Clustering clusters: Unsupervised machine learning on globular cluster structural parameters

Globular clusters (GCs) have historically been subdivided in either two (disc/halo) or three (disc/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 σ₀, 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 favoured 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 disc GC group. With k = 3 the three groups can be interpreted as disc/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 disc, inner halo, and outer halo, respectively), and a measure of how strongly each GC is associated with its group, the so-called silhouette width. Using the latter, we find a correlation with age for both disc and outer halo GCs where the stronger the association of a GC with the disc (outer halo) group, the younger (older) it is. Our findings are aligned with previous work based on very different approaches, such as cladistic analysis, suggesting that the grouping we obtain is quite robust and represents some genuine underlying physical subdivision of GCs. We provide a catalogue where we list the assigned group for each GC.