Self-enrichment in globular clusters I. An analytic approach

By means of analytical calculations, we explore the self-enrichment scenario for Globular Cluster formation. According to this scenario, an initial burst of star formation occurs inside the core radius of the initial gaseous distribution. The outward-propagating shock wave sweeps up a shell in which gravitational instabilities may arise, leading to the formation of a second, metal-enriched, population of stars. We find a minimum mass of the proto-globular cluster of the order of 10(6) M-circle dot. We also find that the observed spread in the magnitude-metallicity relation can be explained assuming cluster-to-cluster variations of some parameters like the thermalization efficiency, the mixing efficiency and the Initial Mass Function, as well as variations of the external pressure.