Waveform Of Gravitational Waves Research Articles

Cost of Inferred Nuclear Parameters toward the f-mode Dynamical Tide in Binary Neutron Stars

Gravitational-wave (GW) observations from neutron stars (NSs) in a binary system provide an excellent scenario to constrain the nuclear parameters. The investigation of Pratten et al. has shown that the ignorance of f-mode dynamical tidal correction in the GW waveform model of the binary NS system can lead to substantial bias in the measurement of NS properties and NS equations of state. In this work, we investigate the bias in the nuclear parameters resulting from the ignorance of dynamical tidal correction. In addition, this work demonstrates the sensitivity of the nuclear parameters and the estimated constraints on nuclear parameters and NS properties from future GW observations. We infer the nuclear parameters from GW observations by describing the NS matter within the relativistic mean field model. For a population of GW events, we notice that the ignorance of dynamical tide predicts a lower median for nucleon effective mass (m*) by ∼6% compared to the scenario when dynamical tidal correction is considered. Whereas, at a 90% credible interval, m* gets constrained up to ∼5% and ∼3% in A+ (the LIGO-Virgo detectors with a sensitivity of the fifth observing run) and Cosmic Explorer, respectively. We also discuss the resulting constraints on all other nuclear parameters, including compressibility, symmetry energy, and slope of symmetry energy, considering an ensemble of GW events. We do not notice any significant impact in analyzing nuclear parameters other than m* due to the ignorance of f-mode dynamical tides.

Combining chirp mass, luminosity distance, and sky localization from gravitational wave events to detect the cosmic dipole

ABSTRACT A key test of the isotropy of the Universe on large scales consists in comparing the dipole in the cosmic microwave background (CMB) temperature with the dipole in the distribution of sources at low redshift. Current analyses find a dipole in the number counts of quasars and radio sources that is 2–5 times larger than expected from the CMB, leading to a tension reaching 5σ. In this paper, we derive a consistent framework to measure the dipole independently from gravitational wave (GW) detections. We exploit the fact that the observer velocity does not only change the distribution of events in the sky, but also the luminosity distance and redshifted chirp mass, which can be extracted from the GW waveform. We show that the estimator with higher signal-to-noise ratio is the dipole in the chirp mass measured from a population of binary neutron stars. Combining all estimators (accounting for their covariance) improves the detectability of the dipole by 30–50 per cent compared to number counting of binary black holes alone. We find that a few 106 events are necessary to detect a dipole consistent with the CMB one, whereas if the dipole is as large as predicted by radio sources, it will already be detectable with 105 events, which would correspond to a single year of observation with next-generation GW detectors. GW sources provide therefore a robust and independent way of testing the isotropy of the Universe.

Effects of a Late Gravitational Transition on Gravitational Waves and Anticipated Constraints

We investigate the evolution of gravitational waves through discontinuous evolution (transition) of the Hubble expansion rate H(z) at a sudden cosmological singularity, which may be due to a transition of the value of the gravitational constant. We find the evolution of the scale factor and the gravitational wave waveform through the singularity by imposing the proper boundary conditions. We also use existing cosmological data and mock data of future gravitational wave experiments (the ET) to impose current and anticipated constraints on the magnitude of such a transition. We show that mock data of the Einstein Telescope can reduce the uncertainties by up to a factor of three depending on the cosmological parameter considered.

Two-body problem in curved spacetime: exploring gravitational wave transient cases

Gravitational-Wave Transient Catalogues (GWTC) from the LIGO-Virgo-KAGRA collaborations (LVC and LVK) contain almost a hundred gravitational wave (GW) detection cases. We explore them from the perspective of the two-body problem in curved spacetime, starting with the first case, GW150914, which marks the GW discovery []. In this paper, the LVC authors estimated the characteristic (chirp) mass of the binary blackhole system emitted this signal. Their calculation was based on Numerical-Relativity (NR) templates and presumably accounted fully for the non-linearity of GR. The same team later presented an alternative analysis of GW150914 [], using the quadrupole post-Newtonian (PN) approximation of GR. Both analyses gave similar results, despite being based on quite different assumptions about the linearity or non-linearity of the coordinate reference frame near the GW source. Here we revisit the PN-analysis of GW150914 for which we use less noisy input GW frequencies, as we have filtered them by reading them from the time-frequency map of GW150914. As in paper [], our result also agrees with the NR-based chirp mass value published in []. Additionally, we apply the PN-approximation formalism to the rest of the GWTC cases, finding that practically all of their PN-approximated chirp masses coincide with the published NR-based values from GWTC. In our view, this implies that the NR-based theory, which is currently in use for processing GW signals, does not fully account for the difference between the source and detector reference frames because the PN-approximation, which is used for the comparison, does not account for this difference by design, given the flat-spacetime initial assumptions of this approximation. We find that the basis of this issue lies in the source-to-detector coordinate transformation. For example, when obtaining the equation of motion of a coalescing binary system by integrating its energy-momentum tensor and varying the corresponding reduced action functional, the lapse and shift functions are not involved within the Arnowitt-Deser-Misner (ADM) parametrisation scheme, which is typically used for the NR-based calculation of GW waveforms A similar non-involvement of the lapse and shift functions is known to occur in the description of motion of an orbiter around a Schwarzschild blackhole. Here the GR expression for the orbital angular frequency, as seen by a remote observer, coincides with the Keplerian non-relativistic formula until the very last orbits before the plunge phase (although being fully GR-compliant). This non-involvement of the time lapse function renders the source-to-detector coordinate transformation suitable for building GW waveforms corresponding to the detector frame. However, the inverse (detector-to-source) transformation requires the derivatives of GW frequencies to be known in the source reference frame. The lack of this knowledge leads to a systematic error in the estimated chirp masses of GW sources. The corresponding luminosity distances of these sources also turn out to be overestimated.

LitePIG: a lite parameter inference system for the gravitational wave in the millihertz band

We present a Python based parameter inference system for the gravitational wave (GW) measured in the millihertz band. This system includes the following features: the GW waveform originated from the massive black hole binaries (MBHB), the stationary instrumental Gaussian noise, the higher-order harmonic modes, the full response function from the time delay interferometry and the Gaussian likelihood function with the dynamic nested parameter sampler. In particular, we highlight the role of higher-order modes. By including these modes, the luminosity distance estimation precision can be improved roughly by a factor of 50, compared with the case with only the leading order (ℓ = 2, ∣m∣ = 2) mode. This is due to the response functions of different harmonic modes on the inclination angle are different. Hence, it can help to break the distance-inclination degeneracy. Furthermore, we show the robustness of testing general relativity (GR) by using higher-order harmonics. Our results show that the GW from MBHB can simultaneously constrain four of the higher harmonic amplitudes (deviation from GR) with 95% confidence level of , , and , respectively.

An autoencoder neural network integrated into gravitational-wave burst searches to improve the rejection of noise transients

The gravitational-wave (GW) detector data are affected by short-lived instrumental or terrestrial transients, called ‘glitches’, which can simulate GW signals. Mitigation of glitches is particularly difficult for algorithms which target generic sources of short-duration GW transients (GWT), and do not rely on GW waveform models to distinguish astrophysical signals from noise, such as coherent WaveBurst (cWB). This work is part of the long-term effort to mitigate transient noises in cWB, which led to the introduction of specific estimators, and a machine-learning based signal-noise classification algorithm. Here, we propose an autoencoder neural network, integrated into cWB, that learns transient noises morphologies from GW time-series. We test its performance on the glitch family known as ‘blip’. The resulting sensitivity to generic GWT and binary black hole mergers significantly improves when tested on LIGO detectors data from the last observation period (O3b). At false alarm rate of one event per 50 years the sensitivity volume increases up to 30% for signal morphologies similar to blip glitches. In perspective, this tool can adapt to classify different transient noise classes that may affect future observing runs, enhancing GWT searches.

Application of Newtonian approximate model to LIGO gravitational wave data processing

With the observation of a series of ground-based laser interferometer gravitational wave (GW) detectors such as LIGO and Virgo, nearly 100 GW events have been detected successively. At present, all detected GW events are generated by the mergers of compact binary systems and are identified through the data processing of matched filtering. Based on matched filtering, we use the GW waveform of the Newtonian approximate (NA) model constructed by linearized theory to match the events detected by LIGO and injections to determine the coalescence time and utilize the frequency curve for data fitting to estimate the parameters of the chirp masses of binary black holes (BBHs). The average chirp mass of our results is , which is very close to provided by GWOSC. In the process, we can analyze LIGO GW events and estimate the chirp masses of the BBHs. This work presents the feasibility and accuracy of the low-order approximate model and data fitting in the application of GW data processing. It is beneficial for further data processing and has certain research value for the preliminary application of GW data.

Beyond the linear tide: impact of the non-linear tidal response of neutron stars on gravitational waveforms from binary inspirals

ABSTRACT Tidal interactions in coalescing binary neutron stars modify the dynamics of the inspiral and hence imprint a signature on their gravitational wave (GW) signals in the form of an extra phase shift. We need accurate models for the tidal phase shift in order to constrain the supranuclear equation of state from observations. In previous studies, GW waveform models were typically constructed by treating the tide as a linear response to a perturbing tidal field. In this work, we incorporate non-linear corrections due to hydrodynamic three- and four-mode interactions and show how they can improve the accuracy and explanatory power of waveform models. We set up and numerically solve the coupled differential equations for the orbit and the modes and analytically derive solutions of the system’s equilibrium configuration. Our analytical solutions agree well with the numerical ones up to the merger and involve only algebraic relations, allowing for fast phase shift and waveform evaluations for different equations of state over a large parameter space. We find that, at Newtonian order, non-linear fluid effects can enhance the tidal phase shift by $\gtrsim 1\, {\rm radian}$ at a GW frequency of 1000 Hz, corresponding to a $10{{\%}}-20{{\%}}$ correction to the linear theory. The scale of the additional phase shift near the merger is consistent with the difference between numerical relativity and theoretical predictions that account only for the linear tide. Non-linear fluid effects are thus important when interpreting the results of numerical relativity and in the construction of waveform models for current and future GW detectors.

Deep learning model based on a bidirectional gated recurrent unit for the detection of gravitational wave signals

The application of deep learning to the detection of gravitational wave (GW) signals has attracted much attention in recent years, and nearly all of the existing deep learning-based GW detection algorithms are based on the convolutional neural network (CNN), which can be used to identify the GW merger moment and produce responding triggers. However, current CNN-based models are not best optimized tools in modeling the causal logic of sequential data in the time dimension to incorporate the information of the inspiral, merger and ringdown phases of the GW waveform. To address this issue we propose a deep learning model designed based on the bidirectional gated recurrent unit (BiGRU), a variant of the recurrent neural network (RNN) that is sensitive to the sequential logic of GW data. We train the neural network and implement the GW detection task by using the data obtained during the first, second and third observation runs (O1/O2/O3) of the LIGO-VIGRO scientific collaboration. We find that our BiGRU model achieves a false alarm probability (FAP) of $4.88\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ (corresponding false alarm rate is about 1 per 18.2 hours) and maintains a detection ratio of about 89.6%. We also construct a model ensemble containing two independently trained BiGRU models and find it does not trigger any false alarm events on our testing dataset. Meanwhile, our BiGRU model not only recovers all the reported GW events of O1-O2 runs, including the unique (as of today) confident (with observed electromagnetic counterparts) GW event originating from a binary neutron star (BNS) merger (GW170817), but also achieves a detection ratio of about 80% of the O3 run. By calculating and comparing the receiver operator characteristic (ROC) curves we demonstrate the superiority of the BiGRU model over traditional CNN-based models, and show that the BiGRU model, being optimized to deal with GW waveform that sequentially contains the inspiral, merger and ringdown phases, is a potentially powerful tool to study the GW data in the future.

Forecasting the Detection Capabilities of Third-generation Gravitational-wave Detectors Using GWFAST

We introduce GWFAST, a novel Fisher-matrix code for gravitational-wave studies, tuned toward third-generation gravitational-wave detectors such as Einstein Telescope (ET) and Cosmic Explorer (CE). We use it to perform a comprehensive study of the capabilities of ET alone, and of a network made by ET and two CE detectors, as well as to provide forecasts for the forthcoming O4 run of the LIGO-Virgo-KAGRA (LVK) collaboration. We consider binary neutron stars, binary black holes, and neutron star–black hole binaries, and compute basic metrics such as the distribution of signal-to-noise ratio (S/N), the accuracy in the reconstruction of various parameters (including distance, sky localization, masses, spins, and, for neutron stars, tidal deformabilities), and the redshift distribution of the detections for different thresholds in S/N and different levels of accuracy in localization and distance measurement. We examine the expected distribution and properties of golden events, with especially large values of the S/N. We also pay special attention to the dependence of the results on astrophysical uncertainties and on various technical details (such as choice of waveforms, or the threshold in S/N), and we compare with other Fisher codes in the literature. In the companion paper Iacovelli et al., we discuss the technical aspects of the code. Together with this paper, we publicly release the code GWFAST, (https://github.com/CosmoStatGW/gwfast) and the library WF4Py (https://github.com/CosmoStatGW/WF4Py) implementing state-of-the-art gravitational-wave waveforms in pure Python.

Constraint on the mass of graviton with gravitational waves

We consider the effects of the mass of graviton on both the waveform of gravitational waves and the antenna response to gravitational waves. We find the effect on the response function is negligible for small mass. By using the Fisher matrix method, we make parameter estimations with space-based gravitational wave detectors for massive black hole binaries in massive gravity theory. The wavelength of massive graviton is constrained to be $\lambda_g\gtrsim 10^{17}$ m and the mass is constrained to be $m_g\lesssim 10^{-60}$ kg by one year's observation of massive black hole binaries with space-based gravitational wave detectors.

GWFAST: A Fisher Information Matrix Python Code for Third-generation Gravitational-wave Detectors

We introduce GWFAST (https://github.com/CosmoStatGW/gwfast), a Fisher information matrix Python code that allows for easy and efficient estimation of signal-to-noise ratios and parameter measurement errors for large catalogs of resolved sources observed by networks of gravitational-wave (GW) detectors. In particular, GWFAST includes the effects of the Earth’s motion during the evolution of the signal, supports parallel computation, and relies on automatic differentiation rather than on finite differences techniques, which makes possible the computation of derivatives with accuracy close to machine precision. We also release the library WF4Py (https://github.com/CosmoStatGW/WF4Py) implementing state-of-the-art GW waveforms in Python. In this paper we provide a documentation of GWFAST and WF4Py with practical examples and tests of performance and reliability. In the companion paper Iacovelli et al. we present forecasts for the detection capabilities of the second and third generation of ground-based GW detectors, obtained with GWFAST.

Probing dark matter spikes via gravitational waves of extreme-mass-ratio inspirals

The exact properties of dark matter remain largely unknown despite the accumulating evidence. If dark matter is composed of weakly interacting massive particles, it would be accreted by the black hole in the galactic center and form a dense, cuspy spike. Dynamical friction from this spike may have observable effects in a binary system. We consider extreme-mass-ratio inspiral (EMRI) binaries comprising massive black holes harbored in dark matter spikes and stellar mass objects in elliptic orbits. We find that the gravitational-wave waveforms in the frequency domain can be substantially modified. In particular, we show that dark matter can suppress the characteristic strain of a gravitational wave at low frequency but enhance it at a higher domain. These effects are more dramatic as the dark matter density increases. The results indicate that the signal-to-noise ratio of EMRIs can be strongly reduced near 10−3−0.3 Hz but enhanced near 1.0 Hz with a higher sensitivity, which can be probed via the future space-borne gravitational-wave (GW) detectors, LISA and TAIJI. The findings will have important impacts on the detection and parameter inference of EMRIs.

Assessing the model waveform accuracy of gravitational waves

With the improvement in sensitivity of gravitational wave (GW) detectors and the increasing diversity of GW sources, there is a strong need for accurate GW waveform models for data analysis. While the current model accuracy assessments require waveforms generated by numerical relativity (NR) simulations as the ``true waveforms,'' in this paper we propose an assessment approach that does not require NR simulations, which enables us to assess model accuracy everywhere in the parameter space. By measuring the difference between two waveform models, we derive a necessary condition for a pair of waveform models to both be accurate, for a particular set of parameters. We then apply this method to the parameter estimation samples of the Gravitational-Wave Transient Catalogs GWTC-3 and GWTC-2.1, and find that the waveform accuracy for high signal-to-noise ratio events in some cases fails our assessment criterion. Based on analysis of real events' posterior samples, we discuss the correlation between our quantified accuracy assessments and systematic errors in parameter estimation. We find that waveform models that perform worse in our assessment are more likely to give inconsistent estimations. We also investigate waveform accuracy in different parameter regions, and find that the accuracy degrades as the spin effects go up, the mass ratio deviates from one, or the orbital plane is nearly aligned with the line of sight. Furthermore, we make predictions of waveform accuracy requirements for future detectors and find that the accuracy of current waveform models should be improved by at least 3 orders of magnitude, which is consistent with previous works.

Gravitational Wave Signatures of Black Hole Quasinormal Mode Instability.

Black hole (BH) spectroscopy has emerged as a powerful approach to extracting spacetime information from gravitational wave (GW) observed signals. Yet, quasinormal mode (QNM) spectral instability under small scale perturbations has been recently shown to be a common classical general relativistic phenomenon [J. L. Jaramillo et al., Phys. Rev. X 11, 031003 (2021)PRXHAE2160-330810.1103/PhysRevX.11.031003]. This requires assessing its impact on the BH QNM spectrum, in particular on BH QNM overtone frequencies. We conclude (i)perturbed BH QNM overtones are indeed potentially observable in the GW waveform, providing information on small-scale environment BH physics, and (ii)their detection poses a challenging data analysis problem of singular interest for LISA astrophysics. We adopt a twofold approach, combining theoretical results from scattering theory with a fine-tuned data analysis on a highly accurate numerical GW ringdown signal. The former introduces a set of effective parameters (partially relying on a BH Weyl law) to characterize QNM instability physics. The latter provides a proof of principle demonstrating that the QNM spectral instability is indeed accessible in the time-domain GW waveform, though certainly requiring large signal-to-noise ratios. Particular attention is devoted to discussing the patterns of isospectrality loss under QNM instability, since the disentanglement between axial and polar GW parities may already occur within the near-future detection range.

Field excitation in fuzzy dark matter near a strong gravitational wave source

The axion-like particles with ultralight mass ($\sim10^{-22}$eV) can be a possible candidate of dark matter, known as the fuzzy dark matter (FDM). These particles form Bose-Einstein condensate in the early Universe which can explain the dark matter density distribution in galaxies at the present time. We study the time evolution of ultralight axion-like field in the near region of a strong gravitational wave (GW) source, such as binary black hole merger. We show that GWs can lead to the generation of field excitations in a spherical shell about the source that eventually propagate out of the shell to minimize the energy density of the field configuration. These excitations are generated toward the end of the merger and in some cases even in the ringdown phase of the merger, therefore it can provide a qualitatively distinct prediction for changes in the GW waveform due to the presence of FDM. This would be helpful in investigating the existence of FDM in galaxies.

Detecting gravitational lensing in hierarchical triples in galactic nuclei with space-borne gravitational-wave observatories

Stellar-mass binary black holes (BBHs) may merge in the vicinity of a supermassive black hole (SMBH). It is suggested that the gravitational-wave (GW) emitted by a BBH has a high probability to be lensed by the SMBH if the BBH's orbit around the SMBH (i.e., the outer orbit) has a period of less than a year and is less than the duration of observation of the BBH by a space-borne GW observatory. For such a BBH + SMBH triple system, the de Sitter precession of the BBH's orbital plane is also significant. In this work, we thus study GW waveforms emitted by the BBH and then modulated by the SMBH due to effects including Doppler shift, de Sitter precession, and gravitational lensing. We show specifically that for an outer orbital period of 0.1 yr and an SMBH mass of $10^7 M_\odot$, there is a 3\%-10\% chance for the standard, strong lensing signatures to be detectable by space-borne GW detectors such as LISA and/or TianGO. For more massive lenses ($\gtrsim 10^8 M_\odot$) and more compact outer orbits with periods <0.1 yr, retro-lensing of the SMBH might also have a 1%-level chance of detection. Furthermore, by combining the lensing effects and the dynamics of the outer orbit, we find the mass of the central SMBH can be accurately determined with a fraction error of $\sim 10^{-4}$. This is much better than the case of static lensing because the degeneracy between the lens' mass and the source's angular position is lifted by the outer orbital motion. Including lensing effects also allows the de Sitter precession to be detectable at a precession period 3 times longer than the case without lensing. Lastly, we demonstrate that one can check the consistency between the SMBH's mass determined from the orbital dynamics and the one inferred from gravitational lensing, which serves as a test on theories behind both phenomena. The statistical error on the deviation can be constrained to a 1% level.

Tidal heating of black holes and exotic compact objects on the brane

During the early phase of in-spiral of a binary system, the tidal heating of a compact object due to its companion plays a significant role in the determination of the orbital evolution of the binary. The phenomenon depends crucially on the `hairs', as well as on the nature of the compact object. It turns out that the presence of extra dimension affects both these properties, by incorporating an extra tidal charge for braneworld black holes and also by introducing quantum effects, leading to possible existence of exotic compact objects. It turns out that the phasing information from tidal heating in the gravitational wave waveform can constrain the tidal charge inherited from extra dimension to a value $\sim 10^{-6}$, the most stringent constraint, to date. Moreover, second order effects in tidal heating for exotic compact objects, also reveals an oscillatory behaviour with respect to spin, which has unique signatures.

Anisotropic neutrinos and gravitational waves from black hole neutrino-dominated accretion flows in fallback core-collapse supernovae

ABSTRACT Fallback in core-collapse supernovae (CCSNe) plays an important role in determining the properties of the central compact remnants, which might produce a black hole (BH) hyperaccretion system in the centre of a massive CCSN. When the accretion rate is extremely high and neutrino cooling is dominant, the hyperaccretion should be in the phase of the neutrino-dominated accretion flows (NDAFs), and thus a large number of anisotropic MeV neutrinos will be launched from the disc along with the strong gravitational waves (GWs). In this paper, we perform a series of one-dimensional CCSN simulations with the initial explosion energy in the range of 2−8 B (1 B = 1051 erg) to investigate the fallback processes. By considering the evolution of the central BH mass and spin in the fallback accretion, we present the effects of the initial explosion energies, masses, and metallicities of the massive progenitor stars on the spectra of anisotropic MeV neutrinos and the waveform of GWs from NDAFs. These neutrino or GW signals might be detected by operational or future detectors, and the multimessenger joint detections could constrain the properties of CCSNe and progenitor stars.

Anomaly detection in gravitational waves data using convolutional autoencoders

As of this moment, 50 gravitational wave (GW) detections have been announced, thanks to the observational efforts of the LIGO-Virgo collaboration, working with the Advanced LIGO and the Advanced Virgo interferometers. The detection of signals is complicated by the noise-dominated nature of the data. Conventional approaches in GW detection procedures require either precise knowledge of the GW waveform in the context of matched filtering searches or coincident analysis of data from multiple detectors. Furthermore, the analysis is prone to contamination by instrumental or environmental artifacts called glitches which either mimic astrophysical signals or reduce the overall quality of data. In this paper, we propose an alternative generic method of studying GW data based on detecting anomalies. The anomalies we study are transient signals, different from the slow non-stationary noise of the detector. The anomalies presented in the manuscript are mostly based on the GW emitted by the mergers of binary black hole systems. However, the presented study of anomalies is not limited only to GW alone, but also includes glitches occurring in the real LIGO/Virgo dataset available at the Gravitational Waves Open Science Center. To search for anomalies we employ deep learning algorithms, namely convolutional autoencoders, which are trained on both simulated and real detector data. We demonstrate the capabilities of our deep learning implementation in the reconstruction of injected signals. We study the influence of the GW strength, defined in terms of matched filter signal-to-noise ratio, on the detection of anomalies. Moreover, we present the application of our method for the localization in time of anomalies in the studied time-series data. We validate the results of anomaly searches on real data containing confirmed gravitational wave detections; we thus prove the generalization capabilities of our method, towards detecting GWs unknown to our deep learning models during training.