Multi-layered characterization 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 using
stellar mass ($M_s$), effective radius ($R_e$) and mass-to-luminosity ratio
($M_s/L_\nu$), 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 another merging phase, revealing two complex-structured
groups at the highest level. A nonparametric bootstrap procedure was also used
to estimate the confidence of each of our group assignments. These assignments
generally had high confidence in classification, indicating great degree of
certainty of the HSS assignments into our complex-structured groups. The
physical and kinematic properties of the two groups were assessed in terms of
$M_s$, $R_e$, surface density and $M_s/L_\nu$. The first group consisted of
older, smaller and less bright HSS while the second group consisted of brighter
and younger HSS. Our analysis provides novel insight into the physical and
evolutionary properties of HSS and also helps understand physical and
evolutionary properties of candidate globular clusters. Further, the candidate
globular clusters (GCs) are seen to have very high chance of really being GCs
rather than dwarfs or dwarf ellipticals that are also indicated to be quite
distinct from each other.
