Unveiling the Hierarchical Structure of Open Star Clusters: the Perseus Double Cluster

TL;DR

This paper presents a new hierarchical clustering method using proper motions and celestial coordinates to analyze the structure of open star clusters, successfully applied to the Perseus double cluster, revealing substructures consistent with known components.

Contribution

The paper introduces a novel hierarchical clustering algorithm for star cluster analysis that effectively identifies substructures using kinematic data.

Findings

The algorithm achieves over 91% completeness in mock tests.

It successfully separates the Perseus double cluster into known subclusters.

The method can unveil complex kinematic structures in star clusters.

Abstract

We introduce a new kinematic method to investigate the structure of open star clusters. We adopt a hierarchical clustering algorithm that uses the celestial coordinates and the proper motions of the stars in the field of view of the cluster to estimate a proxy of the pairwise binding energy of the stars and arrange them in a binary tree. The cluster substructures and their members are identified by trimming the tree at two thresholds, according to the $\sigma$-plateau method. Testing the algorithm on 100 mock catalogs shows that, on average, the membership of the identified clusters is $(91.5\pm 3.5)$\% complete and the fraction of unrelated stars is $(10.4\pm 2.0)$\%. We apply the algorithm to the stars in the field of view of the Perseus double cluster from the Data Release 2 of Gaia. This approach identifies a single structure, Sub1, that separates into two substructures, Sub1-1 and Sub1-2. These substructures coincide with $h$ Per and $\chi$ Per: the distributions of the proper motions and the color-magnitude diagrams of the members of Sub1-1 and Sub1-2 are fully consistent with those of $h$ Per and $\chi$ Per reported in the literature. These results suggest that our hierarchical clustering algorithm can be a powerful tool to unveil the complex kinematic information of star clusters.