Accurate and efficient waveforms for compact binaries on eccentric orbits

Compact binaries that emit gravitational waves in the sensitivity band of ground-based detectors can have non-negligible eccentricities just prior to merger, depending on the formation scenario. We develop a purely analytic, frequency-domain model for gravitational waves emitted by compact binaries on orbits with small eccentricity, which reduces to the quasicircular post-Newtonian approximant TaylorF2 at zero eccentricity and to the postcircular approximation of Yunes et al. [Phys. Rev. D 80, 084001 (2009)] at small eccentricity. Our model uses a spectral approximation to the (post-Newtonian) Kepler problem to model the orbital phase as a function of frequency, accounting for eccentricity effects up to $\mathcal{O}({e}^{8})$ at each post-Newtonian order. Our approach accurately reproduces an alternative time-domain eccentric waveform model for $e\ensuremath{\in}[0,0.4]$ and binaries with total mass $\ensuremath{\lesssim}12{M}_{\ensuremath{\bigodot}}$. As an application, we evaluate the signal amplitude that eccentric binaries produce in different networks of existing and forthcoming gravitational waves detectors. Assuming a population of eccentric systems containing black holes and neutron stars that is uniformly distributed in comoving volume, we estimate that second-generation detectors like Advanced LIGO could detect approximately 0.1--10 events per year out to redshift $z\ensuremath{\sim}0.2$, while an array of Einstein Telescope detectors could detect hundreds of events per year to redshift $z\ensuremath{\sim}2.3$.

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