The Hierarchical Structure of the Open Cluster NGC 752

The structure of open clusters provides key insights into their evolution and the dynamics of the Milky Way. Using Gaia DR3 data, we applied a hierarchical clustering algorithm to the open cluster NGC 752 based on the kinematical information and identified four substructures corresponding to different stages of disintegration. The cluster exhibits a pronounced signature of mass segregation. Its outer members show a clear expansion trend with a velocities of 0.25 $\rm{kms^{-1}}$ in the plane of the sky. In addition, the system shows a projected rotational pattern with an angular velocity of approximately 0.03 $\rm{radMyr^{-1}}$. We also identified a correlation between the escape times of disturbed members and the epochs at which the cluster crossed the Galactic disk, highlighting the role of Galactic tidal forces in accelerating cluster dissolution. We conclude that hierarchical clustering based on projection bounding energy is effective for studying the internal structure of star clusters, but it has limitations when dealing with unconstrained structures such as tidal tails.

💡 Research Summary

The authors present a hierarchical clustering analysis of the old open cluster NGC 752 using Gaia DR3 astrometric and proper‑motion data. By defining a projected binding energy between pairs of stars (including a tunable parameter p that balances potential and kinetic terms) they construct a binary‑tree dendrogram and identify plateaus in the velocity‑dispersion profile along the main branch. Gaussian‑Mixture‑Model fitting of these plateaus, guided by the Bayesian Information Criterion, yields four distinct substructures (Sub 1–Sub 4). Sub 1 corresponds to the dense core, Sub 2 lies mainly to the west, Sub 3 to the east, and Sub 4 is the most diffuse component containing the southeast tidal tail.

The method selects 388 high‑purity members (p = 11 maximises the plateau weight) and shows a 97 % overlap with the Cantat‑Gaudin (2020) catalogue and 79 % with the high‑probability subset of Hunt & Reffert (2023). The authors note that the HDBSCAN algorithm used by Hunt & Reffert recovers many low‑probability members in the outskirts, which inflate the overall velocity dispersion to 1.5 km s⁻¹, indicating that HDBSCAN is more sensitive to escaped or loosely bound stars, whereas the hierarchical approach preferentially isolates bound members.

Kinematic analysis reveals a clear expansion of the outer members at ~0.25 km s⁻¹ in the plane of the sky and a projected rotation with an angular velocity of ~0.03 rad Myr⁻¹. The cluster exhibits strong mass segregation, with massive stars concentrated in Sub 1 and lower‑mass stars populating the outer substructures and tidal tail. By estimating escape times for disturbed members and comparing them with the epochs of Galactic‑disk crossings, the authors find a positive correlation, supporting the hypothesis that tidal shocks during disk passages accelerate cluster dissolution.

The authors also fit PARSEC isochrones (metallicity