# On the star formation efficiencies and evolution of multiple stellar generations in Globular Clusters

## TL;DR

This paper uses empirical helium enhancement data to constrain star formation efficiencies in globular clusters, revealing how stellar generations evolve and how their present mass ratios depend on initial star formation conditions.

## Contribution

It introduces a novel method linking helium enhancement to star formation efficiency, providing new constraints on globular cluster evolution models.

## Key findings

- Star formation efficiency is determined by helium enhancement between generations.
- The present mass ratio of stellar generations depends on initial helium enrichment.
- Cluster evolution is influenced by star loss mechanisms and initial star formation parameters.

## Abstract

By adopting empirical estimates of the Helium enhancement (Delta Y) between consecutive stellar generations for a sample of Galactic globular clusters (GGC), we uniquely constraint the star formation efficiency of each stellar generation in these stellar systems. In our approach, the star formation efficiency 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, the star formation efficiency is here shown to be fully defined by the He enhancement between successive stellar generations in a GC. Our approach has also 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 and the present total mass of Galactic globular clusters. Such considerations suffice to determine the relative proportion of stars of consecutive generations that remain today in globular clusters. The latter is also shown to directly depend on the values of Delta Y and thus the He enhancement between consecutive stellar generations in GGC places major constraints on models of star formation and evolution of GC.