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General Relativity and Quantum Cosmology, gr-qc
Abstract:
Compact binaries can have non-negligible orbital eccentricities in the
frequency band of ground-based gravitational-wave detectors, depending on their
astrophysical formation channels. To accurately determine the parameters of
such systems, waveform models need to incorporate eccentricity effects. In this
paper, we consider an eccentric binary of spinning nonprecessing compact
objects, and derive the energy and angular momentum fluxes at infinity, as well
as the gravitational waveform modes to the third post-Newtonian order. The
novel results of this paper include the next-to-leading order instantaneous
spin-orbit and spin-spin contributions to the waveform modes, in addition to
the hereditary (tail and memory) contributions to the modes and fluxes for
eccentric orbits. The instantaneous contributions are derived for generic
motion, while the hereditary contributions are computed in a small-eccentricity
expansion, but we consider a resummation that makes them valid for large
eccentricities. We employ a quasi-Keplerian parametrization of the motion using
harmonic coordinates and the covariant spin-supplementary condition, which
complements some results in the literature in other coordinates. Our results
can be useful in improving the accuracy of waveform models for spinning
binaries on eccentric orbits.
