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Wardell B, Pound A, Warburton N, Miller J, Durkan L, Le Tiec A. Gravitational Waveforms for Compact Binaries from Second-Order Self-Force Theory. PHYSICAL REVIEW LETTERS 2023; 130:241402. [PMID: 37390425 DOI: 10.1103/physrevlett.130.241402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Revised: 02/01/2023] [Accepted: 03/28/2023] [Indexed: 07/02/2023]
Abstract
We produce gravitational waveforms for nonspinning compact binaries undergoing a quasicircular inspiral. Our approach is based on a two-timescale expansion of the Einstein equations in second-order self-force theory, which allows first-principles waveform production in tens of milliseconds. Although the approach is designed for extreme mass ratios, our waveforms agree remarkably well with those from full numerical relativity, even for comparable-mass systems. Our results will be invaluable in accurately modeling extreme-mass-ratio inspirals for the LISA mission and intermediate-mass-ratio systems currently being observed by the LIGO-Virgo-KAGRA Collaboration.
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Affiliation(s)
- Barry Wardell
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, D04 V1W8, Ireland
| | - Adam Pound
- School of Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Niels Warburton
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, D04 V1W8, Ireland
| | - Jeremy Miller
- Shamoon College of Engineering, Jabotinsky 84, Ashdod, 77245, Israel
| | - Leanne Durkan
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, D04 V1W8, Ireland
| | - Alexandre Le Tiec
- Laboratoire Univers et Théories, Observatoire de Paris, CNRS, Université PSL, Université de Paris, F-92190 Meudon, France
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2
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Nasipak Z. Adiabatic evolution due to the conservative scalar self-force during orbital resonances. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.064042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Isoyama S, Fujita R, Chua AJK, Nakano H, Pound A, Sago N. Adiabatic Waveforms from Extreme-Mass-Ratio Inspirals: An Analytical Approach. PHYSICAL REVIEW LETTERS 2022; 128:231101. [PMID: 35749171 DOI: 10.1103/physrevlett.128.231101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Accepted: 05/06/2022] [Indexed: 06/15/2023]
Abstract
Scientific analysis for the gravitational wave detector LISA will require theoretical waveforms from extreme-mass-ratio inspirals (EMRIs) that extensively cover all possible orbital and spin configurations around astrophysical Kerr black holes. However, on-the-fly calculations of these waveforms have not yet overcome the high dimensionality of the parameter space. To confront this challenge, we present a user-ready EMRI waveform model for generic (eccentric and inclined) orbits in Kerr spacetime, using an analytical self-force approach. Our model accurately covers all EMRIs with arbitrary inclination and black hole spin, up to modest eccentricity (≲0.3) and separation (≳2-10 M from the last stable orbit). In that regime, our waveforms are accurate at the leading "adiabatic" order, and they approximately capture transient self-force resonances that significantly impact the gravitational wave phase. The model fills an urgent need for extensive waveforms in ongoing data-analysis studies, and its individual components will continue to be useful in future science-adequate waveforms.
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Affiliation(s)
- Soichiro Isoyama
- School of Mathematics and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
- International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal-RN 59078-970, Brazil
| | - Ryuichi Fujita
- Institute of Liberal Arts, Otemon Gakuin University, Osaka 567-8502, Japan
- Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Alvin J K Chua
- Theoretical Astrophysics Group, California Institute of Technology, Pasadena, California 91125, USA
| | | | - Adam Pound
- School of Mathematics and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Norichika Sago
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
- Advanced Mathematical Institute, Osaka City University, Osaka 558-8585, Japan
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4
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Bonetto R, Pound A, Sam Z. Deformed Schwarzschild horizons in second-order perturbation theory: Mass, geometry, and teleology. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.105.024048] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Albanesi S, Nagar A, Bernuzzi S. Effective one-body model for extreme-mass-ratio spinning binaries on eccentric equatorial orbits: Testing radiation reaction and waveform. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.104.024067] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Chua AJK, Katz ML, Warburton N, Hughes SA. Rapid Generation of Fully Relativistic Extreme-Mass-Ratio-Inspiral Waveform Templates for LISA Data Analysis. PHYSICAL REVIEW LETTERS 2021; 126:051102. [PMID: 33605747 DOI: 10.1103/physrevlett.126.051102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2020] [Accepted: 11/20/2020] [Indexed: 06/12/2023]
Abstract
The future space mission LISA will observe a wealth of gravitational-wave sources at millihertz frequencies. Of these, the extreme-mass-ratio inspirals of compact objects into massive black holes are the only sources that combine the challenges of strong-field complexity with that of long-lived signals. Such signals are found and characterized by comparing them against a large number of accurate waveform templates during data analysis, but the rapid generation of templates is hindered by computing the ∼10^{3}-10^{5} harmonic modes in a fully relativistic waveform. We use order-reduction and deep-learning techniques to derive a global fit for the ≈4000 modes in the special case of an eccentric Schwarzschild orbit, and implement the fit in a complete waveform framework with hardware acceleration. Our high-fidelity waveforms can be generated in under 1 s, and achieve a mismatch of ≲5×10^{-4} against reference waveforms that take ≳10^{4} times longer. This marks the first time that analysis-length waveforms with full harmonic content can be produced on timescales useful for direct implementation in LISA analysis algorithms.
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Affiliation(s)
- Alvin J K Chua
- Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA
| | - Michael L Katz
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
- Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Evanston, Illinois 60208, USA
| | - Niels Warburton
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
| | - Scott A Hughes
- Department of Physics and MIT Kavli Institute, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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van de Meent M, Pfeiffer HP. Intermediate Mass-Ratio Black Hole Binaries: Applicability of Small Mass-Ratio Perturbation Theory. PHYSICAL REVIEW LETTERS 2020; 125:181101. [PMID: 33196223 DOI: 10.1103/physrevlett.125.181101] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 09/14/2020] [Indexed: 06/11/2023]
Abstract
The inspiral phasing of binary black holes at intermediate mass ratios (m_{2}/m_{1}∼10^{-3}) is important for gravitational wave observations, but not accessible to standard modeling techniques: The accuracy of the small mass-ratio (SMR) expansion is unknown at intermediate mass ratios, whereas numerical relativity simulations cannot reach this regime. This article assesses the accuracy of the SMR expansion by extracting the first three terms of the SMR expansion from numerical relativity data for nonspinning, quasicircular binaries. We recover the leading term predicted by SMR theory and obtain a robust prediction of the next-to-leading term. The influence of higher-order terms is bounded to be small, indicating that the SMR series truncated at next-to-leading order is quite accurate at intermediate mass ratios and even at nearly comparable mass binaries. We estimate the range of applicability for SMR and post-Newtonian series for nonspinning, quasicircular inspirals.
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Affiliation(s)
- Maarten van de Meent
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Potsdam, Germany
| | - Harald P Pfeiffer
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Potsdam, Germany
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8
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Han WB, Chen X. Testing general relativity using binary extreme-mass-ratio inspirals. ACTA ACUST UNITED AC 2019. [DOI: 10.1093/mnrasl/slz021] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Affiliation(s)
- Wen-Biao Han
- Shanghai Astronomical Observatory, Shanghai 200030, China
- School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xian Chen
- Astronomy Department, School of Physics, Peking University, Beijing 100871, China
- Kavli Institute for Astronomy and Astrophysics at Peking University, Beijing 100871, China
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9
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Bini D, Damour T, Geralico A, Kavanagh C, van de Meent M. Gravitational self-force corrections to gyroscope precession along circular orbits in the Kerr spacetime. Int J Clin Exp Med 2018. [DOI: 10.1103/physrevd.98.104062] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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11
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Warburton N, Osburn T, Evans CR. Evolution of small-mass-ratio binaries with a spinning secondary. Int J Clin Exp Med 2017. [DOI: 10.1103/physrevd.96.084057] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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13
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van de Meent M. Gravitational self-force on eccentric equatorial orbits around a Kerr black hole. Int J Clin Exp Med 2016. [DOI: 10.1103/physrevd.94.044034] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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14
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Amaro-Seoane P, Gair JR, Pound A, Hughes SA, Sopuerta CF. Research Update on Extreme-Mass-Ratio Inspirals. ACTA ACUST UNITED AC 2015. [DOI: 10.1088/1742-6596/610/1/012002] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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15
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Cardoso V, Gualtieri L, Herdeiro C, Sperhake U. Exploring New Physics Frontiers Through Numerical Relativity. LIVING REVIEWS IN RELATIVITY 2015; 18:1. [PMID: 28179851 PMCID: PMC5255938 DOI: 10.1007/lrr-2015-1] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/29/2014] [Indexed: 05/13/2023]
Abstract
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.
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Affiliation(s)
- Vitor Cardoso
- CENTRA, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 Canada
| | - Leonardo Gualtieri
- Dipartimento di Fisica, Università di Roma “La Sapienza” & Sezione INFN Roma1, P.A. Moro 5, 00185 Roma, Italy
| | - Carlos Herdeiro
- Departamento de Física da Universidade de Aveiro and CIDMA, Campus de Santiago, 3810-183 Aveiro, Portugal
| | - Ulrich Sperhake
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA UK
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Grossman R, Levin J, Perez-Giz G. Faster computation of adiabatic extreme mass-ratio inspirals using resonances. Int J Clin Exp Med 2013. [DOI: 10.1103/physrevd.88.023002] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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17
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Flanagan EE, Hinderer T. Transient resonances in the inspirals of point particles into black holes. PHYSICAL REVIEW LETTERS 2012; 109:071102. [PMID: 23006355 DOI: 10.1103/physrevlett.109.071102] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2011] [Indexed: 06/01/2023]
Abstract
We show that transient resonances occur in the two-body problem in general relativity for spinning black holes in close proximity to one another when one black hole is much more massive than the other. These resonances occur when the ratio of polar and radial orbital frequencies, which is slowly evolving under the influence of gravitational radiation reaction, passes through a low order rational number. At such points, the adiabatic approximation to the orbital evolution breaks down, and there is a brief but order unity correction to the inspiral rate. The resonances cause a perturbation to orbital phase of order a few tens of cycles for mass ratios ∼10(-6), make orbits more sensitive to changes in initial data (though not quite chaotic), and are genuine nonperturbative effects that are not seen at any order in a standard post-Newtonian expansion. Our results apply to an important potential source of gravitational waves, the gradual inspiral of white dwarfs, neutron stars, or black holes into much more massive black holes. Resonances' effects will increase the computational challenge of accurately modeling these sources.
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Affiliation(s)
- Eanna E Flanagan
- Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853, USA
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Pan Y, Buonanno A, Fujita R, Racine E, Tagoshi H. Post-Newtonian factorized multipolar waveforms for spinning, nonprecessing black-hole binaries. Int J Clin Exp Med 2011. [DOI: 10.1103/physrevd.83.064003 10.1103/physrevd.87.109901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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19
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Han WB. Gravitational radiation from a spinning compact object around a supermassive Kerr black hole in circular orbit. Int J Clin Exp Med 2010. [DOI: 10.1103/physrevd.82.084013] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Sasaki M, Tagoshi H. Analytic Black Hole Perturbation Approach to Gravitational Radiation. LIVING REVIEWS IN RELATIVITY 2003; 6:6. [PMID: 28936117 PMCID: PMC5591631 DOI: 10.12942/lrr-2003-6] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/05/2003] [Indexed: 05/27/2023]
Abstract
We review the analytic methods used to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive, compact body, based on black hole perturbation theory. There exist two different methods of performing the post-Newtonian expansion. Both are based on the Teukolsky equation. In one method, the Teukolsky equation is transformed into a Regge-Wheeler type equation that reduces to the standard Klein Gordon equation in the flat-space limit, while in the other method (which was introduced by Mano, Suzuki, and Takasugi relatively recently, the Teukolsky equation is used directly in its original form. The former's advantage is that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one goes to higher and higher post-Newtonian orders. In contrast, the latter's advantage is that a systematic calculation to higher post-Newtonian orders can be implemented relatively easily, but otherwise, it is so mathematical that it is hard to understand the interplay of higher order terms. In this paper, we review both methods so that their pros and cons may be seen clearly. We also review some results of calculations of gravitational radiation emitted by a particle orbiting a black hole.
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Affiliation(s)
- Misao Sasaki
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502 Japan
| | - Hideyuki Tagoshi
- Department of Earth and Space Science, Osaka University, Toyonaka, Osaka, 560-0043 Japan
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