Formation and disruption of wide binaries in star clusters revealed by N-body simulations

Abstract

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.

Figures (4)

• Figure 1: (a): Evolution of total number of stars (blue), single stars (orange), and binaries (green) of the simulation set $N15k\_10hb\_40sb$ from Table \ref{['tab:models']}. (b): number of close, intermediate (brown), and wide (purple) binaries for the same simulation set. Solid curves and shaded regions represent the mean and standard deviation values among randomized models in the set.
• Figure 2: Events of disruption (red), formation (blue), and escape (orange) for all binaries as a function of time (a), distributions of semi-major axis (b), and eccentricity (c) for the set $N15k\_10hb\_40sb$ from Table \ref{['tab:models']}. The age axis in (a) is logarithmic, early-time bins span much shorter intervals than those at later ages. (d) shows the evolution of actual separation (orange) and semi-major axis (blue) as a function of time of specific case of very wide binary with chaotic evolution or highly perturbed by stellar encounters. Temporary disruption and formation events during the evolution of wide binaries of this type were excluded from (a), (b), and (c).
• Figure 3: Wide binary evolution models and the evolution of number of wide binaries $N_{\rm wide}$ (purple) in one model from the set $N15k\_10hb\_40sb$ (Table \ref{['tab:models']}). The green curve is the exponential model (equation (\ref{['eq:model']})), and the red curve is the broken power-law model (equation (\ref{['eq:model2']})).
• Figure 4: Radial binary fraction of simulations ($f_{\rm b,r}$, a) of the models with $N15k\_10hb\_40sb$ from Table \ref{['tab:models']}. Lines represent the mean value of different randomizations, and the shaded region represents the standard deviation. Colors represent ages from 0.0 to 2000 Myr. (b) shows the binary fraction of all (green), close (red), intermediate (brown), and wide (purple) binaries as a function of time for the same simulation set.