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

TL;DR

This paper demonstrates that gravitational wave signals from eccentric binary black hole mergers can be decomposed into harmonic series, enabling estimation of orbital eccentricity through harmonic filtering.

Contribution

It introduces a harmonic decomposition method for eccentric gravitational waveforms and shows how to estimate eccentricity from harmonic amplitude ratios.

Findings

Most signal power is in the k= -1, 0, 1 harmonics for moderate eccentricities.

Filtering these harmonics allows accurate eccentricity estimation.

Harmonic frequencies depend on radial and azimuthal orbital frequencies, affected by periapsis advance.

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.