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 e \in [ 0 , 0.4 ] and binaries with total mass \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 12 M% _ { \odot } .
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 .