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 $\sim 10^6$--$10^7 {\rm M}_\odot$. 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. Calibrated with observations, our model can reproduce a range of observational statistics, including those for GC masses, sizes, metallicities, spatial distributions, and the relation of GC systems with host galaxies/halos. Significant discrepancies between model results and existing observations are discussed in connection to processes implemented in the model. 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.