On the Star Formation Efficiencies and Evolution of Multiple Stellar Generations in Globular Clusters

Abstract

By adopting empirical estimates of the helium enhancement (Δ Y ) between consecutive stellar generations for a sample of Galactic globular clusters (GGCs), we uniquely constraint the star formation efficiency ( ϵ ) of each stellar generation in these stellar systems. In our approach, the star formation efficiency ( ϵ ) is the central factor that links stellar generations as it defines both their stellar mass and the remaining mass available for further star formation, fixing also the amount of matter required to contaminate the next stellar generation. In this way, ϵ is here shown to be fully defined by the He enhancement between successive stellar generations in a GC. Our approach also has an impact on the evolution of clusters and thus considers the possible loss of stars through evaporation, tidal interactions and stellar evolution. We focus on the present mass ratio between consecutive stellar generations ( M ( j −1) G / M ( j ) G ) and the present total mass of GGCs ( M GC ). Such considerations suffice to determine the relative proportion of stars of consecutive generations that remain today in globular clusters ( α ( j −1) G / α ( j ) G ). The latter is also shown to directly depend on the values of Δ Y and thus the He enhancement between consecutive stellar generations in GGC places major constraints on models of star formation and evolution of GC.