First supernovae in Galactic globular clusters

We address the question of whether globular clusters (GC) in a protogalaxy could evolve chemically for some time as isolated systems, enriching themse lves with heavy elements produced in the first supernova events that follow initial star formation. We determine both the critical mass of a protoglob ular cluster (proto-GC) that is needed to retain the ejects of the very fir st supernova, and the critical energy (i.e. number of supernovae) that is n eeded 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 x 10(5) to 10(6) M.. The critical star formation efficiency (resul ting in a certain number of supernova events) that is needed to expel the r esidual gas is about 1-3 per cent. Assuming that all the star-forming activ ity in the cluster stops after the critical number of supernovae have explo ded, we reproduce the 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 x 10(7) to 10(8) M.. When all the remaining gas is lost from the cluster, its mass is about a f ew times 10(5) M.. A significant fraction (similar to 97 per cent) of an in itial protocluster cloud is then available for 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 accu mulates metals until the gas thermal energy (increased due to supernova exp losions) exceeds its binding energy leads to the same conclusions. We also comment on the observed homogeneity of the iron distribution in globular cl usters, which is often considered as a primary argument against self-enrich ment. According to the current paradigm, iron originates mainly in Type Ia supernovae with long-lived progenitors. If one states that iron has existed in globular clusters prior to their formation, it should have had a pre-Ga lactic origin. We argue that it is hard to reconcile this with the observed correlation of average iron abundances in extragalactic GC systems with th e luminosities of parent galaxies.