It was suggested by Harris & Pudritz (1994) that GCs form within the dense cores of supergiant molecular clouds (SGMCs): i.e., an hypothesized population of pressure-confined, self-gravitating, isothermal, magnetized clouds. These SGMCs, they argued, were supported against gravitational collapse by magnetic field pressure and Alfvénic turbulence. Though most SGMCs would presumably have been disrupted during the assembly of the host galaxy, any surviving SGMCs would, if left in isolation, have masses of M ~ 109 M and diameters of D ~ 1 kpc. In short, they would resemble dwarf galaxies.
Subsequent cosmological N-body/TREESPH simulations by Weil & Pudritz (2001) confirmed that gravitationally-bound objects having masses and sizes similar to these SGMCs do indeed form, and that they have a roughly power-law mass spectrum, N(M) M dM, with ~ -1.7. Since star and GC formation was not included in their simulations, no conclusion could be drawn regarding GC MDFs.
An empirical method of studying GC MDFs has been has been explored in a series of papers by my collaborators and I (Côté et al. 1998, 2000, 2002) where a Monte-Carlo algorithm was developed to simulate the GC MDFs of galaxies that are assembled from "proto-galactic fragments". In this picture, both the total number of GCs and their metallicities are determined solely by the mass of the proto-galactic fragment in which they formed; no GCs are formed during the merger and accretion process. The left panels of Figure 1 show simulated and observed MDFs for nine of the 28 galaxies examined in Côté et al. (2002). The right panel shows proto-galactic mass spectra for the 28 galaxies, along with the ensemble mass spectrum. These simulations suggest that the mass spectrum of proto-galactic fragments had an approximate power-law form with index ~ -1.8, in close agreement with the N-body results.
Figure 1. (Left Panels) Representative color/metallicity distributions for GCs belonging to nine of the 28 galaxies in the study of Kundu & Whitmore (2001). The galaxy name and its luminosity in units of L* are given in each panel. In each case, the best-fit distribution obtained from Monte-Carlo simulations of hierarchical galaxy formation is shown by the dashed curve (Côté et al. 2002). (Right Panel) Individual and combined mass spectra of proto-galactic fragments for the same 28 galaxies (dotted curves and open squares, respectively). The dashed line shows a Press-Schechter (1974) mass function with M* = 5 × 1011 M and n = - 2, where n is the index of the cosmological power spectrum.
It is remarkable that two completely independent lines of evidence (i.e., N-body simulations of the gravitational collapse of primordial density fluctuations and Monte-Carlo simulations of the GC MDFs) point to a steep proto-galactic mass spectrum. Although this agreement lends credibility to the results, it is important to recall that the inferred mass spectrum is much steeper than measured luminosity function of galaxies in the local universe. Thus, the formation of GC systems seems inevitably linked to the so-called "missing satellite" problem (Klypin et al. 1999; Moore et al. 1999).
In a recent paper that further demonstrates the utility of GC systems in constraining cosmological models of galaxy formation, Beasley et al. (2002) used the GALFORM semi-analytic code to simulate the GC systems of 450 elliptical galaxies. The relative number of MP and MR GCs in their simulations - which include shock heating of the gas, radiative cooling, feedback, mergers and stellar evolution - were then compared to the observed numbers in M49, where the census of GCs is very nearly complete. This comparison revealed that two ad hoc assumptions were necessary to reproduce the MP and MR GCs in the correct numbers. First, the formation efficiency of MR GCs must exceed that of MP GCs by a factor of 3-4 (see below for an examination of the plausibility of this assumption). Second, the formation of MP GCs, which occur in low-mass halos that Beasley et al. term "proto-galactic disks", must be truncated abruptly at ztrunc 5. Without these assumptions, the predicted population of MP GCs would dominate the MR population by up to two orders of magnitude at z = 0. Unlike previous simulations, Beasley et al. were able to estimate ages for the GCs. The MP GCs have, by virtue of the assumed value of ztrunc, a mean age of T 12 Gyr. The MR GCs are then found to be 1-7 Gyr younger, with a mean age difference of 3 Gyr, although this too hinges on the assumed ztrunc.