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Uncovering the formation of ultra-compact dwarf galaxies by multivariate statistical analysis

We present a statistical analysis of the properties of a large sample of dynamically hot old stellar systems, from globular clusters to giant ellipticals, which was performed in order to investigate the origin of ultra-compact dwarf galaxies. The data were mostly drawn from Forbes et al. (2008). We recalculated some of the effective radii, computed mean surface brightnesses and mass-to-light-ratios, estimated ages and metallicities. We completed the sample with globular clusters of M31. We used a multivariate statistical technique (K-Means clustering), together with a new algorithm (Gap Statistics) for finding the optimum number of homogeneous sub-groups in the sample, using a total of six parameters (absolute magnitude, effective radius, virial mass-to-light ratio, stellar mass-to-light ratio and metallicity). We found six groups. FK1 and FK5 are composed of high- and low-mass elliptical galaxies respectively. FK3 and FK6 are composed of high-metallicity and low-metallicity objects, respectively, and both include globular clusters and ultra-compact dwarf galaxies. Two very small groups, FK2 and FK4, are composed of Local Group dwarf spheroidals. Our groups differ in their mean masses and virial mass-to-light ratios. The relations between these two parameters are also different for the various groups. The probability density distributions of metallicity for the four groups of galaxies is similar to that of the globular clusters and UCDs. The brightest low-metallicity globular clusters and ultra-compact dwarf galaxies tend to follow the mass-metallicity relation like elliptical galaxies. The objects of FK3 are more metal-rich per unit effective luminosity density than high-mass ellipticals.