On the Formation of Globular Clusters. I. Dynamical Limits on Globular Cluster Metallicities

The efficiency with which supernova ejecta are dispersed into the ISM, and its implications for the metal abundances of early stellar populations are addressed. Based upon the dynamical limits imposed by the dispersive physical processes, a permitted range of metallicities is derived for a closed system such as a globular cluster. The mean supernova progenitor mass, an adjustable parameter in these models, is taken to be about 30 solar masses. This choice is discussed in the context of observed abundance patterns and an assumed IMF. This lower metallicity limit arises from the fact that at most about 8 percent of the input energy is available for gas motions (dispersion). The upper metallicity limit is rather a consequence of momentum conservation: the minimum energy that can be retained is about 0.4 percent, implying very inefficient mixing and therefore a higher achieved metallicity.