A geometric template bank for the detection of spinning low-mass compact binaries with moderate orbital eccentricity

Compact binaries on eccentric orbits are another class of gravitational-wave (GW) sources that can provide a wealth of information on binary formation pathways and astrophysical environments. However, historically, eccentricity is often neglected in modelled GW searches for compact binaries. We show that currently used modelled searches that employ quasi-circular template banks are highly ineffectual in detecting binary neutron star (BNS) and neutron star--black hole (NSBH) systems with orbital eccentricities in the range of $[10^{-5},0.15]$ at a GW frequency of $15$Hz. For populations of moderately eccentric BNS and NSBH binaries with (anti-)aligned component spins, we demonstrate that quasi-circular template banks fail to detect up to $\sim 40\%$ of such systems. To alleviate these inefficiencies, we develop the first \emph{geometric} template bank for the search of BNSs and NSBH binaries that includes masses, (anti-)aligned spins and moderate eccentricity. Utilising the post-Newtonian inspiral waveform {\tt TaylorF2Ecc} and a global coordinate transformation, we construct a globally flat metric to efficiently place eccentric templates. Our geometric template bank is highly effectual, and significantly improves the recovery of eccentric signals with less than $6\%$ of signals missed due to the finite template spacing in the bank.