A two-phase model of galaxy formation: III. The formation of globular clusters

We develop a model of globular cluster (GC) formation within the cosmological hierarchy of structure formation. The model is rooted in the `two-phase' scenario of galaxy formation developed in Paper-I, where the fast accretion of dark matter halos at high redshift leads to the formation of self-gravitating, turbulent gas clouds that subsequently fragment into dynamically hot systems of dense sub-clouds with masses $\sim 10^6$-$10^7 M_\odot$. Here we elaborate on the formation, evolution, and fate of these sub-clouds, and show that some of the sub-clouds can be compactified via two distinctive channels into a 'supernova-free' regime to form two distinct populations of GCs. The model is simple, characterized by a small number of free parameters underpinned by physical considerations, and can be efficiently implemented into cosmological N-body simulations to generate a coherent sample of halos, galaxies, and GCs. Our model can reproduce a range of observations on GCs, including the mass function, the size-mass relation, the frequency per unit host galaxy/halo mass, the bimodal metallicity distribution, and the spatial profile. Predictions for GCs are made for both the local Universe and for redshift up to $z \approx 10$, and can be tested by upcoming observations.