The Formation of Globular Cluster Systems. I. The Luminosity Function

We present a numerical model for the globular cluster luminosity function (GCLF) which characterizes globular cluster systems (GCSs) around galaxies. This model is based on the idea that globular clusters formed in the cores of self-gravitating, magnetized, supergiant molecular clouds (SGMCs). A distribution of core masses is built up through a series of collisions within a parent SGMC. Massive cores are assumed to be destroyed (at a mass-dependent rate) by the act of star formation, allowing for the establishment of a unique, steady state mass spectrum. The model, which allows only for coalescent collisions between cores, fits observed GCS mass spectra very well above the GCLF peak mass m* ≃ 1.6 × 10⁵ Msun, which is remarkably constant from galaxy to galaxy. We suggest that it represents the critical mass above which the cores of SGMCs become susceptible to internal disruption. Our fits to the mass spectra of the Milky Way, M31, and M87 GCSs predict that, in a given SGMC, the lifetimes of such cores should decrease at higher masses. The crucial factor in determining the shape of the GCLF is the ratio β of characteristic core disruption and collision timescales. It is shown that β does not differ between SGMCs in a single protogalaxy; this accounts for observations that GCLFs are independent of galactocentric radius. However, p does differ, and the overall shape of the GCLF along with it, between GCSs. Finally, our model suggests an "inside-out" sequence of GCS formation.