Formation of globular clusters in hierarchical cosmology

We study the formation of globular clusters in a Milky Way-size galaxy using a high-resolution cosmological simulation. The clusters in our model form in the strongly baryon-dominated cores of supergiant molecular clouds in the gaseous disks of high-redshift galaxies. The properties of clusters are estimated using a physically motivated subgrid model of the isothermal cloud collapse. The first clusters in the simulation form at z approximate to 12, while we conjecture that the best conditions for globular cluster formation appear to be at z similar to 3-5. Most clusters form in the progenitor galaxies of the virial mass M-h > 10(9) M-circle dot, and the total mass of the cluster population is strongly correlated with the mass of its host galaxy: M-GC = 3 x 10(6) M-circle dot(M-h/10(11) M-circle dot)(1:1). This corresponds to a fraction similar to 2 x 10(-4) of the galactic baryons being in the form of globular clusters. In addition, the mass of the globular cluster population and the maximum cluster mass in a given region strongly correlate with the local average star formation rate. We find that the mass, size, and metallicity distributions of the globular cluster population identified in the simulation are remarkably similar to the corresponding distributions of the Milky Way globular clusters. We find no clear mass-metallicity or age-metallicity correlations for the old clusters. The zero-age mass function of globular clusters can be approximated by a power law dN/dM proportional to M-alpha with alpha approximate to 2, in agreement with the mass function of young stellar clusters in starbursting galaxies. We discuss in detail the origin and universality of the globular cluster mass function. Our results indicate that globular clusters with properties similar to those of observed clusters can form naturally within dense gaseous disks at z greater than or similar to 3 in the concordance Lambda CDM cosmology.