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Published December 15, 2022 | Published
Journal Article Open

Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory

Abstract

The modeling of unequal mass binary black hole systems is of high importance to detect and estimate parameters from these systems. Numerical relativity (NR) is well suited to study systems with comparable component masses, m₁ ∼ m₂, whereas small mass ratio (SMR) perturbation theory applies to binaries where q = m₂/m₁ ≪ 1. This work investigates the applicability for NR and SMR as a function of mass ratio for eccentric nonspinning binary black holes. We produce 52 NR simulations with mass ratios between 1:10 and 1:1 and initial eccentricities up to 0.8. From these we extract quantities like gravitational wave energy and angular momentum fluxes and periastron advance, and assess their accuracy. To facilitate comparison, we develop tools to map between NR and SMR inspiral evolutions of eccentric binary black holes. We derive post-Newtonian accurate relations between different definitions of eccentricity. Based on these analyses, we introduce a new definition of eccentricity based on the (2,2)-mode of the gravitational radiation, which reduces to the Newtonian definition of eccentricity in the Newtonian limit. From the comparison between NR simulations and SMR results, we quantify the unknown next-to-leading order SMR contributions to the gravitational energy and angular momentum fluxes, and periastron advance. We show that in the comparable mass regime these contributions are subdominant and higher order SMR contributions are negligible.

Additional Information

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society. It is a pleasure to thank Arif Shaik and Vijay Varma for helpful discussions about eccentricity definitions, and Aaron Zimmerman for useful comments on the manuscript. We also thank the authors of [63,88] for providing the reference data points used in Fig. 14. The NR computational work for this manuscript was carried out on the computer cluster Minerva at the Max Planck Institute for Gravitational Physics in Potsdam. This work was supported by the Sherman Fairchild Foundation and NSF Grants No. PHY1912081, No. PHY-2207342, and No. OAC1931280 at Cornell. Hannes R. Rüter acknowledges support from the Fundação para a Ciência e Tecnologia (FCT) within the Projects No. UID/04564/2021, No. UIDB/04564/2020, No. UIDP/04564/2020, and No. EXPL/FIS-AST/0735/2021.

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Additional details

Created:
August 20, 2023
Modified:
October 25, 2023