environmental effects will not prevent the development of precision gravitational-wave astronomy.

Quartz tuning fork as in situ sensor of bacterial biofilm

Piezoelectric quartz tuning forks (QTFs) were used as in situ sensors of biofilm formation. Modulated excitation technique allowed to measure the current generated by the QTF during the ring-down of the oscillations at conductive environments such as a liquid culture growth medium. New algorithm of the digital analysis of the ring-down signal was elaborated and used to determine the decay time constant of the vibrations and the damped vibration frequency. The dependence of these parameters on the time for QTF placed in liquid growth medium contained four strains of Pseudomonas aeruginosa was measured. It allowed to detect the biofilm formation at the QTF after few hours of incubation for all used strains at 106cfu/ml initial concentration (2h for PA01 strain) or 10h for ATCC 27853 strain at 10cfu/ml initial concentration.

Testing the no-hair theorem with black hole ringdowns using TIGER

The Einstein Telescope (ET), a proposed third-generation gravitational wave observatory, would enable tests of the no-hair theorem by looking at the characteristic frequencies and damping times of black hole ringdown signals. In previous work it was shown that with a single $500 - 1000\,M_\odot$ black hole at distance $\lesssim 6$ Gpc (or redshift $z \lesssim 1$), deviations of a few percent in the frequencies and damping times of dominant and sub-dominant modes would be within the range of detectability. Given that such sources may be relatively rare, it is of interest to see how well the no-hair theorem can be tested with events at much larger distances and with smaller signal-to-noise ratios, thus accessing a far bigger volume of space and a larger number of sources. We employ a model selection scheme called TIGER (Test Infrastructure for GEneral Relativity), which was originally developed to test general relativity with weak binary coalescence signals that will be seen in second-generation detectors such as Advanced LIGO and Advanced Virgo. TIGER is well-suited for the regime of low signal-to-noise ratio, and information from a population of sources can be combined so as to arrive at a stronger test. By performing a range of simulations using the expected noise power spectral density of Einstein Telescope, we show that with TIGER, similar deviations from the no-hair theorem as considered in previous work will be detectable with great confidence using $\mathcal{O}(10)$ sources distributed uniformly in co-moving volume out to 50 Gpc ($z \lesssim 5$).