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

Fuente: arXiv
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Main Authors: Patterson, Ben G., Tomson, Sharon Mary, Fairhurst, Stephen
Format: Preprint
Published: 2024
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author Patterson, Ben G.
Tomson, Sharon Mary
Fairhurst, Stephen
author_facet Patterson, Ben G.
Tomson, Sharon Mary
Fairhurst, Stephen
contents 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, $f_ϕ$, 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 $f = 2 f_ϕ + k f_{\mathrm{r}}$. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_04187
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Identifying Eccentricity in Binary Black Hole mergers using a Harmonic Decomposition of the Gravitational Waveform
Patterson, Ben G.
Tomson, Sharon Mary
Fairhurst, Stephen
General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
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, $f_ϕ$, 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 $f = 2 f_ϕ + k f_{\mathrm{r}}$. 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.
title Identifying Eccentricity in Binary Black Hole mergers using a Harmonic Decomposition of the Gravitational Waveform
topic General Relativity and Quantum Cosmology
High Energy Astrophysical Phenomena
url https://arxiv.org/abs/2411.04187