Abstract
We study the dynamical evolution of globular clusters in a hierarchical model of formation of a Milky Way- type galaxy. The time-dependent potential of dark matter is taken from a cosmological N-body simulation, and each massive dark halo is supplemented by an analytic baryonic disk. Globular clusters are assumed to form within the disks of massive progenitor halos (M_h > 10^9 solar masses) at high redshifts (z ∼ 4), which later merge into the common halo of the galaxy. This scenario is motivated by the results of gas dynamics simulations of Kravtsov & Gnedin (2005), who found that giant molecular clouds in those high-redshift disks may produce star clusters with masses and sizes of observed globular clusters. The initial mass function of these clusters is a power law dN/dM ∝ M^{-2}, similar to that of young star clusters in interacting galaxies. We set model clusters on circular orbits within their host galaxies and follow their orbits through the hierarchical merging until the present, obtaining the final spatial distribution, which we compare with the observed distribution of old globular clusters in the Galaxy. The masses of globular clusters decrease with time as a result of several dynamical processes, among the most important: stellar evolution, two-body relaxation, and tidal shocks. We model all these processes, including the information of the orbits to calculate tidal heating and the effect of tidal shocks, and we compare the mass function of model clusters with the observed mass function of the Milky Way clusters.
