Horizontal branch morphology of globular clusters: A multivariate statistical analysis

The proper interpretation of horizontal branch (HB) morphology is crucial to the understanding of the formation history of stellar populations. In the present study a multivariate analysis is used (principal component analysis) for the selection of appropriate HB morphology parameter, which, in our case, is the logarithm of effective temperature extent of the HB (log T _effHB). Then this parameter is expressed in terms of the most significant observed independent parameters of Galactic globular clusters (GGCs) separately for coherent groups, obtained in a previous work, through a stepwise multiple regression technique. It is found that, metallicity ([Fe/H]), central surface brightness (μ_v), and core radius (r_c ) are the significant parameters to explain most of the variations in HB morphology (multiple R ² 0.86) for GGC elonging to the bulge/disk while metallicity ([Fe/H]) and absolute magnitude (M_v ) are responsible for GGC belonging to the inner halo (multiple R ² 0.52). The robustness is tested by taking 1000 bootstrap samples. A cluster analysis is performed for the red giant branch (RGB) stars of the GGC belonging to Galactic inner halo (Cluster 2). A multi-episodic star formation is preferred for RGB stars of GGC belonging to this group. It supports the asymptotic giant branch (AGB) model in three episodes instead of two as suggested by Carretta etal. for halo GGC while AGB model is suggested to be revisited for bulge/disk GGC.