Observability of eccentricity in a population of merging compact binaries

We investigate the prospects of observing residual eccentricity in a population of compact binaries by calculating the power in the eccentric harmonics, following the methodology in arXiv:2411.04187. Although most observed compact binary coalescences are expected to circularize before entering the sensitivity band of the ground-based gravitational-wave (GW) detectors, dynamical interactions in dense star clusters can lead to a fraction of these binaries with non-negligible eccentricity at the time of detection. To quantify the observability of eccentricity, we simulate a population of merging compact binaries and identify those which have sufficient power in sub-dominant eccentric harmonics to be clearly distinguishable from quasi-circular systems. We consider a binary black hole (BBH) population derived from globular cluster simulations with residual eccentricity distribution obtained from Cluster Monte Carlo (CMC) catalogs as well as a fiducial log-uniform model. Assuming the LIGO-Virgo network of GW detectors with their sensitivities achieved during LIGO-Virgo-KAGRA (LVK) Observing Run (O4), we find that the BBH population with measurable eccentricity will have a significantly higher median eccentricity $e_{\mathrm{10Hz}}\sim 0.3$ (with $90\%$ range: $0.1 - 0.5$) and signal-to-noise ratio (SNR) $\sim 20$ ($90\%$ range: $13 - 57$) compared to the observable population of BBHs. We compare our predictions of the regions of parameter space where eccentricity is detectable with the claimed observations of eccentricity in GW events from third Gravitational Wave Transient Catalog (GWTC-3).