Identifying eccentricity in binary black hole mergers using a harmonic decomposition of the gravitational waveform

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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 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 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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Funding Information
  • National Science Foundation (PHY-0757058, PHY-0823459)
  • Cardiff University
  • Science and Technology Facilities Council (ST/I006285/1, ST/V005618/1, ST/Y509152/1)

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