1 Introduction

Galactic Globular Clusters are among the very first bound structures that formed in what later became the Galaxy. As such, individual globular clusters and the Globular Cluster System provide us with important insights concerning the age, the formation and the early evolution of the Galaxy.

This paper is the third of a series devoted to the study of a formation scenario of galactic halo globular clusters, namely the self-enrichment hypothesis, which develops the Fall & Rees (1985) cluster formation model. The model is detailed in Parmentier et al. (1999) (hereafter Paper I) and a summary is provided in Parmentier et al. (2000) (hereafter Paper II), Sect. 2.

The model assumes that primordial cold clouds embedded in a hot and diffuse protogalactic background (Fall & Rees 1985) are the gaseous progenitors of galactic halo globular clusters, that is, this model assumes baryon assembly predates star formation. Our model explores the ability of these proto-globular cluster clouds to retain the ejecta of a first generation of zero-metal abundance stars, born in the central regions of the clouds. When the massive stars explode as type II supernovae, they chemically enrich the surrounding pristine interstellar medium and trigger the expansion of a supershell in which a second generation of nonzero-metal abundance stars may form. The aim of a self-enrichment scenario is therefore to explain both the formation of a globular cluster and the origin of its metal content.

One of the key parameters of this class of model is the external pressure exerted by the hot protogalactic background on the proto-clusters. The higher the pressure is (i.e. the deeper the proto-cluster is located in the protoGalaxy in the simplest implementation of the model), the smaller its mass is, the higher its metallicity will be (see Table 1 of Paper I). An in-depth discussion of the ensuing Galactic metallicity gradient is presented in Paper II. We show that, when combined with a pressure profile scaling as $P_{\rm h} \propto D^{-2}$, where $P_{\rm h}$ is the hot protogalactic background pressure and D is the galactocentric distance, the model is consistent with the metallicity gradient observed for the Old Halo globular cluster system.

There are three aspects of globular cluster formation which self-enrichment models must specifically address. The disruptive effects of supernovae, and the internal chemical homogeneity are discussed in Paper I. This paper considers the third aspect, the extent to which a mass(luminosity)-metallicity relation is expected and observed. The Galactic globular cluster system is used as a specific example.