Multi-layered Characterisation of hot stellar systems with confidence

Understanding the physical and evolutionary properties of Hot Stellar Systems (HSS) is a major challenge in astronomy. We studied the dataset on 13456 HSS of Misgeld and Hilker (2011) that includes 12763 candidate globular clusters and found multi-layered homogeneous grouping among these stellar systems. Our methods elicited eight homogeneous ellipsoidal groups at the finest sub-group level. Some of these groups have high overlap and were merged through a multi-phased syncytial algorithm motivated from Almod\'ovar-Rivera and Maitra (2020). Five groups were merged in the first phase, resulting in three complex-structured groups. Our algorithm determined further complex structure and permitted one more merging phase, revealing two complex-structured groups at the highest level. A nonparametric bootstrap procedure found our group assignments to generally have high confidences in classification, indicating stability of our HSS assignments. The physical and kinematic properties of the two highest-level groups were assessed in terms of mass, effective radius, surface density and mass-luminosity ratio. The first group consisted of older, smaller and less bright HSS while the second group consisted of the brighter and younger HSS. Our analysis provides novel insight into the physical and evolutionary properties of HSS and specifically of %also helps to understand physical and evolutionary properties of candidate globular clusters. Further, the candidate globular clusters are seen to have very high probability of being globular clusters rather than dwarfs or dwarf ellipticals that are also indicated to be quite distinct from each other.