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Learning orbital dynamics of binary black hole systems from gravitational wave measurements

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Physical Review research 2021年第4期3卷 043101-043101页

作者： Brendan Keith Akshay Khadse Scott E. Field Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA and Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA

We introduce a gravitational waveform inversion strategy that discovers mechanical models of binary black hole (BBH) systems. We show that only a single time series of (possibly noisy) waveform data is necessary to construct the equations of motion for a BBH system. Starting with a class of universal differential equations parameterized by feed-forward neural networks, our strategy involves the construction of a space of plausible mechanical models and a physics-informed constrained optimization within that space to minimize the waveform error. We apply our method to various BBH systems including extreme and comparable mass ratio systems in eccentric and noneccentric orbits. We show that the resulting differential equations apply to time durations longer than the training interval, and relativistic effects, such as perihelion precession, radiation reaction, and orbital plunge, are automatically accounted for. The methods outlined here provide a data-driven approach to studying the dynamics of binary black hole systems.

关键词： General relativity equations & solutions Gravitational waves

Gravitational-wave template banks for novel compact binaries

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arXiv 2023年

作者： Schmidt, Stefano Gadre, Bhooshan Caudill, Sarah Nikhef Science Park 105 Amsterdam1098 XG Netherlands Utrecht University Princetonplein 1 Utrecht3584 CC Netherlands Department of Physics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States

We introduce a novel method to generate a bank of gravitational-waveform templates of binary black hole (BBH) mergers for matched-filter searches in LIGO, Virgo and Kagra data. We derive a novel expression for the metric approximation to the distance between templates, which is suitable for precessing BBHs and/or systems with higher-order modes (HM) imprints and we use it to meaningfully define a template probability density across the parameter space. We employ a masked autoregressive normalizing flow model which can be conveniently trained to quickly reproduce the target probability distribution and sample templates from it. Thanks to the normalizing flow, our code takes a few hours to produce random template banks with millions of templates, making it particularly suitable for high-dimensional spaces, such as those associated to precession, eccentricity and/or HM. After validating the performance of our method, we generate a bank for precessing black holes and a bank for aligned-spin binaries with HMs: with only 5% of the injections with fitting factor below the target of 0.97, we show that both banks cover satisfactorily the space. Our publicly released code mbank will enable searches of high-dimensional regions of BBH signal space, hitherto unfeasible due to the prohibitive cost of bank generation. Copyright © 2023, The Authors. All rights reserved.

关键词： Matched filters

Interplay between numerical relativity and perturbation theory: Finite size effects

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Physical Review D 2023年第4期108卷 044012-044012页

作者： Tousif Islam Gaurav Khanna Department of Physics University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Physics and Center for Computational Research University of Rhode Island Kingston Rhode Island 02881 USA

We investigate the interplay between numerical relativity (NR) and point-particle black hole perturbation theory (ppBHPT) in the comparable mass ratio regime. In the ppBHPT framework, the secondary black hole is treated as a point particle, neglecting its finite size. Our study focuses on addressing the missing finite size effect in the ppBHPT framework and proposing a method for incorporating the size of the secondary into the perturbation theory framework. We demonstrate that by considering the secondary as a finite size object, the BHPT waveforms closely match NR waveforms. Additionally, we revisit the α−β scaling technique, which was previously introduced by Islam et al. [Phys. Rev. D 106, 104025 (2022)], as a means to effectively match ppBHPT waveforms to NR waveforms. We further analyze the scaling procedure and decompose it into different components, attributing them to various effects, including the corrections arising from the finite size of the secondary black hole.

关键词： General relativity Gravitational waves

Gravitational wave surrogate model for spinning, intermediate mass ratio binaries based on perturbation theory and numerical relativity

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arXiv 2024年

作者： Rink, Katie Bachhar, Ritesh Islam, Tousif Rifat, Nur E.M. González-Quesada, Kevin Field, Scott E. Khanna, Gaurav Hughes, Scott A. Varma, Vijay Department of Physics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Gravitational Physics University of Texas AustinTX78712 United States Department of Physics Center for Computational Research University of Rhode Island East Hall KingstonRI02881 United States Kavli Institute for Theoretical Physics University of California Santa Barbara Kohn Hall Lagoon Rd Santa BarbaraCA93106 United States Kavli Institute for Theoretical Physics University of California Santa BarbaraCA93106 United States Department of Physics University of Virginia 1827 University Avenue CharlottesvilleVA22903 United States Case Western Reserve University ClevelandOH44106 United States Department of Mathematics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics Massachusetts Institute of Technology CambridgeMA02139 United States

We present BHPTNRSur2dq1e3, a reduced order surrogate model of gravitational waves emitted from binary black hole (BBH) systems in the comparable to large mass ratio regime with aligned spin (χ1) on the heavier mass (m1). We trained this model on waveform data generated from point particle black hole perturbation theory (ppBHPT) with mass ratios varying from 3 ≤ q ≤ 1000 and spins from −0.8 ≤ χ1 ≤ 0.8. The waveforms are 13,500 m1 long and include all ≤ 4 spin-weighted spherical harmonic modes except the (4, 1) and m = 0 modes. We find that for binaries with χ1 −0.5, retrograde quasi-normal modes are significantly excited, thereby complicating the modeling process. To overcome this issue, we introduce a domain decomposition approach to model the inspiral and merger-ringdown portion of the signal separately. The resulting model can faithfully reproduce ppBHPT waveforms with a median time-domain mismatch error of 8 × 10−5. We then calibrate our model with numerical relativity (NR) data in the comparable mass regime (3 ≤ q ≤ 10). By comparing with spin-aligned BBH NR simulations at q = 15, we find that the dominant quadrupolar (subdominant) modes agree to better than ≈ 10−3 (≈ 10−2) when using a time-domain mismatch error, where the largest source of calibration error comes from the transition-to-plunge and ringdown approximations of perturbation theory. Mismatch errors are below ≈ 10−2 for systems with mass ratios between 6 ≤ q ≤ 15 and typically get smaller at larger mass ratio. Our two models – both the ppBHPT waveform model and the NR-calibrated ppBHPT model – will be publicly available through gwsurrogate and the Black Hole Perturbation Toolkit packages. © 2024, CC BY.

关键词： Perturbation techniques

Gravitational tuning forks and hierarchical triple systems

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Physical Review D 2021年第8期103卷 L081501-L081501页

作者： Vitor Cardoso Francisco Duque Gaurav Khanna Department of Physics and Center for Scientific Computing and Visualization Research University of Massachusetts Darthmouth Massachusetts 02747 USA and Department of Physics The University of Rhode Island Kingston Rhode Island 02881

We study gravitational wave (GW) emission in the strong-field regime by a hierarchical triple system composed of a binary system placed in the vicinity of a supermassive black hole (SMBH). The LIGO-Virgo Collaboration recently reported evidence for coalescences with this dynamical origin. These systems are common in galactic centers and thus, are a target for the space-based LISA mission as well as other advanced detectors. Doppler shifts, aberration, lensing, and strong amplitude modulations are features present in the GW signal from these systems, built into our framework and with no need for phenomenological patches. We find that the binary can resonantly excite the quasinormal modes of the SMBH, as in the resonant excitation of two tuning forks with matching frequencies. The flux of energy crossing the SMBH horizon can be significant, when compared with that from standard extreme-mass-ratio inspirals. Therefore, these triple systems are excellent probes of strong-field physics and of the BH nature of compact objects.

关键词： Astrophysical studies of gravity General relativity equations & solutions Gravitational waves Classical black holes Galactic nuclei & quasars

Optimizing post-Newtonian parameters and fixing the BMS frame for numerical-relativity waveform hybridizations

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Physical Review D 2024年第10期110卷 104076-104076页

作者： Dongze Sun Michael Boyle Keefe Mitman Mark A. Scheel Leo C. Stein Saul A. Teukolsky Vijay Varma Theoretical Astrophysics 350-17 California Institute of Technology 1200 E California Boulevard Pasadena California 91125 USA Cornell Center for Astrophysics and Planetary Science Cornell University Ithaca New York 14853 USA Department of Physics and Astronomy University of Mississippi University Mississippi 38677 USA Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA Max Planck Institute for Gravitational Physics (Albert Einstein Institute) D-14476 Potsdam Germany

Numerical relativity (NR) simulations of binary black holes provide precise waveforms, but are typically too computationally expensive to produce waveforms with enough orbits to cover the whole frequency band of gravitational-wave observatories. Accordingly, it is important to be able to hybridize NR waveforms with analytic, post-Newtonian (PN) waveforms, which are accurate during the early inspiral phase. We show that to build such hybrids, it is crucial to both fix the Bondi-Metzner-Sachs (BMS) frame of the NR waveforms to match that of PN theory, and optimize over the PN parameters to mitigate the error caused by the discrepancy between NR and PN parameters. We test such a hybridization procedure including all spin-weighted spherical harmonic modes with |m|≤ℓ for ℓ≤8, using 29 NR waveforms with mass ratios q≤10 and spin magnitudes |χ1|,|χ2|≤0.8. We find that for spin-aligned systems, the PN and NR waveforms agree very well. The difference is limited by the small nonzero orbital eccentricity of the NR waveforms, or equivalently by the lack of eccentric terms in the PN waveforms. To maintain full accuracy of the simulations, the matching window for spin-aligned systems should be at least 5 orbits long and end at least 15 orbits before merger. For precessing systems, the errors are larger than for spin-aligned cases. The errors are likely limited by the absence of precession-related spin-spin PN terms. Using 105M long NR waveforms, we find that there is no optimal choice of the matching window within this time span, because the hybridization result for precessing cases is always better if using earlier or longer matching windows. We provide the mean orbital frequency of the smallest acceptable matching window as a function of the target error between the PN and NR waveforms and the black hole spins.

关键词： General relativity Gravitation Gravitational waves Astronomical black holes Numerical relativity Numerical simulations in gravitation & astrophysics

White dwarf mass-radius relation in theories beyond general relativity

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arXiv 2023年

作者： Alam, Khursid Islam, Tousif Department of Physical Sciences Indian Institute of Science Education and Research Kolkata WB Mohanpur741 246 India Department of Physics University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States

We explore the internal structures of the white dwarfs in two different modified theories of gravity: (i) scalar-tensor-vector gravity and (ii) beyond Horndeski theories of G3 type. The modification of the gravitational force inside the white dwarf results in the modification of the mass and radius of the white dwarf. We use observational data from various astrophysical probes including Gaia to test the validity of these two classes of modified theories of gravity. We update the constraints on the parameters controlling the deviation from general relativity (and Newtonian gravity in the weak field limit) as: 0.007 ≤ α for the scalar-tensor-vector gravity and −0.08 ≤ γ ≤ 0.007 for the beyond Horndeski theories of G3 type. Finally, we demonstrate the selection effect of the astrophysical data on the tests of the nature of gravity using white dwarf mass-radius relations specially in cases where the number of data-points are not many. Copyright © 2023, The Authors. All rights reserved.

关键词： White dwarfs

Remnant black hole properties from numerical-relativity-informed perturbation theory and implications for waveform modelling

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arXiv 2023年

作者： Islam, Tousif Field, Scott E. Khanna, Gaurav Department of Physics University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics University of Rhode Island KingstonRI02881 United States

During binary black hole (BBH) mergers, energy and momenta are carried away from the binary system as gravitational radiation. Access to the radiated energy and momenta allows us to predict the properties of the remnant black hole. We develop a Python package gw_remnant to compute the remnant mass, remnant spin, peak luminosity, and the final kick imparted on the remnant black hole from the gravitational radiation. Using this package, we compute the remnant properties of the final black hole in case of non-spinning BBH mergers with mass ratios ranging from q = 2.5 to q = 1000 using waveform modes generated from BHPTNRSur1dq1e4, a recently developed numerical-relativity-informed surrogate model based on black-hole perturbation theory framework. We validate our results against the remnant properties estimated from numerical relativity (NR) surrogate models in the comparable mass ratio regime and against recently available high-mass-ratio NR simulations at q = [15, 32, 64]. We find that our remnant property estimates computed from fluxes at future null infinity closely match the estimates obtained from the NR surrogate model of apparent horizon data. Using Gaussian process regression fitting methods, we train a surrogate model, BHPTNR_Remnant, for the properties of the remnant black hole arising from BBH mergers with mass ratios from q = 2.5 to q = 1000. Finally, we discuss potential improvements in the BHPTNRSur1dq1e4 waveform model when including remnant information. We make both the gw_remnant and BHPTNR_Remnant packages publicly available. Copyright © 2023, The Authors. All rights reserved.

关键词： Black holes

Surrogate modeling of gravitational waves microlensed by spherically symmetric potentials

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arXiv 2025年

作者： Deka, Uddeepta Prabhu, Gopalkrishna Shaikh, Md Arif Kapadia, Shasvath J. Varma, Vijay Field, Scott E. International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore560089 India Inter-University Centre for Astronomy and Astrophysics Post Bag 4 Ganeshkhind Pune411007 India Department of Physics Vivekananda Satavarshiki Mahavidyalaya Vidyasagar University West Bengal Manikpara721513 India Department of Physics and Astronomy Seoul National University Seoul08826 Korea Republic of Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States

The anticipated observation of the gravitational microlensing of gravitational waves (GWs) promises to shed light on a host of astrophysical and cosmological questions. However, extracting the parameters of the lens from the modulated GWs requires accurate modeling of the lensing amplification factor, accounting for wave-optics effects. Analytic solutions to the lens equation have not been found to date, except for a handful of simplistic lens models. While numerical solutions to this equation have been developed, the time and computational resources required to evaluate the amplification factor numerically make large-scale parameter estimation of the lens (and source) parameters prohibitive. On the other hand, surrogate modeling of GWs has proven to be a powerful tool to accurately, and rapidly, produce GW templates at arbitrary points in parameter space, interpolating from a finite set of available waveforms at discrete parameter values. In this work, we demonstrate that surrogate modeling can also effectively be applied to the evaluation of the time-domain microlensing amplification factor eF(t), for arbitrary lens configurations. We show this by constructing eF(t) for two lens models, viz. point-mass lens, and singular isothermal sphere. We benchmark the evaluation times, and accuracy, of the surrogate microlensed templates, and show that indeed surrogate modeling is a powerful tool to make large-scale parameter estimation in the context of microlensed GWs practicable. © 2025, CC BY.

关键词： Time domain analysis