Accurate and efficient waveforms for compact binaries on eccentric orbits

TL;DR

This paper presents an analytic frequency-domain waveform model for eccentric compact binaries, improving detection accuracy for gravitational waves from systems with small eccentricities, and estimates detection rates for current and future detectors.

Contribution

The authors develop a purely analytic, frequency-domain eccentric waveform model that extends existing approximations and accurately matches time-domain models for small eccentricities.

Findings

Model accurately reproduces time-domain waveforms for eccentricities up to 0.4

Estimated detection rates: 0.1-10 per year for Advanced LIGO

Hundreds of detections per year expected with Einstein Telescope

Abstract

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 quasi-circular post-Newtonian approximant TaylorF2 at zero eccentricity and to the post-circular approximation of Yunes et al. (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 ${\cal{O}}(e^8)$ at each post-Newtonian order. Our approach accurately reproduces an alternative time-domain eccentric waveform model for eccentricities $e\in [0, 0.4]$ and binaries with total mass less than 12 solar masses. 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 co-moving volume, we estimate that second generation detectors like Advanced LIGO could detect approximately 0.1-10 events per year out to redshift $z\sim 0.2$, while an array of Einstein Telescope detectors could detect hundreds of events per year to redshift $z \sim 2.3$.