Formation and Detectability of PSR J0653+0443-like Extremely Eccentric Binary Neutron Stars in the Milky Way

Recently, the Five-hundred-meter-Aperture-Spherical-radio-Telescope (FAST) Galactic Plane Pulsar Snapshot (GPPS) survey discovers an extraordinary binary neutron star (BNS) system, PSR J0653+0443, possessing the highest known orbital eccentricity ($e\approx 0.992$) among Galactic BNSs (Yang et al., 2026), which provides a unique probe into the formation and evolution of BNSs. In this Letter, we perform compact binary population synthesis calculations with self-consistent neutron star spin evolution to model extremely eccentric BNS population detectable by the FAST GPPS survey, explicitly incorporating observational selection effects. We find that BNSs with $e>0.99$ constitute only $\sim 0.6\mathrm{\%}$ of the detectable population, with an expected detection number of ${\lambda }_{\mathrm{G}\mathrm{P}\mathrm{P}\mathrm{S}}\approx 0.31$ over the full planned footprint. Thus, although rare, systems as eccentric as PSR J0653+0443 are compatible with standard binary evolution. We further demonstrate that extremely eccentric BNSs arise preferentially from core-collapse supernovae, whereas imposing $P\lesssim 0.1$ s select older, more frequently recycled systems, which naturally reproduce the observed properties of PSR J0653+0443. We further predict that the completed GPPS sample has a $\sim 15\mathrm{\%}$ chance of finding another $e>0.99$ BNS, but a much higher $\sim 88\mathrm{\%}$ chance for $e>0.90$ systems. By contrast, future facilities are expected to enlarge the detectable highly eccentric BNS population, with SKA potentially detecting PSR J0653+0443-like systems and sub-mHz gravitational-wave detectors probing a larger population with $e>0.9$, enabling much more in-depth population-level constraints.