Gravitational-wave Parameter Estimation Research Articles

Probabilistic model for the gravitational wave signal from merging black holes

Parametrized models that predict the gravitational-wave (GW) signal from merging black holes are used to extract source properties from GW observations. The majority of research in this area has focused on developing methods capable of producing highly accurate, point estimate, predictions for the GW signal. A key element missing from every model used in the analysis of GW data is an estimate for how confident the model is in its prediction. This omission increases the risk of biased parameter estimation of source properties. Current strategies include running analyses with multiple models to measure systematic bias however, this fails to accurately reflect the true uncertainty in the models. In this work we develop a probabilistic extension to the phenomenological modeling workflow for nonspinning black holes and demonstrate that the model not only produces accurate point estimates for the GW signal but can be used to provide well-calibrated local estimates for its uncertainty. Our analysis highlights that there is a lack of numerical relativity (NR) simulations available at multiple resolutions which can be used to estimate their numerical error and implore the NR community to continue to improve their estimates for the error in NR solutions published. Waveform models that are not only accurate in their point-estimate predictions but also in their error estimates are a potential way to mitigate bias in GW parameter estimation of compact binaries due to unconfident waveform model extrapolations. Published by the American Physical Society 2024

Deep learning for parameter estimation of supermassive binary black holes with simulated LISA data

Previous studies have demonstrated that deep learning is an effective approach for processing gravitational wave (GW) data obtained from ground-based detectors, as it can enhance the efficiency of data processing and offer great potential for real-time parameter estimation. In this paper, we explore three different deep learning architectures (MCD, TFP, and VI) for inferring the chirp mass (Mc) and the luminosity distance (DL) of supermassive binary black holes (SMBBHs) using simulated data from the Laser Interferometer Space Antenna (LISA). We train the neural networks with the simulated data and evaluate their performance on predicting the parameters (Mc,DL). The results show that more than 97.5% of the true values fall within the 3σ confidence interval of the predicted values with the optimal network. To verify the accuracy of the network on parameter estimation, we also calculate the estimation error of the parameters using the Fisher Information Matrix (FIM) with the same simulated data. By comparing the root-mean-square error (RMSE) between deep learning and FIM, we find that the two methods are comparable, which implies that deep learning can be reliable for GW parameter estimation.

Adapting to noise distribution shifts in flow-based gravitational-wave inference

Deep learning techniques for gravitational-wave parameter estimation have emerged as a fast alternative to standard samplers---producing results of comparable accuracy. These approaches (e.g., DINGO) enable amortized inference by training a normalizing flow to represent the Bayesian posterior conditional on observed data. By conditioning also on the noise power spectral density (PSD) they can even account for changing detector characteristics. However, training such networks requires knowing in advance the distribution of PSDs expected to be observed and therefore can only take place once all data to be analyzed have been gathered. Here, we develop a probabilistic model to forecast future PSDs, greatly increasing the temporal scope of trained deep learning models. Using PSDs from the second LIGO-Virgo observing run (O2)---plus just a single PSD from the beginning of the third (O3)---we show that we can train a DINGO network to perform accurate inference throughout O3 (on 37 real events). We therefore expect this approach to be a key component to enable the use of deep learning techniques for low-latency analyses of gravitational waves.

Parameter estimation of eccentric gravitational waves with a decihertz observatory and its cosmological implications

Eccentricity of compact binaries can improve the parameter estimation of gravitational waves (GWs), which is due to the fact that the multiple harmonics induced by eccentricity can provide more information and break the degeneracy between waveform parameters. In this paper, we first investigate the parameter estimation of eccentric GWs with decihertz observatory. We consider two scenarios for the configuration of DECIGO, i.e., the one cluster of DECIGO with its design sensitivity and B-DECIGO which also has one cluster but with inferior sensitivity as a comparison. We adopt the Fisher matrix to estimate the parameter errors. By mocking up the typical binaries in GWTC-3, we find a nonvanishing eccentricity can significantly improve the estimation for almost all waveform parameters. In particular, the localization of typical binary black holes (BBH) can achieve $\mathcal{O}(10--{10}^{3.5})$ factors of improvement when the initial eccentricity ${e}_{0}=0.4$ at 0.1 Hz. The precise localization of binary neutron stars (BNS) and neutron star--black hole binaries (NSBH), together with the large improvement of localization of BBH from eccentricity in the midband, inspire us to construct the catalogs of golden dark sirens whose host galaxies can be uniquely identified. We find that with only one cluster of DECIGO running 1 year in its design sensitivity, hundreds of golden dark BNS, NSBH, and tens of golden dark BBH can be observed. Eccentricity can greatly increase the population of golden dark BBH from $\ensuremath{\sim}7({e}_{0}=0)$ to $\ensuremath{\sim}65({e}_{0}=0.2)$. Such an increase of population of golden dark BBH events can improve the precision of Hubble constant measurement from 2.06% to 0.68%, matter density parameter from 64% to 16% in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Through the phenomenological parametrization of GW propagation, the constraints of modified gravity can be improved from 6.2% to 1.6%. Our results show the remarkable significance of eccentricity for the detection and parameter estimation of GW events, allowing us to probe the Universe precisely.

Breaking bad degeneracies with Love relations: Improving gravitational-wave measurements through universal relations

The distance-inclination degeneracy limits gravitational-wave parameter estimation of compact binary mergers. Although the degeneracy can be partially broken by including higher-order modes or precession, these effects are suppressed in binary neutron stars. In this work, we implement a new parametrization of the tidal effects in the binary neutron-star waveform, exploiting the binary Love relations, that breaks the distance-inclination degeneracy. The binary Love relations prescribe the tidal deformability of a neutron star as a function of its source-frame mass in an equation-of-state insensitive way and, thus, allows direct measurement of the redshift of the source. If the cosmological parameters are assumed to be known, the redshift can be converted to a luminosity distance, and the distance-inclination degeneracy can thus be broken. We implement this new approach, studying a range of binary neutron-star observing scenarios using Bayesian parameter estimation on synthetic data. In the era of the third-generation detectors, for observations with signal-to-noise ratios ranging from 6 to 167, we forecast up to an $\ensuremath{\sim}70%$ decrease in the 90% credible interval of the distance and inclination and up to an $\ensuremath{\sim}50%$ decrease in that of the source-frame component masses. For edge-on systems, our approach can result in moderate ($\ensuremath{\sim}50%$) improvement in the measurements of distance and inclination for binaries with a signal-to-noise ratio as low as 10. This prescription can be used to better infer the source-frame masses and, hence, refine population properties of neutron stars, such as their maximum mass, impacting nuclear astrophysics. When combined with the search for electromagnetic counterpart observations, the work presented here can be used to put improved bounds on the opening angle of jets from binary neutron-star mergers.

Concurrent estimation of noise and compact-binary signal parameters in gravitational-wave data

Gravitational-wave parameter estimation for compact binary signals typically relies on sequential estimation of the properties of the detector Gaussian noise and of the binary parameters. This procedure assumes that the noise variance, expressed through its power spectral density, is perfectly known in advance. We assess the impact of this approximation on the estimated parameters by means of an analysis that simultaneously estimates the noise and compact binary parameters, thus allowing us to marginalize over uncertainty in the noise properties. We compare the traditional sequential estimation method and the new full marginalization method using events from the GWTC-3 catalog. We find that the recovered signals and inferred parameters agree to within their statistical measurement uncertainty. At current detector sensitivities, uncertainty about the noise power spectral density is a subdominant effect compared to other sources of uncertainty.

Eccentricity of Long Inspiraling Compact Binaries Sheds Light on Dark Sirens

The localization and distance inference of gravitational waves are two crucial factors for dark sirens as precise probes of cosmology, astrophysics, and fundamental physics. In this Letter, for the first time we investigate the parameter estimation of gravitational waves emitted by the eccentric compact binaries in the midfrequency (0.1-10Hz) band. Based on the configuration of one cluster of DECIGO (B-DECIGO), we simulate five types of typical compact binaries in GWTC-3 with component mass ranging from O(1∼100) M_{⊙}. For each type of binaries, we assign discrete eccentricities from 0 to 0.4 at 0.1Hz in 10^{3} random orientations. The multiple harmonics induced by eccentricity can break the degeneracy between parameters. We find that with eccentricity e_{0}=0.4, these typical binaries can achieve O(10^{2}-10^{4}) improvement for the distance inference in the near face-on orientations, compared to the circular case. More importantly, a nonvanishing eccentricity (0.01-0.4) can significantly improve the source localization of the typical binary black holes, most by 1.5-3.5 orders of magnitude. Our result shows the remarkable significance of eccentricity for dark sirens in the midband as precise probes of the Universe.

Systematic bias due to eccentricity in parameter estimation for merging binary neutron stars

We study the impact of eccentricity on gravitational-wave parameter estimation for binary neutron star systems. For signals with small eccentricity injected into the advanced LIGO sensitivity, we perform Bayesian parameter estimation using the circular waveform model and show how the recovered parameters can be biased from their true values, focusing on the intrinsic parameters the chirp mass ($M_c$), the symmetric mass ratio ($\eta$), and the tidal deformability ($\tilde{\lambda}$). By comparing the results between the Bayesian and the analytic Fisher-Cutler-Vallisneri (FCV) methods, we obtain the valid criteria for the FCV approach. Employing the FCV method and using the realistic population of binary neutron star sources distributed in the $m_1$-$m_2$-$e_0$ space, where $e_0$ indicates the eccentricity at 10Hz, we calculate the measurement errors ($\sigma_{\theta}$) and the systematic biases ($\Delta \theta/\sigma_{\theta}$) and obtain their generalized distributions in the range of $0 \leq e_0 \leq 0.025$. We find that for all of the three parameters, the biases increase with increasing $e_0$, and this increase is faster for larger $e_0$. The bias is mainly dependent on the value of $e_0$ and weakly dependent on the component masses, and thus the distribution shows a narrow band in the $e_0$-$\Delta \theta/\sigma_{\theta}$ plane. We present various posterior examples to illustrate our new findings, such as the bimodality of posteriors. In particular, we give a specific injection-recovery example to demonstrate the importance of including eccentricity in parameter estimation to avoid incorrect predictions of the neutron star equation of state.

Parameter estimation with gravitational waves

The new era of gravitational wave astronomy truly began on September 14, 2015 with the detection of GW150914, the sensational first direct observation of gravitational waves from the inspiral and merger of two black holes by the two Advanced LIGO detectors. In the subsequent first three observing runs of the LIGO/Virgo network, gravitational waves from $\sim 50$ compact binary mergers have been announced, with more results to come. The events have mostly been produced by binary black holes, but two binary neutron star mergers have so far been observed, as well as the mergers of two neutron star - black hole systems. Furthermore, gravitational waves emitted by core-collapse supernovae, pulsars and the stochastic gravitational wave background are within the LIGO/Virgo/KAGRA sensitivity band and are likely to be observed in future observation runs. Beyond signal detection, a major challenge has been the development of statistical and computational methodology for estimating the physical waveform parameters and quantifying their uncertainties in order to accurately characterise the emitting system. These methods depend on the sources of the gravitational waves and the gravitational waveform model that is used. This article reviews the main waveform models and parameter estimation methods used to extract physical parameters from gravitational wave signals detected to date by LIGO and Virgo and from those expected to be observed in the future, which will include KAGRA, and how these methods interface with various aspects of LIGO/Virgo/KAGRA science. Also presented are the statistical methods used by LIGO and Virgo to estimate detector noise, test general relativity, and draw conclusions about the rates of compact binary mergers in the universe. Furthermore, a summary of major publicly available gravitational wave parameter estimation software packages is given.

Real-Time Gravitational Wave Science with Neural Posterior Estimation.

We demonstrate unprecedented accuracy for rapid gravitational wave parameter estimation with deep learning. Using neural networks as surrogates for Bayesian posterior distributions, we analyze eight gravitational wave events from the first LIGO-Virgo Gravitational-Wave Transient Catalog and find very close quantitative agreement with standard inference codes, but with inference times reduced from O(day) to 20s per event. Our networks are trained using simulated data, including an estimate of the detector noise characteristics near the event. This encodes the signal and noise models within millions of neural-network parameters and enables inference for any observed data consistent with the training distribution, accounting for noise nonstationarity from event to event. Our algorithm-called "DINGO"-sets a new standard in fast and accurate inference of physical parameters of detected gravitational wave events, which should enable real-time data analysis without sacrificing accuracy.

On the importance of source population models for gravitational-wave cosmology

Knowledge of the shape of the mass spectrum of compact objects can be used to help break the degeneracy between the mass and redshift of the gravitational wave (GW) sources, and thus can be used to infer cosmological parameters in the absence of redshift measurements obtained from electromagnetic observations. In this paper, we study extensively different aspects of this approach, including its computational limits and achievable accuracy. We focus on ground-based detectors with current and future sensitivities, we first perform the analysis of an extensive set of simulated data with a hierarchical Bayesian scheme inferring population and cosmological parameters. We consider a population model (power-law plus Gaussian) which exhibits characteristic scales (extremes of the mass spectrum, presence of an accumulation point) that allows an indirect estimate of the source redshift. Our analysis of this catalog highlights and quantifies the tight interplay between source population and cosmological parameters, as well as the influence of initial assumptions (whether formulated on the source or cosmological parameters). We then validate our results by an "end-to-end" analysis using simulated GW data and posterior samples generated from Bayesian samplers used for GW parameter estimation, thus mirroring the analysis chain used for observational data for the first time in literature. Our results then lead us to re-examine the estimation of $H_0$ obtained with GWTC-1, and we show explicitly how population assumptions impact the final $H_0$ result. Our results underline the importance of inferring population and cosmological parameters jointly (and not separately as is often assumed). The only exception, as we discuss, is if an electromagnetic counterpart was to be observed for all the BBH events: then the population assumptions have less impact on the estimation of cosmological parameters.

Python-based reduced order quadrature building code for fast gravitational wave inference

The next generation of gravitational wave observatories will reach low frequency limits on the orders of a few Hz, thus enabling the detection of gravitational wave signals of very long duration. The run time of standard parameter estimation techniques with these long waveforms can be months or even years, making it impractical with existing Bayesian inference pipelines. Reduced order modeling and the reduced order quadrature integration rule have recently been exploited as promising techniques that can greatly reduce parameter estimation computational costs. We describe a Python-based reduced order quadrature building code, pyroq, which builds the reduced order quadrature data needed to accelerate parameter estimation of gravitational waves. We present the first bases for the imrphenomxphm waveform model of binary-black-hole coalescences, including subdominant harmonic modes and precessing spins effects.

Accelerating parameter estimation of gravitational waves from compact binary coalescence using adaptive frequency resolutions

Bayesian parameter estimation of gravitational waves from compact binary coalescence (CBC) typically requires the generation of millions of computationally expensive template waveforms. We propose a technique to reduce the cost of waveform generation by exploiting the chirping behavior of CBC signal. Our technique does not require waveforms at all frequencies in the frequency range used in the analysis, and does not suffer from the fixed cost due to the upsampling of waveforms. Our technique speeds up the parameter estimation of typical binary neutron star signal by a factor of $\mathcal{O}(10)$ for the low-frequency cutoff of 20 Hz, and $\mathcal{O}({10}^{2})$ for 5 Hz. It does not require any offline preparations or accurate estimates of source parameters provided by detection pipelines.

Detection and parameter estimation of gravitational waves from binary neutron-star mergers in real LIGO data using deep learning

One of the key challenges of real-time detection and parameter estimation of gravitational waves from compact binary mergers is the computational cost of conventional matched-filtering and Bayesian inference approaches. In particular, the application of these methods to the full signal parameter space available to the gravitational-wave detectors, and/or real-time parameter estimation is computationally prohibitive. On the other hand, rapid detection and inference are critical for prompt follow-up of the electromagnetic and astro-particle counterparts accompanying important transients, such as binary neutron-star and black-hole neutron-star mergers. Training deep neural networks to identify specific signals and learn a computationally efficient representation of the mapping between gravitational-wave signals and their parameters allows both detection and inference to be done quickly and reliably, with high sensitivity and accuracy. In this work we apply a deep-learning approach to rapidly identify and characterize transient gravitational-wave signals from binary neutron-star mergers in real LIGO data. We show for the first time that artificial neural networks can promptly detect and characterize binary neutron star gravitational-wave signals in real LIGO data, and distinguish them from noise and signals from coalescing black-hole binaries. We illustrate this key result by demonstrating that our deep-learning framework classifies correctly all gravitational-wave events from the Gravitational-Wave Transient Catalog, GWTC-1 [Abbott et al. (2019) [4]]. These results emphasize the importance of using realistic gravitational-wave detector data in machine learning approaches, and represent a step towards achieving real-time detection and inference of gravitational waves.

Multimessenger Parameter Estimation of GW170817: From Jet Structure to the Hubble Constant

Abstract The electromagnetic radiation that followed the neutron star merger event GW170817 revealed that gamma-ray burst afterglows from jets misaligned with our line of sight exhibit a light curve with slowly rising flux. The slope of the rising light curve depends sensitively on the angle of the observer with respect to the jet axis, which is likely to be perpendicular to the merger plane of the neutron star binary. Therefore, the afterglow emission can be used to constrain the inclination of the merging system. Here, we calculate the gamma-ray burst afterglow emission based on the realistic jet structure derived from general-relativistic magnetohydrodynamical simulations of a black hole torus system for the central engine of the gamma-ray burst. Combined with gravitational wave parameter estimation, we fit the multi-epoch afterglow emission of GW170817. We show that with such a jet model, the observing angle can be tightly constrained by multimessenger observations. The best fit observing angle of GW170817 is θ v = 0.38 ± 0.02 rad. With such a constraint, we can break the degeneracy between inclination angle and luminosity distance in gravitational wave parameter estimation, and substantially increase the precision with which the Hubble constant is constrained by the standard siren method. Our estimation of the distance is D L = 43.4 ± 1 Mpc and the Hubble constant constraint is 69.5 ± 4 km s−1 Mpc−1. As a result, multimessenger observations of short-duration gamma-ray bursts, combined with a good theoretical understanding of the jet structure, can be powerful probes of cosmological parameters.

Inferring physical properties of stellar collapse by third-generation gravitational-wave detectors

Galactic core-collapse supernovae are among the possible sources of gravitational waves. We investigate the ability of gravitational-wave observatories to extract the properties of the collapsing progenitor from the gravitational waves radiated. We use simulations of supernovae that explore a variety of progenitor core rotation rates and nuclear equations of state and examine the ability of current and future observatories to determine these properties using gravitational-wave parameter estimation. We use principal component analysis of the simulation catalog to determine the dominant features of the waveforms and create a map between the measured properties of the waveform and the physical properties of the progenitor. We use Bayesian parameter inference and the parameter map to calculate posterior probabilities for the physical properties given a gravitational-wave observation. We estimate the ratio of the progenitor's core rotational kinetic energy to potential energy ($\beta$) and the post bounce oscillation frequency. For a supernovae at the distance of the galactic center (8.1 kpc) with $\beta = 0.02$ our method can estimate $\beta$ with a $90\%$ credible interval of $0.004$ for Advanced LIGO, improving to $0.0008$ for Cosmic Explorer. We demonstrate that if the core is rotating sufficiently rapidly for a signal observed by Cosmic Explorer, our method can also extract the post bounce oscillation frequency of the protoneutron star to a precision of within $5$~Hz ($90\%$ credible interval) allowing us to constrain the nuclear equation of state. For a supernovae at the distance of the Magellanic Clouds (48.5 kpc) Cosmic Explorer's ability to measure these parameters decreases slightly to $0.003$ for rotation and $11$~Hz for the postbounce oscillation frequency ($90\%$ credible interval). Sources in Magellanic Clouds will be too distant for Advanced LIGO to measure these properties.

Gravitational-wave parameter estimation with autoregressive neural network flows

We introduce the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a sample space that can be used to induce a transformation from a simple probability distribution to a more complex one: if the simple distribution can be rapidly sampled and its density evaluated, then so can the complex distribution. Our first application to gravitational waves uses an autoregressive flow, conditioned on detector strain data, to map a multivariate standard normal distribution into the posterior distribution over system parameters. We train the model on artificial strain data consisting of IMRPhenomPv2 waveforms drawn from a five-parameter $(m_1, m_2, \phi_0, t_c, d_L)$ prior and stationary Gaussian noise realizations with a fixed power spectral density. This gives performance comparable to current best deep-learning approaches to gravitational-wave parameter estimation. We then build a more powerful latent variable model by incorporating autoregressive flows within the variational autoencoder framework. This model has performance comparable to Markov chain Monte Carlo and, in particular, successfully models the multimodal $\phi_0$ posterior. Finally, we train the autoregressive latent variable model on an expanded parameter space, including also aligned spins $(\chi_{1z}, \chi_{2z})$ and binary inclination $\theta_{JN}$, and show that all parameters and degeneracies are well-recovered. In all cases, sampling is extremely fast, requiring less than two seconds to draw $10^4$ posterior samples.

Rapid parameter estimation of gravitational waves from binary neutron star coalescence using focused reduced order quadrature

Rapid parameter estimation of gravitational waves from binary neutron star coalescence, in particular accurate sky localisation in minutes after the initial detection stage, is crucial for the success of multi-messenger observations. One of the techniques to speed up the parameter estimation, which has been applied for the production analysis of the LIGO-Virgo collaboration, is reduced order quadrature (ROQ). While it speeds up parameter estimation significantly, the time required is still on the order of hours. Focusing on the fact that the parameter-estimation follow-up can be tuned with the information available at the detection stage, we improve the ROQ technique and develop a new technique, which we designate focused reduced order quadrature (FROQ). We find that FROQ speeds up the parameter estimation by a factor of $\mathcal{O}(10^3)$ to $\mathcal{O}(10^4)$ and enables providing accurate source properties such as the location of a source in several tens of minutes after detection.

Setting the cornerstone for a family of models for gravitational waves from compact binaries: The dominant harmonic for nonprecessing quasicircular black holes

In this paper we present IMRPhenomXAS, a thorough overhaul of the IMRPhenomD [1,2] waveform model, which describes the dominant $l=2, \:| m | = 2$ spherical harmonic mode of non-precessing coalescing black holes in terms of piecewise closed form expressions in the frequency domain. Improvements include in particular the accurate treatment of unequal spin effects, and the inclusion of extreme mass ratio waveforms. IMRPhenomD has previously been extended to approximately include spin precession [3] and subdominant spherical harmonics [4], and with its extensions it has become a standard tool in gravitational wave parameter estimation. Improved extensions of IMRPhenomXAS are discussed in companion papers [5,6].

Counting on Short Gamma-Ray Bursts: Gravitational-wave Constraints of Jet Geometry

Abstract The detections of GW170817 and GRB 170817A revealed that at least some short gamma-ray bursts (sGRB) are associated with the merger of neutron-star compact binaries. The gamma-rays are thought to result from the formation of collimated jets, but the details of this process continue to elude us. One important feature of gamma-ray bursts is the emission profile of the jet as a function of viewing angle. We present two related methods to measure the effective angular width, , of sGRB jets using gravitational-wave (GW) and gamma-ray data, assuming all sGRBs have the same angular dependence for their luminosities. The first is a counting experiment that requires minimal knowledge about each event, beyond whether or not they were detected in gamma-rays. The second method uses GW and electromagnetic data to estimate parameters of the source. We additionally outline a model-independent method to infer the full jet structure of sGRBs using a nonparametric approach. Applying our methods to GW170817 and GW190425, we find weak constraints on the sGRB luminosity profile. We project that with 5 and 100 binary neutron star detections, the counting method would constrain the relative uncertainty in to within and , respectively. Incorporating GW parameter estimation provides only marginal improvements. We conclude that the majority of the information about jet structure comes from the relative sensitivities of GW and gamma-ray detectors as encoded in simple counting experiments.