The formation and hierarchical assembly of globular cluster populations
  We use a semi-analytic model for globular cluster (GC) formation built on
dark matter merger trees to explore the relative role of formation physics and
hierarchical assembly in determining the properties of GC populations. Many
previous works have argued that the observed linear relation between total GC
mass and halo mass points to a fundamental GC -- dark matter connection or
indicates that GCs formed at very high redshift before feedback processes
introduced nonlinearity in the baryon-to-dark matter mass relation. We
demonstrate that at $M_{\rm vir}(z=0) \gtrsim 10^{11.5} M_{\odot}$, a constant
ratio between halo mass and total GC mass is in fact an almost inevitable
consequence of hierarchical assembly: by the central limit theorem, it is
expected at $z=0$ independent of the GC-to-halo mass relation at the time of GC
formation. The GC-to-halo mass relation at $M_{\rm vir}(z=0) < 10^{11.5}
M_{\odot}$ is more sensitive to the details of the GC formation process. In our
fiducial model, GC formation occurs in galaxies when the gas surface density
exceeds a critical value. This model naturally predicts bimodal GC color
distributions similar to those observed in nearby galaxies and reproduces the
observed relation between GC system metallicity and halo mass. It predicts that
the cosmic GC formation rate peaked at $z$ $\sim$ 4, too late for GCs to
contribute significantly to the UV luminosity density during reionization.
