Formation and disruption of wide binaries in star clusters revealed by N-body simulations
Wide (soft) binaries are expected to be rapidly disrupted in dense stellar environments, yet they are observed in both the Galactic field and open clusters (OCs). In this paper, we investigate the formation and disruption of wide binaries in star clusters using direct N-body simulations. We perform simulations containing 10,000 objects with varying binary fractions and initial bulk rotation to give an in-depth look into the dynamical evolution of wide binaries in star clusters. We find that wide binaries dominate early disruption and formation processes during the initial high-density phase of cluster evolution. We propose two semi-analytical models to reproduce the evolution of the wide-binary population in simulations. The exponential model consists of an early, rapid-disruption phase with a time less than 10 Myr, driven by frequent encounters at high density, and a longer, relaxation-driven phase between 200 and 300 Myr. The broken power-law model provides break timescales when the decrease of wide binaries slows down during the early and long-term disruption. All timescales from both models agree with each other and decrease with increasing stellar density induced by high primordial binary fraction and cluster rotation. Wide binary disruption is mostly responsible for the early decline in the total binary fraction of the cluster. Such disruption leads to the decrease of radial binary fraction toward the cluster center until 500 Myr. Our results suggest low-density OCs or stellar groups younger than 10 Myr as the optimal environments for detecting wide binaries and provide a physical framework for understanding their contribution to the Galactic field population.