Abstract

We address a question if globular clusters (GC) in a protogalaxy could for some time evolve chemically as isolated systems, enriching themselves with heavy elements produced in first supernova events that follow initial star formation. We determine both the critical mass of a protoglobular cluster that is needed to retain the ejecta of the very first supernova, and the critical energy (i.e., number of supernovae) that is needed to expel the residual gas from a cluster of a given mass. We show that the critical mass of a proto-GC for a wide range of parameters (size, degree of fragmentation, degree of central concentration) does not exceed 8·10⁵-10⁶ M_sun. The critical star formation efficiency (resulted in the certain number of supernova events) that is needed to expel the residual gas is about 1-3%. Assuming that all the star-forming activity in the cluster stops after the critical number of suprenovae have exploded, we reproduce basic parameters of the present-day globular clusters, i.e., their final masses and oxygen abundances. A typical globular cluster in our model originates from a cloud with a mass of 5·10⁷-10⁸ M_sun. When all the remaining gas is lost from the cluster, its mass is about a few times 10⁵ M_sun. A significant fraction (about 97%) of an initial protocluster cloud is then available for the galactic disc formation.

We check our results with the method that is usually applied to elliptical galaxy modelling. The assumption that a protocluster cloud evolves and accumulates metals until the gas thermal energy, increased due to SN explosions, exceeds its binding energy, leads to the same conclusions.

We also comment on the observed homogeneity of iron distribution in globular clusters, that is often considered as a primary argument against the self-enrichment. According to current paradigm, iron originates mainly in supernovae type Ia with long-living progenitors. If one states that iron has existed in globular clusters prior to their formation, it should have had a pre-galactic origin. We argue that it is hard to reconcile this with the observed correlation of average iron abundances in extragalactic GC systems with the luminosities of parent galaxies.