Stellar populations in $\omega$ Centauri: a multivariate analysis
  We have performed multivariate statistical analyses of photometric and
chemical abundance parameters of three large samples of stars in the globular
cluster $\omega$ Centauri. The statistical analysis of a sample of 735 stars
based on seven chemical abundances with the method of Maximum Parsimony
(cladistics) yields the most promising results: seven groups are found,
distributed along three branches with distinct chemical, spatial and
kinematical properties. A progressive chemical evolution can be traced from one
group to the next, but also within groups, suggestive of an inhomogeneous
chemical enrichment of the initial interstellar matter. The adjustment of
stellar evolution models shows that the groups with metallicities
[Fe/H]\textgreater{}-1.5 are Helium-enriched, thus presumably of second
generation. The spatial concentration of the groups increases with chemical
evolution, except for two groups, which stand out in their other properties as
well. The amplitude of rotation decreases with chemical evolution, except for
two of the three metal-rich groups, which rotate fastest, as predicted by
recent hydrodynamical simulations. The properties of the groups are interpreted
in terms of star formation in gas clouds of different origins. In conclusion,
our multivariate analysis has shown that metallicity alone cannot segregate the
different populations of $\omega$ Centauri.
