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1. Computational techniques for parameter estimation of gravitational wave signals

   https://doi.org/10.1002/wics.1532  

   Meyer, Renate ; Edwards, Matthew C. ; Maturana‐Russel, Patricio ; Christensen, Nelson ( September 2020 , WIREs Computational Statistics)

   Since the very first detection of gravitational waves from the coalescence of two black holes in 2015, Bayesian statistical methods have been routinely applied by LIGO and Virgo to extract the signal out of noisy interferometric measurements, obtain point estimates of the physical parameters responsible for producing the signal, and rigorously quantify their uncertainties. Different computational techniques have been devised depending on the source of the gravitational radiation and the gravitational waveform model used. Prominent sources of gravitational waves are binary black hole or neutron star mergers, the only objects that have been observed by detectors to date. But also gravitational waves from core‐collapse supernovae, rapidly rotating neutron stars, and the stochastic gravitational‐wave background are in the sensitivity band of the ground‐based interferometers and expected to be observable in future observation runs. As nonlinearities of the complex waveforms and the high‐dimensional parameter spaces preclude analytic evaluation of the posterior distribution, posterior inference for all these sources relies on computer‐intensive simulation techniques such as Markov chain Monte Carlo methods. A review of state‐of‐the‐art Bayesian statistical parameter estimation methods will be given for researchers in this cross‐disciplinary area of gravitational wave data analysis.

   This article is categorized under:

   Applications of Computational Statistics > Signal and Image Processing and Coding

   Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)

   Statistical Models > Time Series Models

    

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2. Statistically-informed deep learning for gravitational wave parameter estimation

   https://doi.org/10.1088/2632-2153/ac3843  

   Shen, Hongyu ; Huerta, E A ; O’Shea, Eamonn ; Kumar, Prayush ; Zhao, Zhizhen ( November 2021 , Machine Learning: Science and Technology)

   Abstract We introduce deep learning models to estimate the masses of the binary components of black hole mergers, ( m 1 , m 2 ) , and three astrophysical properties of the post-merger compact remnant, namely, the final spin, a f , and the frequency and damping time of the ringdown oscillations of the fundamental ℓ = m = 2 bar mode, ( ω R , ω I ) . Our neural networks combine a modified WaveNet architecture with contrastive learning and normalizing flow. We validate these models against a Gaussian conjugate prior family whose posterior distribution is described by a closed analytical expression. Upon confirming that our models produce statistically consistent results, we used them to estimate the astrophysical parameters ( m 1 , m 2 , a f , ω R , ω I ) of five binary black holes: GW150914 , GW170104 , GW170814 , GW190521 and GW190630 . We use PyCBC Inference to directly compare traditional Bayesian methodologies for parameter estimation with our deep learning based posterior distributions. Our results show that our neural network models predict posterior distributions that encode physical correlations, and that our data-driven median results and 90% confidence intervals are similar to those produced with gravitational wave Bayesian analyses. This methodology requires a single V100 NVIDIA GPU to produce median values and posterior distributions within two milliseconds for each event. This neural network, and a tutorial for its use, are available at the Data and Learning Hub for Science . 

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3. Joint analysis of gravitational-wave and electromagnetic data of mergers: breaking an afterglow model degeneracy in GW170817 and in future events

   https://doi.org/10.1093/mnras/stad1728  

   Gianfagna, Giulia ; Piro, Luigi ; Pannarale, Francesco ; Van Eerten, Hendrik ; Ricci, Fulvio ; Ryan, Geoffrey ; Troja, Eleonora ( June 2023 , Monthly Notices of the Royal Astronomical Society)

   On 2017 August 17, Advanced LIGO and Virgo observed GW170817, the first gravitational-wave (GW) signal from a binary neutron star merger. It was followed by a short-duration gamma-ray burst, GRB 170817A, and by a non-thermal afterglow emission. In this work, a combined simultaneous fit of the electromagnetic (EM, specifically, afterglow) and GW domains is implemented, both using the posterior distribution of a GW standalone analysis as prior distribution to separately process the EM data, and fitting the EM and GW domains simultaneously. These approaches coincide mathematically, as long as the actual posterior of the GW analysis, and not an approximation, is used as prior for the EM analysis. We treat the viewing angle, θv, as shared parameter across the two domains. In the afterglow modelling with a Gaussian structured jet this parameter and the jet core angle, θc, are correlated, leading to high uncertainties on their values. The joint EM + GW analysis relaxes this degeneracy, reducing the uncertainty compared to an EM-only fit. We also apply our methodology to hypothetical GW170817-like events occurring in the next GW observing run at ∼140 and 70 Mpc. At 70 Mpc the existing EM degeneracy is broken, thanks to the inclusion of the GW domain in the analysis. At 140 Mpc, the EM-only fit cannot constrain θv nor θc because of the lack of detections in the afterglow rising phase. Folding the GW data into the analysis leads to tighter constraints on θv, still leaving θc unconstrained, requiring instruments with higher sensitivities, such as Athena.

    

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4. The impact of the crust equation of state on the analysis of GW170817

   https://doi.org/10.1088/1361-6382/ab5ba4  

   Gamba, R. ; Read, J. S. ; Wade, L. E. ( December 2019 , Classical and Quantum Gravity)

   The detection of GW170817, the first neutron star-neutron star merger observed by Advanced LIGO and Virgo, and its following analyses represent the first contributions of gravitational wave data to understanding dense matter. Parameterizing the high density section of the equation of state of both neutron stars through spectral decomposition, and imposing a lower limit on the maximum mass value, led to an estimate of the stars’ radii ofkm andkm (Abbottet al2018Phys. Rev. Lett.121161101). These values do not, however, take into account any uncertainty owed to the choice of the crust low-density equation of state, which was fixed to reproduce the SLy equation of state model (Douchin and Haensel 2001Astron. Astrophys.380151). We here re-analyze GW170817 data and establish that different crust models do not strongly impact the mass or tidal deformability of a neutron star—it is impossible to distinguish between low-density models with gravitational wave analysis. However, the crust does have an effect on inferred radius. We predict the systematic error due to this effect using neutron star structure equations, and compare the prediction to results from full parameter estimation runs. For GW170817, this systematic error affects the radius estimate by 0.3 km, approximatelyof the neutron stars’ radii.

    

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5. Population synthesis and parameter estimation of neutron stars with continuous gravitational waves and third-generation detectors

   https://doi.org/10.1093/mnras/stad3811  

   Hua, Yuhan ; Wette, Karl ; Scott, Susan M. ; Pitkin, Matthew D. ( December 2023 , Monthly Notices of the Royal Astronomical Society)

   Precise measurement of stellar properties through the observation of continuous gravitational waves from spinning non-axisymmetric neutron stars can shed light onto new physics beyond terrestrial laboratories. Although hitherto undetected, prospects for detecting continuous gravitational waves improve with longer observation periods and more sensitive gravitational wave detectors. We study the capability of the Advanced Laser Interferometer Gravitational-Wave Observatory, and the Einstein Telescope to measure the physical properties of neutron stars through continuous gravitational wave observations. We simulate a population of Galactic neutron stars, assume continuous gravitational waves from the stars have been detected, and perform parameter estimation of the detected signals. Using the estimated parameters, we infer the stars’ moments of inertia, ellipticities, and the components of the magnetic dipole moment perpendicular to the rotation axis. The estimation of the braking index proved challenging and is responsible for the majority of the uncertainties in the inferred parameters. Using the Einstein Telescope with an observation period of $5\, {\rm {yr}}$, point estimates using median can be made on the moments of inertia with error of $\sim 10\!-\!100~{{\ \rm per\ cent}}$ and on the ellipticities with error of $\sim 5\!-\!50~{{\ \rm per\ cent}}$, subject to the inference of the braking index. The perpendicular magnetic dipole moment could not be accurately inferred for neutron stars that emit mainly gravitational waves.

    

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