Item

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.