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.
