Self-enrichment of Galactic halo globular clusters: stimulated star formation and consequences for the halo metallicity distribution

We explore the self-enrichment hypothesis for globular cluster formation with respect to the star formation aspect. Following this scenario, the massive stars of a first stellar generation chemically enrich the globular progenitor cloud up to Galactic halo metallicities and sweep it into an expanding spherical shell of gas. This paper investigates the ability of this swept protoglobular cloud to become gravitationally unstable and, therefore, to seed the formation of second-generation stars which may form a globular cluster later on. We use a simple model based on a linear perturbation theory for transverse motions in a shell of gas to demonstrate that the pressures by which the progenitor clouds are bound and the supernova numbers required to achieve Galactic halo metallicities support the successful development of the shell transverse collapse. Interestingly, the two parameters controlling the metallicity achieved through self-enrichment, namely the number of supernovae and the external pressure, also rule the surface density of the shell and thus its ability to undergo a transverse collapse. Such a supernova-induced origin for the globular cluster stars therefore opens the way to the understanding of the halo metallicity distributions. This model is also able to explain the lower limit of the halo globular cluster metallicity.