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Basis Function Method for Numerical Loop Quantum Cosmology: The Schwarzschild Black Hole Interior

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arXiv 2019年

作者： Yonika, Alec Khanna, Gaurav Department of Physics & Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth North DartmouthMA02747 United States

Loop quantum cosmology is a symmetry-reduced application of loop quantum gravity that has led to the resolution of classical singularities such as the big bang, and those at the center of black holes. This can be seen through numerical simulations involving the quantum Hamiltonian constraint that is a partial difference equation. The equation allows one to study the evolution of sharply-peaked Gaussian wave packets that generically exhibit a quantum "bounce" or a non-singular passage through the classical singularity, thus offering complete singularity resolution. In addition, von-Neumann stability analysis of the difference equation – treated as a stencil for a numerical solution that steps through the triad variables – yields useful constraints on the model and the allowed space of states. In this paper, we develop a new method for the numerical solution of loop quantum cosmology models using a set of basis functions that offer a number of advantages over computing a solution by stepping through the triad variables. We use the Corichi and Singh model for the Schwarzschild interior as the main case study in this effort. The main advantage of this new method is computational efficiency and the ease of parallelization. In addition, we also discuss how the stability analysis appears in the context of this new approach. Copyright © 2019, The Authors. All rights reserved.

关键词： Gravitation

A surrogate model for gravitational wave signals from comparable- to large-mass-ratio black hole binaries

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arXiv 2019年

作者： Rifat, Nur E.M. Field, Scott E. Khanna, Gaurav Varma, Vijay Department of Physics and Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Mathematics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Theoretical Astrophysics California Institute of Technology PasadenaCA91125 United States

Gravitational wave signals from compact astrophysical sources such as those observed by LIGO and Virgo require a high-accuracy, theory-based waveform model for the analysis of the recorded signal. Current inspiral-merger-ringdown models are calibrated only up to moderate mass ratios, thereby limiting their applicability to signals from high-mass ratio binary systems. We present EMRISur1dq1e4, a reduced-order surrogate model for gravitational waveforms of 13, 500M in duration and including several harmonic modes for non-spinning black hole binary systems with mass-ratios varying from 3 to 10, 000 thus vastly expanding the parameter range beyond the current models. This surrogate model is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) both for large mass-ratio and comparable mass-ratio binaries. We observe that the gravitational waveforms generated through a simple application of ppBHPT to the comparable mass-ratio cases agree remarkably (and surprisingly) well with those from full numerical relativity after a rescaling of the ppBHPT’s total mass parameter. This observation and the EMRISur1dq1e4 surrogate model will enable data analysis studies in the high-mass ratio regime, including potential intermediate mass-ratio signals from LIGO/Virgo and extreme-mass ratio events of interest to the future space-based observatory LISA. Copyright © 2019, The Authors. All rights reserved.

关键词： Stars

Removing degeneracy and multimodality in gravitational wave source parameters

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Physical Review D 2022年第12期106卷 123015-123015页

作者： Javier Roulet Seth Olsen Jonathan Mushkin Tousif Islam Tejaswi Venumadhav Barak Zackay Matias Zaldarriaga Kavli Institute for Theoretical Physics University of California at Santa Barbara Santa Barbara California 93106 USA Department of Physics Princeton University Princeton New Jersey 08540 USA Department of Particle Physics and Astrophysics Weizmann Institute of Science Rehovot 76100 Israel 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 University of California at Santa Barbara Santa Barbara California 93106 USA International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore 560089 India School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA

Quasicircular binary black hole mergers are described by 15 parameters, of which gravitational wave observations can typically constrain only ∼10 independent combinations to varying degree. In this work, we devise coordinates that remove correlations, and disentangle well- and poorly-measured quantities. Additionally, we identify approximate discrete symmetries in the posterior as the primary cause of multimodality, and design a method to tackle this type of multimodality. The resulting posteriors have little structure and can be sampled efficiently and robustly. We provide a python package for parameter estimation, cogwheel, that implements these methods together with other algorithms for accelerating the inference process. One of the coordinates we introduce is a spin azimuth that is measured remarkably well in several events. We suggest this might be a sensitive indicator of orbital precession, and we anticipate that it will shed light on the occurrence of spin-orbit misalignment in nature.

关键词： Gravitational waves Astronomical black holes

Factorized Parameter Estimation for Real-Time Gravitational Wave Inference

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arXiv 2022年

作者： Islam, Tousif Roulet, Javier Venumadhav, Tejaswi Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Department of Physics University of Massachusetts DartmouthMA02747 United States Kavli Institute for Theoretical Physics University of California at Santa Barbara Santa BarbaraCA93106 United States TAPIR Walter Burke Institute for Theoretical Physics California Institute of Technology PasadenaCA91125 United States Department of Physics University of California at Santa Barbara Santa BarbaraCA93106 United States International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore560089 India

We present a parameter estimation framework for gravitational wave (GW) signals that brings together several ideas to accelerate the inference process. First, we use the relative binning algorithm to evaluate the signal-to-noise-ratio timeseries in each detector for a given choice of intrinsic parameters. Second, we decouple the estimation of the intrinsic parameters (such as masses and spins of the components) from that of the extrinsic parameters (such as distance, orientation, and sky location) that describe a binary compact object coalescence. We achieve this by semi-analytically marginalizing the posterior distribution over extrinsic parameters without repeatedly evaluating the waveform for a fixed set of intrinsic parameters. Finally, we augment samples of intrinsic parameters with extrinsic parameters drawn from their appropriate conditional distributions. We implement the method for binaries with aligned spins, restricted to the quadrupole mode of the signal. Using simulated GW signals, we demonstrate that the method produces full eleven-dimensional posteriors that match those from standard Bayesian inference. Our framework takes only ∼ 200 s to analyze a typical binary-black-hole signal and ∼ 250 s to analyze a typical binary-neutron-star signal using one computing core. Such real-time and accurate estimation of the binary source properties will greatly aid the interpretation of triggers from gravitational wave searches, as well as the search for possible electromagnetic counterparts. We make the framework publicly available via the GW inference package cogwheel. Copyright © 2022, The Authors. All rights reserved.

关键词： Gravity waves

Surrogate modeling of gravitational waves microlensed by spherically symmetric potentials

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Physical Review D 2025年第10期111卷 104042-104042页

作者： Uddeepta Deka Gopalkrishna Prabhu Md Arif Shaikh Shasvath J. Kapadia Vijay Varma Scott E. Field International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore 560089 India Inter-University Centre for Astronomy and Astrophysics Post Bag 4 Ganeshkhind Pune 411007 India Department of Physics Vivekananda Satavarshiki Mahavidyalaya (affiliated to Vidyasagar University) Manikpara 721513 West Bengal India Department of Physics and Astronomy Seoul National University Seoul 08826 South Korea Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA

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 F˜(t). We show this by constructing F˜(t) for two lens models, viz. point-mass lens, and singular isothermal sphere, which notably includes logarithmic divergence behavior. We find both surrogates reproduce the original lens models accurately, with mismatches ≲5×10−4 across a range of plausible microlensed binary black hole sources observed by the Einstein Telescope. This surrogate is between 5 and 103 times faster than the underlying lensing models, and can be evaluated in about 100 ms. The accuracy and efficiency attained by our surrogate models will enable practical parameter estimation analyses of microlensed GWs.

关键词：

A comparison of rendering techniques for large 3D line sets with transparency

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arXiv 2019年

作者： Kern, Michael Neuhauser, Christoph Maack, Torben Han, Mengjiao Usher, Will Westermann, Rüdiger Computer Graphics & Visualization Group Technische Universität München Garching Germany Scientific Computing and Imaging Institute University of Utah United States

This paper presents a comprehensive study of interactive rendering techniques for large 3D line sets with transparency. The rendering of transparent lines is widely used for visualizing trajectories of tracer particles in flow fields. Transparency is then used to fade out lines deemed unimportant, based on, for instance, geometric properties or attributes defined along them. Since accurate blending of transparent lines requires rendering the lines in back-to-front or front-to-back order, enforcing this order for 3D line sets with tens or even hundreds of thousands of elements becomes challenging. In this paper, we study CPU and GPU rendering techniques for large transparent 3D line sets. We compare accurate and approximate techniques using optimized implementations and a number of benchmark data sets. We discuss the effects of data size and transparency on quality, performance and memory consumption. Based on our study, we propose two improvements to per-pixel fragment lists and multi-layer alpha blending. The first improves the rendering speed via an improved GPU sorting operation, and the second improves rendering quality via a transparency-based bucketing. Copyright © 2019, The Authors. All rights reserved.

关键词： Transparency

Surrogate model for gravitational wave signals from nonspinning, comparable-to large-mass-ratio black hole binaries built on black hole perturbation theory waveforms calibrated to numerical relativity

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Physical Review D 2022年第10期106卷 104025-104025页

作者： Tousif Islam Scott E. Field Scott A. Hughes Gaurav Khanna Vijay Varma Matthew Giesler Mark A. Scheel Lawrence E. Kidder Harald P. Pfeiffer 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 Kavli Institute of Theoretical Physics University of California Santa Barbara Santa Barbara California 93106 USA Department of Physics and MIT Kavli Institute Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Physics University of Rhode Island Kingston Rhode Island 02881 USA Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 Potsdam 14476 Germany Cornell Center for Astrophysics and Planetary Science Cornell University Ithaca New York 14853 USA Theoretical Astrophysics Walter Burke Institute for Theoretical Physics California Institute of Technology Pasadena California 91125 USA

We present a reduced-order surrogate model of gravitational waveforms from nonspinning binary black hole systems with comparable to large mass-ratio configurations. This surrogate model, BHPTNRSur1dq1e4, is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) with mass ratios varying from 2.5 to 10,000. BHPTNRSur1dq1e4 extends an earlier waveform model, EMRISur1dq1e4, by using an updated transition-to-plunge model, covering longer durations up to 30,500m1 (where m1 is the mass of the primary black hole), includes several more spherical harmonic modes up to ℓ=10, and calibrates subdominant modes to numerical relativity (NR) data. In the comparable mass-ratio regime, including mass ratios as low as 2.5, the gravitational waveforms generated through ppBHPT agree surprisingly well with those from NR after this simple calibration step. We also compare our model to recent SXS and RIT NR simulations at mass ratios ranging from 15 to 32, and find the dominant quadrupolar modes agree to better than ≈10−3. We expect our model to be useful to study intermediate-mass-ratio binary systems in current and future gravitational-wave detectors.

关键词： Gravitational waves

Survey of gravitational wave memory in intermediate mass ratio binaries

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arXiv 2021年

作者： Islam, Tousif Field, Scott E. Khanna, Gaurav Warburton, Niels 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 Kavli Institute for Theoretical Physics University of California Santa BarbaraCA93106 United States Department of Physics University of Rhode Island KingstonRI02881 United States School of Mathematics and Statistics University College Dublin Belfield Dublin 4 Ireland

The non-linear gravitational wave (GW) memory effect is a distinct prediction in general relativity. While the effect has been well studied for comparable mass binaries, it has mostly been overlooked for intermediate mass ratio inspirals (IMRIs). We offer a comprehensive analysis of the phenomenology and detectability of memory effects, including contributions from subdominant harmonic modes, in heavy IMRIs consisting of a stellar mass black hole and an intermediate mass black hole. When formed through hierarchical mergers, for example when a GW190521-like remnant captures a stellar mass black hole, IMRI systems have a large total mass, large spin on the primary, and possibly residual eccentricity;features that potentially raise the prospect for memory detection. We compute both the displacement and spin non-linear GW memory from the m 6= 0 gravitational waveforms computed within a black hole perturbation theory framework that is partially calibrated to numerical relativity waveforms. We probe the dependence of memory effects on mass ratio, spin, and eccentricity and consider the detectability of a memory signal from IMRIs using current and future GW detectors. We find that (i) while eccentricity introduces additional features in both displacement and spin memory, it does not appreciatively change the prospects of detectability, (ii) including higher modes into the memory computation can increase signal-to-noise (SNR) values by about 7% in some cases, (iii) the SNR from displacement memory dramatically increases as the spin approaches large, positive values, (iv) spin memory from heavy IMRIs would, however, be difficult to detect with future generation detectors even from highly spinning systems. Our results suggest that hierarchical binary black hole mergers may be a promising source for detecting memory and could favorably impact memory forecasts. Copyright © 2021, The Authors. All rights reserved.

关键词： Gravity waves

Surrogate model for gravitational wave signals from non-spinning, comparable- to large-mass-ratio black hole binaries built on black hole perturbation theory waveforms calibrated to numerical relativity

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arXiv 2022年

作者： Islam, Tousif Field, Scott E. Hughes, Scott A. Khanna, Gaurav Varma, Vijay Giesler, Matthew Scheel, Mark A. Kidder, Lawrence E. Pfeiffer, Harald P. 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 Kavli Institute of Theoretical Physics University of California Santa Barbara Santa BarbaraCA93106 United States Department of Physics MIT Kavli Institute Massachusetts Institute of Technology CambridgeMA02139 United States Department of Physics University of Rhode Island KingstonRI02881 United States Am Mühlenberg 1 Potsdam14476 Germany Cornell Center for Astrophysics and Planetary Science Cornell University IthacaNY14853 United States Theoretical Astrophysics Walter Burke Institute for Theoretical Physics California Institute of Technology PasadenaCA91125 United States

We present a reduced-order surrogate model of gravitational waveforms from non-spinning binary black hole systems with comparable to large mass-ratio configurations. This surrogate model, BHPTNRSur1dq1e4, is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) with mass ratios varying from 2.5 to 10,000. BHPTNRSur1dq1e4 extends an earlier waveform model, EMRISur1dq1e4, by using an updated transition-to-plunge model, covering longer durations up to 30,500 m1 (where m1 is the mass of the primary black hole), includes several more spherical harmonic modes up to = 10, and calibrates subdominant modes to numerical relativity (NR) data. In the comparable mass-ratio regime, including mass ratios as low as 2.5, the gravitational waveforms generated through ppBHPT agree surprisingly well with those from NR after this simple calibration step. We also compare our model to recent SXS and RIT NR simulations at mass ratios ranging from 15 to 32, and find the dominant quadrupolar modes agree to better than ≈ 10−3. We expect our model to be useful to study intermediate-mass-ratio binary systems in current and future gravitational-wave detectors. Copyright © 2022, The Authors. All rights reserved.

关键词： Waveform analysis