Binary Waveforms Research Articles

A Pulsed Eddy Current Testing Sensor Made of Low-Cost Off-the-Shelf Components: Overview and Application to Pseudo-Noise Excitation

A low-cost device for eddy current non-destructive testing made of off-the-shelf components is described. The system consists of a dual H-bridge stepper motor driver, a coil wound in-house on an additively manufactured support, a tunneling magnetoresistance sensor, and a data generation/acquisition module. The system is compact, and it can flexibly generate rectangular pulses, square wave bursts and arbitrary binary excitation waveforms. Among these, in this paper pseudo-noise binary signals were used within a pulse-compression measurement protocol to increase the SNR and the inspection sensitivity with respect to pulsed excitation. A benchmark sample was analyzed, and all the defects were correctly located, demonstrating a good detection capability of the overall hardware-software solution proposed. It was also found that pulse-compression output signals can be further processed as standard pulsed eddy current data. Features can be extracted from them for defect classification purposes and the lift-off invariant point can be used for imaging. These results were achieved by assembling a low-cost handy device, which can be further improved in portability and performances using different off-the-shelf components and by integrating it with a single-board PC, paving the way for future developments in this field.

Fast, faithful, frequency-domain effective-one-body waveforms for compact binary coalescences

The inference of binary neutron star properties from gravitational-wave observations requires the generation of millions of waveforms, each one spanning about 3 order of magnitudes in the frequency range. Thus, waveform models must be efficiently generated and, at the same time, be faithful from the post-Newtonian quasiadiabatic inspiral up to the merger regime. A simple solution to this problem is to combine effective-one-body waveforms with the stationary phase approximation to obtain frequency-domain multipolar approximants valid from any low frequency to merger. We demonstrate that effective-one-body frequency-domain waveforms generated in postadiabatic approximation are computationally competitive with current phenomenological and surrogate models, (virtually) arbitrarily long, and faithful up to merger for any binary parameter. The same method can also be used to efficiently generate intermediate mass binary black hole inspiral waveforms detectable by space-based interferometers.

Optoelectronic Oscillator for Arbitrary Microwave Waveform Generation

An optoelectronic oscillator (OEO) for arbitrary microwave waveform generation based on Fourier domain mode-locking (FDML) is proposed. A reconfigurable optical waveform generator (OWG) is implemented via external electro-optical modulation, which serves as the optical source for the proposed OEO. The optical waveform from the OWG can be seen as a series of frequency-scanning optical wavelengths in the frequency domain. At any instant, the number of wavelengths can be from 0 to infinite. By setting the period of the optical waveform or its multiple equal to the cavity round-trip time, an FDML OEO implemented by a frequency-scanning microwave photonic filter (MPF) is realized based on the phase-modulation-to-intensity-modulation conversion using a phase modulator cascaded with a phase-shifted fiber Bragg grating. The scanning characteristics of the MPF changes according to the optical waveform, which can be utilized to generate low-phase-noise arbitrary microwave waveforms using the inherent low-phase-noise merit of an OEO. An experiment is performed. Linearly chirped microwave waveforms and non-linearly chirped microwave waveforms with a scanning bandwidth of 2 GHz, 2-level frequency hopping (FH) microwave waveforms with an FH range of 500 MHz, and 240- and 250-bit binary and quaternary phase-coded microwave waveforms are generated from the OEO. To the best of our knowledge, this is the first time that an OEO is proposed for arbitrary microwave waveform generation.

Recognizing black holes in gravitational-wave observations: Challenges in telling apart impostors in mass-gap binaries

We study how by careful monitoring of the presence or absence of tidal deformability (TD) and tidal-heating (TH) in the inspiral signal of compact object binaries in ground-based gravitational wave (GW) detectors, one can test if its components are black holes or not. The former property (TD) is finite for neutron stars but vanishes for black holes (in general relativity), whereas the latter is finite for black holes and negligible for neutron stars, and affects the GW phase evolution of binaries in a distinctly different way. We introduce waveform parameters that characterize the strength of tidal-heating, and are zero when there is no horizon. We develop Bayesian methods that use TD and TH for distinguishing the presence or absence of horizons in a binary. This is timely owing to several claims that these stellar-mass objects, especially, with masses heavier than those of neutron stars, may not have a horizon but may be black hole mimickers or exotic compact objects (ECOs). It is also astrophysically important to have the tools to test the presence or absence of horizons in mass-gap binaries and, thereby, help detect the heaviest neutron star or the lightest black hole. A proper accounting of tidal-heating in binary waveform models will also be critical for an unbiased measurement of characteristics of the equation of state of neutron stars in GW observations of binaries containing them -- or even to probe the existence of ECOs. We show that purely based on GW waveforms it will not be possible to discern binary horizons in the mass gap in Advanced LIGO, Virgo and KAGRA detectors unless the binary is within a few tens of Mpc. However, third generation ground-based detectors will be able to do so for binaries a few hundred Mpc away.

Assessing the readiness of numerical relativity for LISA and 3G detectors

Future detectors such as LISA promise signal-to-noise ratios potentially in the thousands and data containing simultaneous signals. Accurate numerical relativity waveforms will be essential to maximize the science return. A question of interest to the broad gravitational wave community is: Are the numerical relativity codes ready to face this challenge? Towards answering this question, we provide a new criteria to identify the minimum resolution a simulation must have as a function of signal-to-noise ratio in order for the numerical relativity waveform to be indistinguishable from a true signal. This criteria can be applied to any finite-differencing numerical relativity code with multiple simulations of differing resolutions for the desired binary parameters and waveform length. We apply this criteria to binary systems of interest with the fourth-order MAYA code to obtain the first estimate of the minimum resolution a simulation must have to be prepared for next generation detectors.

Failure of the Fisher matrix when including tidal terms: Considering construction of template banks of tidally deformed binary neutron stars

Recent gravitational-wave observations have begun to constrain the internal physics of neutron stars. However, current detection searches for neutron star systems assume that potential neutron stars are low-mass black holes, ignoring any affect on the gravitational-wave signal due to the internal neutron-star physics. We wish to create a template bank of binary neutron star waveforms including the effect of tidal deformability. However, we find that the Fisher matrix, which is commonly used to approximate match calculations when placing template banks, is unsuitable to predict the match between two binary neutron star waveforms. We find that the Fisher matrix can predict errors on the mismatch that are larger than $100\%$ when attempting to identify waveforms with a match of $0.97$. We explore the regime in which the Fisher matrix cannot be trusted and examine why it breaks down. We demonstrate that including higher-order terms in the Taylor series expansion of the match can reliably compute matches for these examples, but that it is prohibitively computationally expensive to do so. Finally, we demonstrate that stochastic placement can still be used to construct a template bank of tidally deformed neutron-star waveforms.

Bayesian inference of multimessenger astrophysical data: Methods and applications to gravitational waves

We present ${\tt bajes}$, a parallel and lightweight framework for Bayesian inference of multimessenger transients. ${\tt bajes}$ is a Python modular package with minimal dependencies on external libraries adaptable to the majority of the Bayesian models and to various sampling methods. We describe the general workflow and the parameter estimation pipeline for compact-binary-coalescence gravitational-wave transients. The latter is validated against injections of binary black hole and binary neutron star waveforms, including confidence interval tests that demonstrates the inference is well-calibrated. Binary neutron star postmerger injections are also studied using a network of five detectors made of LIGO, Virgo, KAGRA and Einstein Telescope. Postmerger signals will be detectable for sources at ${\lesssim}80\,$Mpc, with Einstein Telescope contributing over 90\% of the total signal-to-noise ratio. As a full scale application, we re-analyze the GWTC-1 black hole transients using the effective-one-body ${\tt TEOBResumS}$ approximant, and reproduce selected results with other approximants. ${\tt bajes}$ inferences are consistent with previous results; the direct comparison of ${\tt bajes}$ and ${\tt bilby}$ analyses of GW150914 shows a maximum Jensen-Shannon divergence of $5.2{\times}10^{-4}$. GW170817 is re-analyzed using ${\tt TaylorF2}$ with 5.5PN point-mass and 7.5PN tides, ${\tt TEOBResumSPA}$, and ${\tt IMRPhenomPv2\_NRTidal}$ with different cutoff-frequencies of $1024\,$Hz and $2048\,$Hz. We find that the former choice minimizes systematics on the reduced tidal parameter, while a larger amount of tidal information is gained with the latter choice. ${\tt bajes}$ can perform these analyses in about 1~day using 128 CPUs.

Importance of mirror modes in binary black hole ringdown waveform

The post-merger signal in binary black hole merger is described by linear, black-hole perturbation theory. Historically, this has been modeled using the dominant positive-frequency (corotating) fundamental mode. Recently, there has been a renewed effort in modeling the post-merger waveform using higher, positive-frequency overtones in an attempt to achieve greater accuracy in describing the waveform at earlier times using linear perturbation theory. It has been shown that the inclusion of higher overtones can shift the linear regime to the peak of $(l,m)=(2,2)$ spherical harmonic mode. In this work, we show that the inclusion of negative-frequency (counterrotating) modes, called 'mirror' modes, extends the validity of linear perturbation theory to even earlier times, with far lower systematic uncertainties in the model in recovering the remnant parameters at these early times. A good description of the signal at early times also enables for a greater signal-to-noise ratio to be accumulated in the ringdown phase, thereby, allowing for a more accurate measurement of remnant parameters and tests of general relativity.

Initial data and eccentricity reduction toolkit for binary black hole numerical relativity waveforms

The production of numerical relativity waveforms that describe quasi-circular binary black hole mergers requires high-quality initial data, and an algorithm to iteratively reduce residual eccentricity. To date, these tools remain closed source, or in commercial software that prevents their use in high performance computing platforms. To address these limitations, and to ensure that the broader numerical relativity community has access to these tools, herein we provide all the required elements to produce high-quality numerical relativity simulations in supercomputer platforms, namely: open source parameter files to numerically simulate spinning black hole binaries with asymmetric mass-ratios; open source Python tools to produce high-quality initial data for numerical relativity simulations of spinning black hole binaries on quasi-circular orbits; and open source Python tools for eccentricity reduction, both as stand-alone software and also deployed in the Einstein Toolkit’s software infrastructure. This open source toolkit fills in a void in the literature at a time when numerical relativity has an ever increasing role in the study and interpretation of gravitational wave sources. As part of our community building efforts, and to streamline and accelerate the use of these resources, we provide tutorials that describe, step by step, how to obtain and use these open source numerical relativity tools.

Assessing and marginalizing over compact binary coalescence waveform systematics with RIFT

As Einstein's equations for binary compact object inspiral have only been approximately or intermittently solved by analytic or numerical methods, the models used to infer parameters of gravitational wave (GW) sources are subject to waveform modeling uncertainty. Using a simple scenario, we illustrate these differences, then introduce a very efficient technique to marginalize over waveform uncertainties, relative to a pre-specified sequence of waveform models. Being based on RIFT, a very efficient parameter inference engine, our technique can directly account for any available models, including very accurate but computationally costly waveforms. Our evidence and likelihood-based method works robustly on a point-by-point basis, enabling accurate marginalization for models with strongly disjoint posteriors while simultaneously increasing the reusability and efficiency of our intermediate calculations.

Numerical relativity simulation of GW150914 in Einstein-dilaton-Gauss-Bonnet gravity

A present challenge in testing general relativity (GR) with binary black hole gravitational wave detections is the inability to perform model-dependent tests due to the lack of merger waveforms in beyond-GR theories. In this study, we produce the first numerical relativity binary black hole gravitational waveform in Einstein dilaton Gauss-Bonnet (EDGB) gravity, a higher-curvature theory of gravity with motivations in string theory. We evolve a binary black hole system in order-reduced EDGB gravity, with parameters consistent with GW150914. We focus on the merger portion of the waveform, due to the presence of secular growth in the inspiral phase. We compute mismatches with the corresponding general relativity merger waveform, finding that from a post-inspiral-only analysis, we can constrain the EDGB lengthscale to be $\sqrt{\alpha_\mathrm{GB}} \lesssim 11$ km.

News from Horizons in Binary Black Hole Mergers.

In a binary black hole merger, it is known that the inspiral portion of the waveform corresponds to two distinct horizons orbiting each other and that the merger and ringdown signals correspond to the final horizon being formed and settling down to equilibrium. However, we still lack a detailed understanding of the relation between the horizon geometry in these three regimes and the observed waveform. Here we show that the well-known inspiral chirp waveform has a clear counterpart on black hole horizons, namely, the shear of the outgoing null rays at the horizon. We demonstrate that the shear behaves very much like a compact binary coalescence waveform with increasing frequency and amplitude. Furthermore, the parameters of the system estimated from the horizon agree with those estimated from the waveform. This implies that even though black hole horizons are causally disconnected from us, assuming general relativity to be true, we can potentially infer some of their detailed properties from gravitational wave observations.

Hybrid waveforms for generic precessing binaries for gravitational-wave data analysis

We construct hybrid binary black holes merger waveforms using analytical model waveforms for the early inspiral phase and numerical relativity waveforms for late inspiral to merger and post merger phases. To hybridize analytical and numerical waveforms, we first perform a 3-dimensional rotation to align the instantaneous orbital planes associated with the two waveforms at some fiducial frequency, we then find appropriate phase and time translations that maximize the overlap of the two waveforms in a hybridization interval. We discuss the accuracy and limitations for hybrids constructed by this procedure in the context of LIGO-Virgo-KAGRA observations. Our goal is to hybridize waveforms for more generic precessing binaries and construct longer waveforms that are sufficiently accurate for the parameter estimation techniques for upcoming LIGO observations.

Probing Einstein-dilaton Gauss-Bonnet gravity with the inspiral and ringdown of gravitational waves

Gravitational waves from extreme gravity events such as the coalescence of two black holes in a binary system fill our observable universe, bearing with them the underlying theory of gravity driving their process. One compelling alternative theory of gravity -- known as Einstein-dilaton Gauss-Bonnet gravity motivated by string theory -- describes the presence of an additional dilaton scalar field coupled directly to higher orders of the curvature, effectively describing a "fifth force" interaction and the emission of scalar dipole radiation between two scalarized black holes. Most previous studies focused on considering only the leading correction to the inspiral portion of the binary black hole waveforms. In our recent paper, we carried out inspiral-merger-ringdown consistency tests in this string-inspired gravity by including corrections to both the inspiral and ringdown portions, as well as those to the mass and spin of remnant black holes, valid to quadratic order in spin. We here extend the analysis by directly computing bounds on the theoretical coupling constant using the full inspiral-merger-ringdown waveform rather than treating the inspiral and merger-ringdown portions separately. We also consider the corrections valid to quartic order in spin to justify the validity of black hole's slow-rotation approximation. We find the quasinormal mode corrections to the waveform to be particularly important for high-mass events such as GW170729, in which the dilaton fields' small-coupling approximation fails without such effects included. We also show that future space-based and multiband gravitational-wave observations have the potential to go beyond existing bounds on the theory. The bounds presented here are comparable to those found in via the inspiral-merger-ringdown consistency tests.

Numerical relativity simulation of GW150914 beyond general relativity

We produce the first astrophysically-relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first LIGO detection, in order-reduced dynamical Chern-Simons gravity, a theory with motivations in string theory and loop quantum gravity. We present results for the leading-order corrections to the merger and ringdown waveforms, as well as the ringdown quasi-normal mode spectrum. We estimate that such corrections may be discriminated in detections with signal to noise ratio $\gtrsim 180-240$, with the precise value depending on the dimension of the GR waveform family used in data analysis.

Tidal Deformations of Hybrid Stars with Sharp Phase Transitions and Elastic Crusts

Abstract Gravitational wave astronomy is expected to provide independent constraints on neutron-star properties, such as their equation of state. This is possible with the measurements of binary components’ tidal deformability, which alter the point-particle gravitational waveforms of neutron-star binaries. Here, we provide a first study of the tidal deformability effects due to the elasticity/solidity of the crust (hadronic phase) in a hybrid neutron star, as well as the influence of a quark-hadronic phase density jump on tidal deformations. We employ the framework of non-radial perturbations with zero frequency and study hadronic phases presenting elastic aspects when perturbed (with the shear modulus approximately 1% of the pressure). We find that the relative tidal deformation change in a hybrid star with a perfect-fluid quark phase and a hadronic phase presenting an elastic part is never larger than about 2%–4% (with respect to a perfect-fluid counterpart). These maximum changes occur when the elastic region of a hybrid star is larger than approximately 60% of the star’s radius, which may happen when its quark phase is small and the density jump is large enough, or even when a hybrid star has an elastic mixed phase. For other cases, tidal deformation changes due to an elastic crust are negligible ( ) and, therefore, unlikely to be measured even with third generation detectors. Thus, only when the size of the elastic hadronic region of a hybrid star is over half of its radius, could the effects of elasticity have a noticeable impact on tidal deformations.

Time-Frequency Linearization of Reactive Cortical Responses for the Early Detection of Balance Losses

Aiming at finding a fast and accurate preimpact fall detection (PIFD) strategy, this paper proposes a novel methodology that precociously discriminates the occurrence of unexpected loss of balance from the steady walking, by analyzing the subject’s cortical signal modifications (at the scalp level) in the time-frequency domain. In this study, the subjects were asked to walk at their preferred speed on the treadmill platform programmed to provide unexpected bilateral slippages. The proposed PIFD method exploits synchronously recorded electromyographic (EMG: 2 channels from the same lower limb muscle bundle, bilaterally) and electro-encephalographic (EEG: 13 channels from motor, sensory-motor and parietal cortex areas) signals. To validate the method offline, also, the lower limb kinematics has been reconstructed via a motion capture system (23 reflective markers and 8 fixed cameras). During the PIFD system functioning, the EMG signals from the lateral gastrocnemii are first translated in a binary waveform and then used to trigger the EEG analysis. Once enabled via EMG (every gait cycle), the EEG computation branch extracts and linearizes the rate of variation in the EEG power spectrum density (PSD) for five bands of interests: θ (4–7 Hz), α (8–12 Hz), β I, β II, β III rhythms (13–15 Hz, 16–20 Hz, and 21–28 Hz). The slope of the linearized trend identifies, in this context, the cortical responsiveness parameter. Experimental results from six subjects revealed that the proposed system can distinguish the loss of balance with an overall accuracy of ~96% (average value between sensitivity and specificity). The discrimination process requests, on average, 370.6 ms. This value could be considered suitable for the implementation of countermeasures aimed at restoring the balance of the subject.

Stability of rotating black holes in Einstein dilaton Gauss-Bonnet gravity

In order to perform model-dependent tests of general relativity with gravitational wave observations, we must have access to numerical relativity binary black hole waveforms in theories beyond general relativity (GR). In this study, we focus on order-reduced Einstein dilaton Gauss-Bonnet gravity (EDGB), a higher curvature beyond-GR theory with motivations in string theory. The stability of single, rotating black holes in EDGB is unknown, but is a necessary condition for being able to simulate binary black hole systems (especially the early-inspiral and late ringdown stages) in EDGB. We thus investigate the stability of rotating black holes in order-reduced EDGB. We evolve the leading-order EDGB scalar field and EDGB spacetime metric deformation on a rotating black hole background, for a variety of spins. We find that the EDGB metric deformation exhibits linear growth, but that this level of growth exponentially converges to zero with numerical resolution. Thus, we conclude that rotating black holes in EDGB are numerically stable to leading-order, thus satisfying our necessary condition for performing binary black hole simulations in EDGB.

Compact binary waveform center-of-mass corrections

We present a detailed study of the center-of-mass (c.m.) motion seen in simulations produced by the Simulating eXtreme Spacetimes (SXS) collaboration. We investigate potential physical sources for the large c.m. motion in binary black hole simulations and find that a significant fraction of the c.m. motion cannot be explained physically, thus concluding that it is largely a gauge effect. These large c.m. displacements cause mode mixing in the gravitational waveform, most easily recognized as amplitude oscillations caused by the dominant (2,$\pm$2) modes mixing into subdominant modes. This mixing does not diminish with increasing distance from the source; it is present even in asymptotic waveforms, regardless of the method of data extraction. We describe the current c.m.-correction method used by the SXS collaboration, which is based on counteracting the motion of the c.m. as measured by the trajectories of the apparent horizons in the simulations, and investigate potential methods to improve that correction to the waveform. We also present a complementary method for computing an optimal c.m. correction or evaluating any other c.m. transformation based solely on the asymptotic waveform data.

Tests of general relativity with the binary black hole signals from the LIGO-Virgo catalog GWTC-1

The detection of gravitational waves by Advanced LIGO and Advanced Virgo provides an opportunity to test general relativity in a regime that is inaccessible to traditional astronomical observations and laboratory tests. We present four tests of the consistency of the data with binary black hole gravitational waveforms predicted by general relativity. One test subtracts the best-fit waveform from the data and checks the consistency of the residual with detector noise. The second test checks the consistency of the low- and high-frequency parts of the observed signals. The third test checks that phenomenological deviations introduced in the waveform model (including in the post-Newtonian coefficients) are consistent with zero. The fourth test constrains modifications to the propagation of gravitational waves due to a modified dispersion relation, including that from a massive graviton. We present results both for individual events and also results obtained by combining together particularly strong events from the first and second observing runs of Advanced LIGO and Advanced Virgo, as collected in the catalog GWTC-1. We do not find any inconsistency of the data with the predictions of general relativity and improve our previously presented combined constraints by factors of 1.1 to 2.5. In particular, we bound the mass of the graviton to be $m_g \leq 4.7 \times 10^{-23} \text{eV}/c^2$ ($90\%$ credible level), an improvement of a factor of 1.6 over our previously presented results. Additionally, we check that the four gravitational-wave events published for the first time in GWTC-1 do not lead to stronger constraints on alternative polarizations than those published previously.