Star cluster formation in cosmological simulations. III. Dynamical and chemical evolution

In previous papers of this series, we developed a new algorithm for modeling the formation of star clusters in galaxy formation simulations. Here we investigate how dissolution of bound star clusters affects the shape of the cluster mass function and the metallicity distribution of surviving clusters. Cluster evolution includes the loss of stars that become unbound due to tidal disruption as well as mass-loss due to stellar evolution. We calculate the tidal tensor along cluster trajectories and use it to estimate the instantaneous mass-loss rate. The typical tidal tensor exhibits large variations on a time-scale of $\sim100$~Myr, with maximum eigenvalue of $10^7$~Gyr$^{-2}$, and median value of $10^4$~Gyr$^{-2}$ for the first Gyr after cluster formation. As a result of dynamical disruption, at the final available output of our simulations at redshift $z\approx1.5$, the cluster mass function has an approximately log-normal shape peaked at $\sim10^{4.3}M_\odot$. Extrapolation of the disruption to $z=0$ results in too many low-mass clusters compared to the observed Galactic globular clusters (GCs). Over 70\% of GC candidates are completely disrupted before the present; only 10\% of the total GC candidate mass remains in surviving clusters. The total mass of surviving clusters at $z=0$ varies from run to run in the range $(2-6)\times10^7M_\odot$, consistent with the observed mass of GC systems in Milky Way-sized galaxies. The metallicity distributions of all massive star clusters and of the surviving GCs have similar shapes but different normalization because of cluster disruption. The model produces a larger fraction of very metal-poor clusters than observed. A robust prediction of the model is the age-metallicity relation, in which metal-rich clusters are systematically younger than metal-poor clusters by up to 3~Gyr.