Ringdown Signal Research Articles

Echoes from braneworld black holes

The holographic interpretation of the Randall-Sundrum model based on the adaptation of the AdS/CFT correspondence to the braneworld scenario states that the black holes localized on the brane are {\it quantum corrected}. This can be better understood from the fact that the classical $AdS_{5}$ bulk dynamics is dual to gravity coupled with CFT on the four dimensional brane. Based on the back reaction of the CFT on the classical black hole geometry, localized on the brane, it is expected that there exist possible near horizon modifications. This may result in the black hole horizon becoming partially reflective, thus giving rise to echoes in the ringdown signal in gravitational wave observations. In this paper, we investigate the existence of such echoes in the ringdown phase of a black hole localized on the brane, carrying a \emph{negative} tidal charge, and establish the layout for future investigation of higher dimensional effects in the ringdown signal. Confirmed detections of echoes at the current levels of instrumental sensitivity can constrain the dimensionless value of tidal charge to $|Q| \lesssim M^2$ .

LISA parameter estimation and source localization with higher harmonics of the ringdown

LISA can detect higher harmonics of the ringdown gravitational-wave signal from massive black-hole binary mergers with large signal-to-noise ratio. The most massive black-hole binaries are more likely to have electromagnetic counterparts, and the inspiral will contribute little to their signal-to-noise ratio. Here we address the following question: can we extract the binary parameters and localize the source using LISA observations of the ringdown only? Modulations of the amplitude and phase due to LISA's motion around the Sun can be used to disentangle the source location and orientation when we detect the long-lived inspiral signal, but they can not be used for ringdown-dominated signals, which are very short-lived. We show that (i) we can still measure the mass ratio and inclination of high-mass binaries by carefully combining multiple ringdown harmonics, and (ii) we can constrain the sky location and luminosity distance by relying on the relative amplitudes and phases of various harmonics, as measured in different LISA channels.

Ringdown overtones, black hole spectroscopy, and no-hair theorem tests

Validating the black-hole no-hair theorem with gravitational-wave observations of compact binary coalescences provides a compelling argument that the remnant object is indeed a black hole as described by the general theory of relativity. This requires performing a spectroscopic analysis of the post-merger signal and resolving the frequencies of either different angular modes or overtones (of the same angular mode). For a nearly-equal mass binary black-hole system, only the dominant angular mode ($l=m=2$) is sufficiently excited and the overtones are instrumental to perform this test. Here we investigate the robustness of modelling the post-merger signal of a binary black hole coalescence as a superposition of overtones. Further, we study the bias expected in the recovered frequencies as a function of the start time of a spectroscopic analysis and provide a computationally cheap procedure to choose it based on the interplay between the expected statistical error due to the detector noise and the systematic errors due to waveform modelling. Moreover, since the overtone frequencies are closely spaced, we find that resolving the overtones is particularly challenging and requires a loud ringdown signal. Rayleigh's resolvability criterion suggests that in an optimistic scenario a ringdown signal-to-noise ratio larger than $\sim 30$ (achievable possibly with LIGO at design sensitivity and routinely with future interferometers such as Einstein Telescope, Cosmic Explorer, and LISA) is necessary to resolve the overtone frequencies. We then conclude by discussing some conceptual issues associated with black-hole spectroscopy with overtones.

The quasinormal modes of quasinormal modes

Modifying black hole horizon can drastically change the spectrum of quasinormal modes. But if the modification is close enough to the horizon the early ringdown signal remains almost unaltered, and well described by the quasinormal modes of the original GR solution. I show how the original quasinormal modes emerge in the sum over the new modes.

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.

Preliminary result of cavity ring-down spectroscopy system for radio frequency negative ion source test facility.

Negative ion source is a core part of the neutral beam injection system for magnetic confinement fusion devices. The density of produced hydrogen negative ions is a critical parameter of the negative ion source. Cavity ring-down spectroscopy (CRDS) is an ultrasensitive absorption diagnostic technique for density measurement. Based on the photodetachment process, CRDS can measure the integrated line-of-sight hydrogen negative ion density in a high power ion source. The CRDS diagnostic system has been applied to Hefei utility negative ion test equipment with the radio frequency (RF) source, which is now one of the references for the China Fusion Engineering Test Reactor neutral beam injection system. Typical ring-down signals are obtained to calculate the density of hydrogen negative ions. The time evolution of hydrogen negative ion density is successfully measured. Preliminary experiments show the accurate relationship between RF power and measured hydrogen negative ion density.

Modeling of Active Fiber Loop Ring-Down Spectroscopy Considering Gain Saturation Behavior of EDFA

Active fiber loop ring-down spectroscopy (FLRDS) can achieve a high-finesse fiber cavity by introducing the erbium-doped fiber amplifier (EDFA) gain for highly sensitive detection. However, gain saturation behavior of the EDFA induces pulse-to-pulse gain fluctuations, which cause the ring-down signal to deviate from the exponential-decay law and greatly destroy the detection accuracy of active FLRDS. In order to analyze active FLRDS more accurately, a theoretical model of active FLRDS considering the gain saturation behavior of the EDFA is established. The performance of the active FLRDS system is simulated and discussed by using the model. The dependence of the system performance on the initial optical power, the inherent cavity loss, the test-gas concentration and the EDFA location is deeply researched. The model is applicable to the active FLRDS systems used for many sensing applications, such as trace gas, temperature, refractive index, strain, and pressure.

Constraining modified gravity with ringdown signals: An explicit example

An explicit example is found showing how a modified theory of gravity can be constrained with the ringdown signals from merger of binary black holes. This has been made possible by the fact that the modified gravitational theory considered in this work has an exact rotating black hole solution and that the corresponding quasi-normal modes can be calculated. With these, we obtain the possible constraint that can be placed on the parameter describing the deviation of this particular alternative theory from general relativity by using the detection of the ringdown signals from binary black holes's merger with future space-based gravitational wave detectors.

Science with the TianQin observatory: Preliminary results on testing the no-hair theorem with ringdown signals

We study the capability of the space-based gravitational wave observatory TianQin to test the no-hair theorem of General Relativity, using the ringdown signal from the coalescence of massive black hole binaries. We parameterize the ringdown signal by the four strongest quasinormal modes and estimate the signal to noise ratio for various source parameters. We consider constraints both from single detections and from all the events combined throughout the lifetime of the observatory, for different astrophysical models. We find that at the end of the mission, TianQin will have constrained deviations of the frequency and decay time of the dominant 22 mode from the general relativistic predictions to within 0.2% and 1.5% respectively, the frequencies of the subleading modes can be also constrained within 0.3%. We also find that TianQin and LISA are highly complementary, by virtue of their different frequency windows. Indeed, LISA can best perform ringdown tests for black hole masses in excess of $\sim 3\times 10^6 M_\odot$, while TianQin is best suited for lower masses.

Twenty-Five-Fold Reduction in Measurement Uncertainty for a Molecular Line Intensity.

To accurately attribute sources and sinks of molecules like CO_{2}, remote sensing missions require line intensities (S) with relative uncertainties u_{r}(S)<0.1%. However, discrepancies in S of ≈1% are common when comparing different experiments, thus limiting their potential impact. Here we report a cavity ring-down spectroscopy multi-instrument comparison which revealed that the hardware used to digitize analog ring-down signals caused variability in spectral integrals which yield S. Our refined approach improved measurement accuracy 25-fold, resulting in u_{r}(S)=0.06%.

Phenomenological inclusion of alternative dispersion relations to the Teukolsky equation and its application to bounding the graviton mass with gravitational-wave measurements

Existing constraints on the graviton mass from gravitational-wave detections rely on the phase difference developed between different frequencies during the propagation. Effects on the quasinormal-mode frequencies of the black-hole ringdown due to the graviton mass are often ignored. While perturbation theories of black holes have been well developed in the context of general relativity, this is not the case for modified gravity theories. We propose a phenomenological modification to the Teukolsky equation of perturbed black holes to include the dispersion relation due to a gravitational field of nonzero mass. Solving this modified Teukolsky equation by logarithmic perturbation theory, we compute the shift of the quasinormal-mode frequencies due to the presence of a graviton mass. This hypothetical shift can be used to constrain the graviton mass with ringdown signals, either standalone or in conjunction with the phase difference accumulated due to the wave propagation. We estimate that constraints on the graviton mass of $m_g \lesssim 10^{-15}\,\textrm{eV}$ can be put with a detection of the ringdown signal alone by second generation gravitational-wave detectors.

Echoes from the scattering of wavepackets on wormholes

It has been recently shown that observing pulses isolated from the gravitational radiation transient (also known as echoes) would prove the existence of exotic compact objects (ECOs). Many features of the ringdown signal can be reproduced by simulating a scattering problem instead of the full coalescence of ECOs. In this paper, we study the dynamics of scalar and tensor wavepackets colliding against a spherically symmetric Morris–Thorne wormhole. Our aim is to extract the features of the time-dependent scattering solutions inside and outside the effective potential cavity in addition to their asymptotic behavior. Using the geometrical optics approximation, we show that the amplitude of the echoes is only large enough in a narrow bandwidth of frequency space. Additionally, we show that the cavity modifies the polarization of the asymptotic gravitational wave solutions. The computer code used to produce these results is publicly available for further applications, including scattering and accretion processes.

Refractive index measurement using OTDR-based ring-down technique with S fiber taper

We proposed and demonstrated a fiber loop ring-down (FLRD) sensor based on S fiber taper (SFT) cascaded with a Faraday rotator mirror (FRM) for refractive index (RI) measurement. The FLRD cavity is established conveniently by an optical time domain reflectometry (OTDR). The net loss of the cavity is modulated by the RI-sensitive SFT. The surrounding refractive index (SRI) measurement can be realized by monitoring the slope of the ring-down pulses envelope. Owing to the compensation provided by the erbium-doped fiber amplifier (EDFA), the ring-down pulses signal of the OTDR-based FLRD cavity is improved effectively. Within the measurement range of 1.3330∼1.3518, the proposed sensor has a linear response to the SRI with a sensitivity of 2646.307 dB/(kmRIU) at the interrogating wavelength of 1550 nm. Compared with the conventional FLRD sensors, the proposed OTDR-based RI sensor has the advantages of simple design and reflective sensing structure, which is easily implementable and cost-effective.

A multi-signal instrumental variable vector fitting method for estimating inter-area electromechanical modes of power systems

When it comes to estimating dynamics (modes) of interconnected power systems through transient (ringdown) data, one can expect more realistic estimates for the compound system if multiple signals distributed over different locations can be used simultaneously during modal estimation. In this context, the contributions of this paper are twofold. First, it is proposed a multi-signal ringdown time-domain Vector Fitting method (‘multi-signal RTD-VF’) which is capable of modeling multiple ringdown signals simultaneously. This method appropriately generalizes the ‘single-signal RTD-VF’ method, which processes ringdown signals independently, i.e., one at a time. Second, it is proposed an instrumental variable (IV) extension of multi-signal RTD-VF. By guaranteeing local optimums after algorithm convergence, such a ‘multi-signal IV-RTD-VF’ formulation may be used for further refining estimates provided by regular multi-signal RTD-VF. Two numerical examples are used to validate the proposed methods. The first example considers actual ringdown data sets extracted from North American Eastern Interconnection (NAEI) and Brazilian Interconnected Power (BIP) systems, whereas the second one considers mode identification of a synthetic signal corrupted by colored noise.

Surrogate model of hybridized numerical relativity binary black hole waveforms

Numerical relativity (NR) simulations provide the most accurate binary black hole gravitational waveforms, but are prohibitively expensive for applications such as parameter estimation. Surrogate models of NR waveforms have been shown to be both fast and accurate. However, NR-based surrogate models are limited by the training waveforms' length, which is typically about 20 orbits before merger. We remedy this by hybridizing the NR waveforms using both post-Newtonian and effective one body waveforms for the early inspiral. We present NRHybSur3dq8, a surrogate model for hybridized nonprecessing numerical relativity waveforms, that is valid for the entire LIGO band (starting at $20~\text{Hz}$) for stellar mass binaries with total masses as low as $2.25\,M_{\odot}$. We include the $\ell \leq 4$ and $(5,5)$ spin-weighted spherical harmonic modes but not the $(4,1)$ or $(4,0)$ modes. This model has been trained against hybridized waveforms based on 104 NR waveforms with mass ratios $q\leq8$, and $|\chi_{1z}|,|\chi_{2z}| \leq 0.8$, where $\chi_{1z}$ ($\chi_{2z}$) is the spin of the heavier (lighter) BH in the direction of orbital angular momentum. The surrogate reproduces the hybrid waveforms accurately, with mismatches $\lesssim 3\times10^{-4}$ over the mass range $2.25M_{\odot} \leq M \leq 300 M_{\odot}$. At high masses ($M\gtrsim40M_{\odot}$), where the merger and ringdown are more prominent, we show roughly two orders of magnitude improvement over existing waveform models. We also show that the surrogate works well even when extrapolated outside its training parameter space range, including at spins as large as 0.998. Finally, we show that this model accurately reproduces the spheroidal-spherical mode mixing present in the NR ringdown signal.

Signatures of Quark-Hadron Phase Transitions in General-Relativistic Neutron-Star Mergers.

Merging binaries of neutron-stars are not only strong sources of gravitational waves, but also have the potential of revealing states of matter at densities and temperatures not accessible in laboratories. A crucial and long-standing question in this context is whether quarks are deconfined as a result of the dramatic increase in density and temperature following the merger. We present the first fully general-relativistic simulations of merging neutron-stars including quarks at finite temperatures that can be switched off consistently in the equation of state. Within our approach, we can determine clearly what signatures a quark-hadron phase transition would leave in the gravitational-wave signal. We show that if after the merger the conditions are met for a phase transition to take place at several times nuclear saturation density, they would lead to a postmerger signal considerably different from the one expected from the inspiral, that can only probe the hadronic part of the equations of state, and to an anticipated collapse of the merged object. We also show that the phase transition leads to a very hot and dense quark core that, when it collapses to a black hole, produces a ringdown signal different from the hadronic one. Finally, in analogy with what is done in heavy-ion collisions, we use the evolution of the temperature and density in the merger remnant to illustrate the properties of the phase transition in a QCD phase diagram.

S Fiber Taper-Based Fiber Loop Ring-Down Refractometer

A fiber-optic refractive index (RI) sensor based on fiber loop ring-down (FLRD) technique with an S fiber taper (SFT) structure is proposed and experimentally investigated. The SFT is served as an in-line Mach-Zehnder interferometer and inserted into a compensated fiber loop for RI measurement. By optimizing the parameters of the fiber loop, the quality of the ring-down signals is improved effectively. The surrounding refractive index can be conveniently measured by interrogating the ring-down time of the fiber loop. The experimental results demonstrate that the proposed sensor has a high sensitivity of -3128.954 μs/RIU in the measurement range of 1.3330-1.3682. The proposed RI sensor combines the specialties of SFT interferometer and FLRD technology, which could be a good candidate in applications.

Black-hole spectroscopy by making full use of gravitational-wave modeling

The Kerr nature of a compact-object-coalescence remnant can be unveiled by observing multiple quasi-normal modes (QNMs) in the post-merger signal. Current methods to achieve this goal rely on matching the data with a superposition of exponentially damped sinusoids with amplitudes fitted to numerical-relativity (NR) simulations of binary black-hole (BBH) mergers. These models presume the ability to correctly estimate the time at which the gravitational-wave (GW) signal starts to be dominated by the QNMs of a perturbed BH. Here we show that this difficulty can be overcome by using multipolar inspiral-merger-ringdown waveforms, calibrated to NR simulations, as already developed within the effective-one-body formalism (EOBNR). We build a parameterized (nonspinning) EOBNR waveform model in which the QNM complex frequencies are free parameters (pEOBNR), and use Bayesian analysis to study its effectiveness in measuring QNMs in GW150914, and in synthetic GW signals of BBHs injected in Gaussian noise. We find that using the pEOBNR model gives, in general, stronger constraints compared to the ones obtained when using a sum of damped sinusoids and using Bayesian model selection, we also show that the pEOBNR model can successfully be employed to find evidence for deviations from General Relativity in the ringdown signal. Since the pEOBNR model properly includes time and phase shifts among QNMs, it is also well suited to consistently combine information from several observations --- e.g., we find on the order of $\sim 30$ GW150914-like BBH events would be needed for Advanced LIGO and Virgo at design sensitivity to measure the fundamental frequencies of both the $(2,2)$ and $(3,3)$ modes, and the decay time of the $(2,2)$ mode with an accuracy of $\lesssim 5\%$ at the $2\mbox{-}\sigma$ level, thus allowing to test the BH's no-hair conjecture.

Operation of a Superconducting Nanowire in Two Detection Modes: KID and SPD

We present the performance of a superconducting nanowire that can be operated in two detection modes: i) as a kinetic inductance detector (KID) or ii) as a single-photon detector (SPD). Two superconducting nanowires developed for use as single-photon detectors (SNSPDs) are embedded as the inductive (L) component in resonant inductor/capacitor (LC) circuits coupled to a microwave transmission line. The capacitors are low loss commercial chip capacitors and limit the internal quality factor of the resonators to approximately $Q_i = 170$. The resonator quality factor, $Q_r \simeq 23$, is dominated by the coupling to the feedline and limits the detection bandwidth to on the order of 1MHz. When operated in KID mode, the detectors are AC biased with tones at their resonant frequencies of 45.85 and 91.81MHz. In the low-bias, standard KID mode, a single photon produces a hot spot that does not turn an entire section of the line normal but only increases the kinetic inductance. In the high-bias, critical KID mode, a photon event turns a section of the line normal and the resonance is destroyed until the normal region is dissipated. When operated as an SPD in Geiger mode, the resonators are DC biased through cryogenic bias tees and each photon produces a sharp voltage step followed by a ringdown signal at the resonant frequency of the detector which is converted to a standard pulse with an envelop detector. We show that AC biasing in the critical KID mode is inferior to the sensitivity achieved in DC-biased SPD mode due to the small fraction of time spent near the critical current with an AC bias.

Sensitivity improvement by optimized optical switching and curve fitting in a cavity ring-down spectrometer.

We presented methods for the improvement of the sensitivity of a cavity ring-down spectrometer other than modifying the cavity length and the mirrors. As for the light switching, a fast driving scheme was proposed to address the slow switching speed of the boost optical amplifier, which makes it have only half of the switching time of that for the common acoustic-optical modulators and electro-optical modulators, as well as have higher extinction ratios. This effectively suppressed the distortions of the ring-down signals. We further adopted a realistic non-exponential curve-fitting method, taking into account the switching speed and the delayed triggering of the optical switch. These methods help accurately determine the ring-down time constants, which in turn reduced the Allan variance of the measurement results and increased the sensitivity. We performed tests at different repetition rates and all of them revealed more than 30% sensitivity improvement. At a rate of 16kHz, we increased the minimal detectable absorption of 9.1×10-11 cm-1 to 5.7×10-11 cm-1. The effectiveness of these upgrades could benefit many spectroscopic applications of the cavity ring-down spectroscopy, especially for frontier research that requires sensitive measurement and high-quality spectral data.