On the origin of globular clusters in a hierarchical Universe

We present an end-to-end description of the formation process of globular clusters (GCs) which combines a treatment for their formation and dynamical evolution within galaxy haloes with a state-of-the-art semi-analytic simulation of galaxy formation. Our approach allows us to obtain exquisite statistics to study the effect of the environment and assembly history of galaxies, while still allowing a very efficient exploration of the parameter space of star cluster physics. Our reference model, including both efficient cluster disruption during galaxy mergers and a model for the dynamical friction of GCs within the galactic potential, accurately reproduces the observed correlation between the total mass in GCs and the parent halo mass. A deviation from linearity is predicted at low halo masses, which is driven by a strong dependence on morphological type: bulge-dominated galaxies tend to host larger masses of GCs than their later-type counterparts of similar stellar mass. While the significance of the difference might be affected by resolution at the lowest halo masses considered, this is a robust prediction of our model and represents a natural consequence of the assumption that cluster migration from the disk to the halo is triggered by galaxy mergers. Our model requires an environmental dependence of GC radii to reproduce the observed mass distribution of GCs in our Galaxy at the low-mass end. At GC masses $>10^6\,{\rm M}_\odot$, our model predicts fewer GCs than observed due to an overly aggressive treatment of dynamical friction. The metallicity distribution measured for Galactic GCs is well reproduced by our model, even though it predicts systematically younger GCs than observed. We argue that this adds further evidence for an anomalously early formation of the stars in our Galaxy.