Gravitational Wave Data Analysis Research Articles

Possibility of primordial black holes as the source of gravitational wave events in the advanced LIGO detector

The analysis of gravitational Wave (GW) data from advanced LIGO provides the mass of each companion of binary black holes as the source of GWs. The mass of events corresponding to the binary black holes from GW is above $20$ M$_\odot$ which is much larger than the mass of astrophysical black holes detected by x-ray observations. In this work, we examine primordial black holes (PBHs) as the source of LIGO events. Assuming that $100\%$ of the dark matter is made of PBHs, we estimate the rate at which these objects make binaries, merge, and produce GWs as a function of redshift. The gravitational lensing of GWs by PBHs can also enhance the amplitude of the strain. We simulate GWs sourced by binary PBHs, with the detection threshold of $S/N>10$ for both Livingston and Hanford detectors. For the log-normal mass function of PBHs, we generate the expected distribution of events, compare our results with the observed events, and find the best value of the mass function parameters (i.e., $M_c =25 M_\odot$ and $\sigma=0.6$) in the log-normal mass function. Comparing the expected number of events with the number of observed ones rules out the present-Universe binary formation PBH scenario as the candidate for the source of GW events detected by LIGO.

Updated universal relations for tidal deformabilities of neutron stars from phenomenological equations of state

Equation of state (EOS) insensitive relations, so-called universal relations, between the neutron star (NS) compactness, its multipolar tidal deformability coefficients, and between the tidal parameters for binary systems are essential to break degeneracies in gravitational wave data analysis. Here, we validate and recalibrate these universal relations using a large set of almost 2 million phenomenological EOSs that are consistent with current observations. In doing so, we extend universal relations to a larger region of the EOS parameter space, most notably to softer EOSs and larger compactnesses. We show that waveform models that neglect higher-than-leading-order tidal deformations of the NSs accumulate as much as $3.5$ radians of dephasing from $20\,{\rm Hz}$ to merger. We also perform a full Bayesian parameter estimation of the GW170817 data, and we compare the NS radius constraints produced using universal relations from the literature and the updated fits we propose here. We find that the new fits yield a NS radius that is smaller by about 500 meters. This difference is less than the statistical uncertainty on the radius at the signal-to-noise-ratio of GW170817, but it is significantly larger than the precision anticipated for next-generation detectors.

Effective-one-body waveforms from dynamical captures in black hole binaries

Dynamical capture is a possible formation channel for BBH mergers leading to highly eccentric merger dynamics and to gravitational wave (GW) signals that are morphologically different from those of quasi-circular mergers. The future detection of these mergers by ground-based or space-based GW interferometers can provide invaluable insights on astrophysical black holes, but it requires precise predictions and dedicated waveform models for the analysis. We present a state-of-the-art effective-one-body (EOB) model for the multipolar merger-ringdown waveform from dynamical capture black-hole mergers with arbitrary mass-ratio and nonprecessing spins. The model relies on analytical descriptions of the radiation reaction and waveform along generic orbits that are obtained by incorporating generic Newtonian prefactors in the expressions used in the quasi-circular case. It provides a tool for generating waveforms for generic binary black hole coalescences and for GW data analysis. We demonstrate that the model reliably accounts for the rich phenomenology of dynamical captures, from direct plunge to successive close encounters up to merger. The parameter space is fully characterized in terms of the initial energy and angular momentum. Our model reproduces to few percent the scattering angle from ten equal-mass, nonspinning, hyperbolic encounter numerical-relativity (NR) simulations. The agreement can be further improved to the by incorporating 6PN-results in one of the EOB potentials and tuning currently unknown analytical parameters. Our results suggest that NR simulations of hyperbolic encounters (and dynamical captures) can be used to inform EOB waveform models for generic BBH mergers/encounters for present and future GW detectors.

Machine learning gravitational waves from binary black hole mergers

We apply machine learning methods to build a time-domain model for gravitational waveforms from binary black hole mergers, called mlgw. The dimensionality of the problem is handled by representing the waveform's amplitude and phase using a principal component analysis. We train mlgw on about $\mathcal{O}({10}^{3})$ teobresums and seobnrv4 effective-one-body waveforms with mass ratios $q\ensuremath{\in}[1,20]$ and aligned dimensionless spins $s\ensuremath{\in}[\ensuremath{-}0.80,0.95]$. The resulting models are faithful to the training sets at the $\ensuremath{\sim}{10}^{\ensuremath{-}3}$ level (averaged on the parameter space). The speed up for a single waveform generation is a factor of 10--50 (depending on the binary mass and initial frequency) for teobresums and approximately an order of magnitude more for seobnrv4. Furthermore, mlgw provides a closed form expression for the waveform and its gradient with respect to the orbital parameters; such an information might be useful for future improvements in gravitational wave (GW) data analysis. As demonstration of the capabilities of mlgw to perform a full parameter estimation, we reanalyze the public data from the first GW transient catalog (GWTC-1). We find broadly consistent results with previous analyses at a fraction of the cost, although the analysis with spin-aligned waveforms gives systematic larger values of the effective spins with respect to previous analyses with precessing waveforms. Since the generation time does not depend on the length of the signal, our model is particularly suitable for the analysis of the long signals that are expected to be detected by third-generation detectors. Future applications include the analysis of waveform systematics and model selection in parameter estimation.

The phenomenology of dynamical neutron star tides

ABSTRACT We introduce a phenomenological, physically motivated, model for the effective tidal deformability of a neutron star, adding the frequency dependence (associated with the star’s fundamental mode of oscillation) that comes into play during the late stages of the binary inspiral. Testing the model against alternative descriptions, we demonstrate that it provides an accurate representation of the dynamical tide up to close to merger. The simplicity of the prescription makes it an attractive alternative for a gravitational-wave data analysis implementation, facilitating an inexpensive construction of a large number of templates covering the relevant parameter space.

Modeling compact binary signals and instrumental glitches in gravitational wave data

Transient non-Gaussian noise in gravitational wave detectors, commonly referred to as glitches, pose challenges for detection and inference of the astrophysical properties of detected signals when the two are coincident in time. Current analyses aim toward modeling and subtracting the glitches from the data using a flexible, morphology-independent model in terms of sine-Gaussian wavelets before the signal source properties are inferred using templates for the compact binary signal. We present a new analysis of gravitational wave data that contain both a signal and glitches by simultaneously modeling the compact binary signal in terms of templates and the instrumental glitches using sine-Gaussian wavelets. The model for the glitches is generic and can thus be applied to a wide range of glitch morphologies without any special tuning. The simultaneous modeling of the astrophysical signal with templates allows us to efficiently separate the signal from the glitches, as we demonstrate using simulated signals injected around real O2 glitches in the two LIGO detectors. We show that our new proposed analysis can separate overlapping glitches and signals, estimate the compact binary parameters, and provide ready-to-use glitch-subtracted data for downstream inference analyses.

Improved deep learning techniques in gravitational-wave data analysis

In recent years, convolutional neural network (CNN) and other deep learning models have been gradually introduced into the area of gravitational-wave (GW) data processing. Compared with the traditional matched-filtering techniques, CNN has significant advantages in efficiency in GW signal detection tasks. In addition, matched-filtering techniques are based on the template bank of the existing theoretical waveform, which makes it difficult to find GW signals beyond theoretical expectation. In this paper, based on the task of GW detection of binary black holes, we introduce the optimization techniques of deep learning, such as batch normalization and dropout, to CNN models. Detailed studies of model performance are carried out. Through this study, we recommend to use batch normalization and dropout techniques in CNN models in GW signal detection tasks. Furthermore, we investigate the generalization ability of CNN models on different parameter ranges of GW signals. We point out that CNN models are robust to the variation of the parameter range of the GW waveform. This is a major advantage of deep learning models over matched-filtering techniques.

Investigating the I-Love-Q and w -mode universal relations using piecewise polytropes

Neutron stars are expected to have a tight relation between their moment of inertia ($I$), tidal deformability ($\lambda$, which is related to the Love number), and rotational mass quadrupole moment ($Q$) that is nearly independent of the unknown equation of state (EoS) of cold dense matter. These and similar relations are often called "universal", and they have been used for various applications including analysis of gravitational wave data. We extend these studies using piecewise polytropic representations of dense matter, including for so-called twin stars that have a second branch of stability at high central densities. The second-branch relations are less tight, by a factor of $\sim 3$, than the relations found in the first stable branch. We find that the relations on both branches become tighter when we increase the lower limit to the maximum mass for the EoS under consideration. We also propose new empirical relations between $I$, $\lambda$, $Q$, and the complex frequency $\omega=\omega_R+i\omega_I$ of the fundamental axial $w$-mode, and find that they are comparably tight to the I-Love-Q correlations.

Time-frequency analysis of gravitational wave data

Data from gravitational wave detectors are recorded as time series that include contributions from myriad noise sources in addition to any gravitational wave signals. When regularly sampled data are available, such as for ground based and future space based interferometers, analyses are typically performed in the frequency domain, where stationary (time invariant) noise processes can be modeled very efficiently. In reality, detector noise is not stationary due to a combination of short duration noise transients and longer duration drifts in the power spectrum. This non-stationarity produces correlations across samples at different frequencies, obviating the main advantage of a frequency domain analysis. Here an alternative time-frequency approach to gravitational wave data analysis is proposed that uses discrete, orthogonal wavelet wavepackets. The time domain data is mapped onto a uniform grid of time-frequency pixels. For locally stationary noise - that is, noise with an adiabatically varying spectrum - the time-frequency pixels are uncorrelated, which greatly simplifies the calculation of quantities such as the likelihood. Moreover, the gravitational wave signals from binary systems can be compactly represented as a collection of lines in time-frequency space, resulting in a computational cost for computing waveforms and likelihoods that scales as the square root of the number of time samples, as opposed to the linear scaling for time or frequency based analyses. Key to this approach is having fast methods for computing binary signals directly in the wavelet domain. Multiple fast transform methods are developed in detail.

Accelerating the evaluation of inspiral–merger–ringdown waveforms with adapted grids

This paper presents an algorithm to accelerate the evaluation of inspiral–merger–ringdown waveform models for gravitational wave data analysis. While the idea can also be applied in the time domain, here we focus on the frequency domain, which is most typically used to reduce computational cost in gravitational wave data analysis. Our work extends the idea of multibanding Vinciguerra S et al (2017 Class. Quantum Grav. 34 115006), which has been developed to accelerate frequency domain waveforms, to include the merger and ringdown and spherical harmonics beyond the dominant quadrupole spherical harmonic. The original method of Vinciguerra S et al (2017 Class. Quantum Grav. 34 115006) is based on a heuristic algorithm based on the inspiral to de-refine the equi-spaced frequency grid used for data analysis where a coarser grid is sufficient for accurate evaluation of a waveform model. Here we use a different criterion, based on the local interpolation error, which is more flexible and can easily be adapted to general waveforms, if their phenomenology is understood. We discuss our implementation in the LIGO Algorithms Library (The LIGO Scientific Collaboration 2015 https://lsc-group.phys.uwm.edu/daswg/projects/lalsuite.html) for the IMRPhenomXHM García Quirós C et al (2020 arXiv:2001.10914) frequency domain model, and report the acceleration in different parts of the parameter space of compact binary systems.

Method of Gravitational Wave Search Based on Adaptive Time-Frequency Analysis and Machine Learning

In simple terms, gravitational waves are ripples in space-time caused by energetic processes in the Universe, such as the movement of mass. One of the exciting things about them is that they can be used to observe systems that are basically impossible to detect using other means. These ripples were predicted by Albert Einstein almost a century ago, but it wasn't until 2016 that scientists announced, for the first time, the detection of gravitational waves. The Laser Interferometer Gravitational-Wave Observatory (LIGO) is the physics experiment responsible for this detection and it has since continued to make a significant impact in the field. LIGO collaborates closely with the Virgo interferometer; a large interferometer designed to detect gravitational waves, and the Japanese Gravitational Wave Detector in Kamioka Mine (KAGRA), the Large Scale Cryogenic Gravitational Wave Telescope; a project of the gravitational wave studies group led by the Institute for Cosmic Ray Research of The University of Tokyo. But there still remain many unknowns, such as challenges related to the data analysis of gravitational waves. Professor Hirotaka Takahashi is carrying out research on gravitational waves that is attempting to address these challenges by developing algorithms that can dramatically increase the speed and efficiency of gravitational wave searches, which he believes are currently insufficient. Takahashi is a member of the KAGRA collaboration, which, as of March 2020, consists of more than 390 researchers from 90 institutions in 14 countries and regions.

Testing spacetime symmetry through gravitational waves from extreme-mass-ratio inspirals

One of the primary aims of upcoming spaceborne gravitational wave detectors is to measure radiation in the mHz range from extreme-mass-ratio inspirals. Such a detection would place strong constraints on hypothetical departures from a Kerr description for astrophysically stable black holes. The Kerr geometry, which is unique in general relativity, admits a higher-order symmetry in the form of a Carter constant, which implies that the equations of motion describing test particle motion in a Kerr background are Liouville-integrable. In this article, we investigate whether the Carter symmetry itself is discernible from a generic deformation of the Kerr metric in the gravitational waveforms for such inspirals. We build on previous studies by constructing a new metric which respects current observational constraints, describes a black hole, and contains two non-Kerr parameters, one of which controls the presence or absence of the Carter symmetry, thereby controlling the existence of chaotic orbits, and another which serves as a generic deformation parameter. We find that these two parameters introduce fundamentally distinct features into the orbital dynamics, and evince themselves in the gravitational waveforms through a significant dephasing. Although only explored in the quadrupole approximation, this, together with a Fisher metric analysis, suggests that gravitational wave data analysis may be able to test, in addition to the governing theory of gravity, the underlying symmetries of spacetime.

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.

Validating the effective-one-body numerical-relativity waveform models for spin-aligned binary black holes along eccentric orbits

Effective-one-body (EOB) numerical-relativity (NR) waveform models for spin-aligned binary black holes (BBHs), known as the SEOBNR waveform models, are based on the EOB theoretical framework and NR simulations. SEOBNR models have played an important role in the LIGO scientific collaboration (LSC) gravitational wave (GW) data analysis for both signal search and parameter estimation. SEOBNR models for quasi-circular orbits have evolved through version 1 to version 4 by extending their validity domain and including more NR results. Along another direction, we recently extended SEOBNRv1 model to SEOBNRE model which is valid for spin-aligned BBH coalescence along eccentric orbits. In this paper we validate this theoretical waveform model by comparing them against the numerical relativity simulation bank, Simulating eXtreme Spacetimes (SXS) catalog. In total, 278 NR waveforms are investigated which include binaries with large eccentricity; large spin and large mass ratio. Our SEOBNRE can model the NR waveforms quite well. The fitting factor for most of the 278 waveforms is larger than 99\%. It indicates that the SEOBNRE model could be used as template waveforms for eccentric spin-aligned BBH coalescence.

Inferring prompt black-hole formation in neutron star mergers from gravitational-wave data

The gravitational-wave GW170817 is associated to the inspiral phase of a binary neutron star coalescence event. The LIGO-Virgo detectors sensitivity at high frequencies was not sufficient to detect the signal corresponding to the merger and post-merger phases. Hence, the question whether the merger outcome was a prompt black hole formation or not must be answered using either the pre-merger gravitational wave signal or electromagnetic counterparts. In this work we present two methods to infer the probability of prompt black hole formation, using the analysis of the inspiral gravitational-wave signal. Both methods combine the posterior distribution from the gravitational-wave data analysis with numerical relativity results. One method relies on the use of phenomenological models for the equation of state and on the estimate of the collapse threshold mass. The other is based on the estimate of the tidal polarizability parameter $\tilde{\Lambda}$ that is correlated in an equation-of-state agnostic way with the prompt BH formation. We analyze GW170817 data and find that the two methods consistently predict a probability of ~ 50-70% for prompt black-hole formation, which however may significantly decrease below 10% if the maximum mass constraint from PSR J0348+0432 or PSR J0740+6620 is imposed.

Identifying and Characterizing Cyclicality and Seasonality in Environmental Data with An Adaptive Filter Implementation of A Phase Locked Loop

Phase Locked Loops are provided as a manner of assessing, monitoring and forecasting with seasonal or cyclical data. Phase Locked Loops using adaptive filtering were initially utilized for gravitational wave data analysis. In this paper we examine this implementation as an alternative approach for identifying the presence of one or more cycles in environmental data. Unlike most techniques for assessing seasonality phase lock loops can identify the presence of cycles without prior suspicion of their nature and existence. This is important for identifying either the initiation of new cycles or changes in existing cycles. As environmental data can be impacted by the presence of numerous cyclical phenomena and these cycles can change over time, this is a suitable and valuable technique. The technique can be used on existing data sets or assessing data streams. Phase Locked Loops are advantageous over many currently as the presence of multiple different cycles can be identified without prior suspicion and specification of the nature of the cyclicality of the data. The speed and parsimonious nature of the technique makes Phase Lock Loops ideal for Big Data and data flows that are so large that they must be assessed on a real time basis. The technique can manage and advise of changes in frequency, amplitude and phase shifts. The technique is illustrated utilizing weather data.

Finite tidal effects in GW170817: Observational evidence or model assumptions?

After the detection of gravitational waves caused by the coalescence of compact objects in the mass range of neutron stars, GW170817, several studies have searched for an imprint of tidal effects in the signal, employing different model assumptions. One important distinction is whether or not to assume that both objects are neutron stars and obey the same equation of state. Some studies assumed independent properties. Others assume a universal equation of state, and in addition that the tidal deformability follows certain phenomenological relations. An important question is whether the gravitational-wave data alone constitute observational evidence for finite tidal effects. All studies provide Bayesian credible intervals, often without sufficiently discussing the impact of prior assumptions, especially in the case of lower limits on the neutron-star tidal deformability or radius. In this article, we scrutinize the implicit and explicit prior assumptions made in those studies. Our findings strongly indicate that existing lower credible bounds are mainly a consequence of prior assumptions combined with information gained about the system's masses. Importantly, those lower bounds are typically not informed by the observation of tidal effects in the gravitational-wave signal. Thus, regarding them as observational evidence might be misleading without a more detailed discussion. Further, we point out technical problems and conceptual inconsistencies in existing studies. We also assess the limitations due to systematic waveform model uncertainties in a novel way, demonstrating that differences between existing models are not guaranteed to be small enough for an unbiased estimation of lower bounds on the tidal deformability. Finally, we propose strategies for gravitational-wave data analysis designed to avoid some of the problems we uncovered.

Noise spectral estimation methods and their impact on gravitational wave measurement of compact binary mergers

Estimating the parameters of gravitational wave signals detected by ground-based detectors requires an understanding of the properties of the detectors' noise. In particular, the most commonly used likelihood function for gravitational wave data analysis assumes that the noise is Gaussian, stationary, and of known frequency-dependent variance. The variance of the colored Gaussian noise is used as a whitening filter on the data before computation of the likelihood function. In practice the noise variance is not known and it evolves over timescales of dozens of seconds to minutes. We study two methods for estimating this whitening filter for ground-based gravitational wave detectors with the goal of performing parameter estimation studies. The first method uses large amounts of data separated from the specific segment we wish to analyze and computes the power spectral density of the noise through the mean-median Welch method. The second method uses the same data segment as the parameter estimation analysis, which potentially includes a gravitational wave signal, and obtains the whitening filter through a fit of the power spectrum of the data in terms of a sum of splines and Lorentzians. We compare these two methods and argue that the latter is more reliable for gravitational wave parameter estimation.

The Equation of State and Some Key Parameters of Neutron Stars: Constraints from GW170817, the Nuclear Data, and the Low-mass X-Ray Binary Data

Abstract In this work we parameterize the equation of state of dense neutron star (NS) matter with four pressure parameters of and then set the combined constraints with the data of GW170817 and the data of six low-mass X-ray binaries (LMXBs) with thermonuclear burst or alternatively the symmetry energy of the nuclear interaction. We find that the nuclear data effectively narrow down the possible range of , the gravitational-wave data plays the leading role in bounding , and the LMXB data as well as the lower bound on the maximal gravitational mass of non-rotating NSs govern the constraints on and . Using posterior samples of pressure parameters and some universal relations, we further investigate how the current data sets can advance our understanding of tidal deformability (Λ), moment of inertia (I), and binding energy (BE) of NSs. For a canonical mass of 1.4 M ⊙, we have , , , and if the constraints from the nuclear data and the gravitational-wave data have been jointly applied. For the joint analysis of gravitational-wave data and the LMXB data, we have , , , and . These results suggest that the current constraints on Λ and R still suffer from significant systematic uncertainties, while I 1.4 and BE1.4 are better constrained.

Viewing Angle of Binary Neutron Star Mergers

The joint detection of the gravitational wave (GW) GW170817 and its electromagnetic (EM) counterparts GRB170817A and kilonova AT 2017gfo has triggered extensive study of the EM emission of binary neutron star mergers. A parameter which is common to and plays a key role in both the GW and the EM analyses is the viewing angle of the binary’s orbit. If a binary is viewed from different angles, the amount of GW energy changes (implying that orientation and distance are correlated) and the EM signatures can vary, depending on the structure of the emission. Information about the viewing angle of the binary orbital plane is therefore crucial to the interpretation of both the GW and the EM data and can potentially be extracted from either side. In the first part of this study, we present a systematic analysis of how well the viewing angle of binary neutron stars can be measured from the GW data. We show that if the sky position and the redshift of the binary can be identified via the EM counterpart and an associated host galaxy, then for 50% of the systems the viewing angle can be constrained to ≤7° uncertainty from the GW data, independent of electromagnetic emission models. On the other hand, if no redshift measurement is available, the measurement of the viewing angle with GWs alone is not informative, unless the true viewing angle is close to 90°. This holds true even if the sky position is measured independently. Then, we consider the case where some constraints on the viewing angle can be placed from the EM data themselves. We show that the EM measurements can then be used in the analysis of GW data to improve the precision of the luminosity distance, and hence of the Hubble constant, by a factor of 2–3.3 MoreReceived 26 July 2018Revised 14 July 2019DOI:https://doi.org/10.1103/PhysRevX.9.031028Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGamma ray burstsGravitational wave sourcesGravitational wavesGravitation, Cosmology & Astrophysics