Kinematic Evidence for Open Cluster Origins of Galactic Binary Neutron Stars

We investigate the potential birthplace of Galactic binary neutron star (BNS) systems through a kinematic analysis. Using high-precision astrometry from Gaia DR3, updated pulsar distances, and Monte Carlo sampling of astrometric errors, we integrate the past trajectories of 11 Galactic BNSs and 167 globular clusters plus 2967 open clusters, to search for past encounters. Our results suggest that BNS origin in globular clusters is unlikely, with low encounter probabilities (e.g., $\lesssim 0.5\%$ for NGC 5139) and requiring excessive ejection velocities. Conversely, our analysis indicates that open clusters are a non-negligible formation channel. Specifically, the double pulsar J0737$-$3039 shows a $13.9\%$ ($5.4\%$) probability of originating from the young cluster OC 0450 (Theia 58). Based on encounter proximity and time, we argue that Theia 58 is its more plausible birthplace. Our work provides kinematic evidence consistent with an open-cluster origin for a subset of field BNSs.