The 3D morphology of open clusters in the solar neighborhood III: Fractal dimension

TL;DR

This study investigates the fractal dimensions of open clusters using Gaia DR3 data, revealing insights into their morphology, dynamical evolution, and hierarchical formation within the Galaxy.

Contribution

It introduces a method to classify open cluster morphology based on fractal dimension and links these dimensions to cluster age, mass, and evolutionary processes.

Findings

Fractal dimension is smaller outside the tidal radius, indicating more clumpy outskirts.

Fractal dimension declines with cluster age, reflecting dynamical evolution.

Higher-mass clusters have larger fractal dimensions, suggesting hierarchical formation.

Abstract

We analyze the fractal dimension of open clusters using 3D spatial data from Gaia DR3 for 93 open clusters from Pang et al. (2024) and 127 open clusters from Hunt & Reffert (2024) within 500 pc. The box-counting method is adopted to calculate the fractal dimension of each cluster in three regions: the all-member region, $r \leq r_t$ (inside the tidal radius), and $r > r_t$ (outside the tidal radius). In both the Pang and Hunt catalogs, the fractal dimensions are smaller for the regions $r > r_t$ than those for $r \leq r_t$, indicating that the stellar distribution is more clumpy in the cluster outskirts. We classify cluster morphology based on the fractal dimension via the Gaussian Mixture Model. Our study shows that the fractal dimension can efficiently classify clusters in the Pang catalog into two groups. The fractal dimension of the clusters in the Pang catalog declines with age, which is attributed to the development of tidal tails. This is consistent with the expectations from the dynamical evolution of open clusters. We find strong evidence that the fractal dimension increases with cluster mass, which implies that higher-mass clusters are formed hierarchically from the mergers of lower-mass filamentary-type stellar groups. The transition of the fractal dimension for the spatial distribution of open clusters provides a useful tool to trace the Galactic star forming structures, from the location of the Local Bubble within the solar neighborhood to the spiral arms across the Galaxy.