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Identifying Eccentricity in Binary Black Hole mergers using a Harmonic Decomposition of the Gravitational Waveform

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arxiv 2411.04187 v1 pith:MD5GZLNJ submitted 2024-11-06 gr-qc astro-ph.HE

Ben G. Patterson , Sharon Mary Tomson , Stephen Fairhurst This is my paper · ORCID
classification gr-qcastro-ph.HE
keywords harmonicsfrequenciesbinarydeterminedeccentricityfrequencygravitationalmathrm
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abstract

We show that the gravitational waveform emitted by a binary on an eccentric orbit can be naturally decomposed into a series of harmonics. The frequencies of these harmonics depend upon the radial frequency, $f_{\mathrm{r}}$, determined by the time to return to apoapsis, and the azimuthal frequency, $f_{\phi}$, determined by the time to complete one orbit relative to a fixed axis. These frequencies differ due to periapsis advance. Restricting to the (2, 2) multipole, we find that the frequencies can be expressed as $f = 2 f_{\phi} + k f_{\mathrm{r}}$. We introduce a straightforward method of generating these harmonics and show that the majority of the signal power is contained in the $k= -1, 0, 1$ harmonics for moderate eccentricities. We demonstrate that by filtering these three leading harmonics, we are able to obtain a good estimate of the orbital eccentricity from their relative amplitudes.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Impact of eccentricity and higher-modes on neutron star-black hole parameter estimation

    astro-ph.HE 2026-07 conditional novelty 6.0 of 10

    Eccentric NSBH signals like GW200105 contain much more information about masses, mass ratio, and effective spin per unit SNR than circular signals, but not about sky position or distance.

  2. Can Eccentric Binary Black Hole Signals Mimic Gravitational-Wave Microlensing?

    gr-qc 2025-12 conditional novelty 6.0 of 10

    Eccentric BBH signals can masquerade as wave-optics microlensing in quasicircular analyses, but eccentric recovery templates break the degeneracy.

  3. Data-driven extraction, phenomenology and modeling of eccentric harmonics in binary black hole merger waveforms

    gr-qc 2025-04 conditional novelty 6.0 of 10

    Eccentric merger waveforms decompose into four smooth harmonics whose phases follow j times a common orbital phase plus an eccentricity-only correction, and whose mean-anomaly dependence can be fitted with simple functions.

  4. gwharmone: first data-driven surrogate for eccentric harmonics in binary black hole merger waveforms

    astro-ph.HE 2025-04 conditional novelty 6.0 of 10

    gwharmone is a data-driven surrogate that reproduces the eccentric harmonics of the dominant quadrupole mode in non-spinning eccentric binary black hole waveforms with average frequency-domain mismatches near 0.004.

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