# Clustering clusters: unsupervised machine learning on globular cluster structural parameters

## TL;DR

This study applies cluster analysis to globular cluster parameters, revealing that their natural grouping is either two or three, with the three-group model aligning with disk, inner-halo, and outer-halo classifications, and correlating with age.

## Contribution

It introduces an unsupervised clustering approach to objectively determine the number of globular cluster groups and interpret their physical significance.

## Key findings

- Two or three intrinsic groups identified, with three favored.
- Cluster analysis recovers known physical groupings (disk, halo).
- Correlation between cluster association strength and age.

## Abstract

Globular Clusters (GCs) have historically been subdivided in either two (disk/halo) or three (disk/inner-halo/outer-halo) groups based on their orbital, chemical and internal physical properties. The qualitative nature of this subdivision makes it impossible to determine whether the natural number of groups is actually two, three, or more. In this paper we use cluster analysis on the $(\log M, \log \sigma_0, \log R_e, [Fe/H], \log | Z |)$ space to show that the intrinsic number of GC groups is actually either $k=2$ or $k=3$, with the latter being favored albeit non-significantly. In the $k=2$ case, the Partitioning Around Medoids (PAM) clustering algorithm recovers a metal-poor halo GC group and a metal-rich disk GC group. With $k=3$ the three groups can be interpreted as disk/inner-halo/outer-halo families. For each group we obtain a medoid, i.e. a representative element (NGC $6352$, NGC $5986$, and NGC $5466$ for the disk, inner halo, and outer halo respectively), and a measure of how strongly each GC is associated to its group, the so-called silhouette width. Using the latter, we find a correlation with age for both disk and outer halo GCs where the stronger the association of a GC with the disk (outer halo) group, the younger (older) it is.