Insights into the 3D layered structure of nearby open clusters through <i>N</i>-body simulations

Context . Open clusters (OCs) are important for understanding star formation, dynamics, and evolution. Previous studies have indicated a relationship between cluster structure and member star properties, but the formation mechanism of the layered structure of OCs remains unclear. Aims . We study the three-dimensional spatial distribution of 279 nearby OCs to understand the formation mechanism of the layered structure. Methods . We analyzed the spatial distribution of member stars within each OC and correlated the presence of a layered structure with the number of member stars. Additionally, we performd N -body simulations to model the evolution of OCSN 125. We assessd the correlation between the binary fraction, the most massive star, and the radius of the layered structure in each simulated OC. Results . Our analysis reveals that OCs with fewer member stars tend to lack a layered structure. The results from N -body simulations indicate that the presence of a layered structure is strongly influenced by dynamical factors, particularly the most massive star and the binary fraction. Massive stars drive mass loss through supernova explosions and stellar winds, which weaken the spatial layering. Furthermore, clusters with higher binary fractions exhibit a weaker layered structure, likely due to energy equipartition, dynamical friction, and perturbations caused by binary systems. These factors contribute to delaying core collapse and slowing the emergence of a layered structure. Conclusions . Our findings suggest that dynamical interactions, including the effects of the most massive stars and binary fraction, play a critical role in the formation and disruption of the layered structure in OCs.