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Improved gravitational radiation time-scales: significance for LISA and LIGO-Virgo sources


Zwick, Lorenz; Capelo, Pedro R; Bortolas, Elisa; Mayer, Lucio; Amaro-Seoane, Pau (2020). Improved gravitational radiation time-scales: significance for LISA and LIGO-Virgo sources. Monthly Notices of the Royal Astronomical Society, 495(2):2321-2331.

Abstract

We present a revised version of Peters’ time-scale for the gravitational wave (GW)-induced decay of two point masses. The new formula includes the effects of the first-order post-Newtonian perturbation and additionally provides a simple fit to account for the Newtonian self-consistent evolution of the eccentricity. The revised time-scale is found by multiplying Peters’ estimate by two factors, R(e0)=81−1−e0√ and Qf(p0) = exp (2.5(rS/p0)), where e0 and p0 are the initial eccentricity and periapsis, respectively, and rS the Schwarzschild radius of the system. Their use can correct errors of a factor of 1–10 that arise from using the original Peters’ formula. We apply the revised time-scales to a set of typical sources for existing ground-based laser interferometers and for the future Laser Interferometer Space Antenna (LISA), at the onset of their GW-driven decay. We argue that our more accurate model for the orbital evolution will affect current event- and detection-rate estimates for mergers of compact object binaries, with stronger deviations for eccentric LISA sources, such as extreme and intermediate mass-ratio inspirals. We propose the correction factors R and Qf as a simple prescription to quantify decay time-scales more accurately in future population synthesis models. We also suggest that the corrected time-scale may be used as a computationally efficient alternative to numerical integration in other applications that include the modelling of radiation reaction for eccentric sources.

Abstract

We present a revised version of Peters’ time-scale for the gravitational wave (GW)-induced decay of two point masses. The new formula includes the effects of the first-order post-Newtonian perturbation and additionally provides a simple fit to account for the Newtonian self-consistent evolution of the eccentricity. The revised time-scale is found by multiplying Peters’ estimate by two factors, R(e0)=81−1−e0√ and Qf(p0) = exp (2.5(rS/p0)), where e0 and p0 are the initial eccentricity and periapsis, respectively, and rS the Schwarzschild radius of the system. Their use can correct errors of a factor of 1–10 that arise from using the original Peters’ formula. We apply the revised time-scales to a set of typical sources for existing ground-based laser interferometers and for the future Laser Interferometer Space Antenna (LISA), at the onset of their GW-driven decay. We argue that our more accurate model for the orbital evolution will affect current event- and detection-rate estimates for mergers of compact object binaries, with stronger deviations for eccentric LISA sources, such as extreme and intermediate mass-ratio inspirals. We propose the correction factors R and Qf as a simple prescription to quantify decay time-scales more accurately in future population synthesis models. We also suggest that the corrected time-scale may be used as a computationally efficient alternative to numerical integration in other applications that include the modelling of radiation reaction for eccentric sources.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute for Computational Science
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Astronomy and Astrophysics
Physical Sciences > Space and Planetary Science
Uncontrolled Keywords:Space and Planetary Science, Astronomy and Astrophysics
Language:English
Date:21 May 2020
Deposited On:15 Feb 2021 10:00
Last Modified:16 Feb 2021 21:00
Publisher:Oxford University Press
ISSN:0035-8711
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1093/mnras/staa1314
Project Information:
  • : FunderSNSF
  • : Grant ID200020_178949
  • : Project TitleMassive black holes as gravitational wave sources in the landscape of galaxy formation

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