Eccentricity as a Magnifying Glass: Precision Population Inference Enabled by Eccentric Neutron Star-Black Hole Mergers

The formation history of compact binary systems remains one of the key open questions in astrophysics. Theoretical studies generally favor isolated binary evolution for neutron star-black hole (NSBH) systems, which tends to produce nearly circular orbits. However, recent analyses of the gravitational-wave event GW200105 indicate that its source has measurable eccentricity, suggesting that alternative formation channels may also contribute. It has been shown that the intrinsic parameters of eccentric NSBH mergers, such as the component masses and spins, are much better measured than circular mergers with LIGO-Virgo-KAGRA (LVK) observatories. We explore how such eccentricity-enhanced parameter measurements can affect the inference of NSBH formation channels. We find that sharper measurements of the effective spin parameter chi eff increase the fraction of systems for which negative values can be confidently identified, allowing for the clear measurement of a spin-orbit misaligned event every about 2.5 eccentric NSBH detections for an isotropically distributed population in the fifth LVK observing run (O5). Improved NS mass measurements provide better constraining power for NS mass distributions, potentially revealing structure and tightening the bounds that can be drawn on their upper and lower masses. Similarly, the recovery of a metallicity-dependent BH mass distribution is improved by eccentricity-enhanced measurements. Finally, we show that the proposed population-level eccentricity distribution for dynamical-formation channels can be tested by the end of O5.