The formation and dynamical evolution of young star clusters
  Recent observations have revealed a variety of young star clusters, including
embedded systems, young massive clusters, and associations. We study the
formation and dynamical evolution of these clusters using a combination of
simulations and theoretical models. Our simulations start with a turbulent
molecular cloud that collapses under its own gravity. The stars are assumed to
form in the densest regions in the collapsing cloud after an initial free-fall
times of the molecular cloud. The dynamical evolution of these stellar
distributions are continued by means of direct $N$-body simulations. The
molecular clouds typical for the Milky Way Galaxy tend to form embedded
clusters which evolve to resemble open clusters. The associations were
initially considerably more clumpy, but lost their irregularity in about a
dynamical time scale due to the relaxation process. The densest molecular
clouds, which are absent in the Milky Way but are typical in starburst
galaxies, form massive young star clusters. They indeed are rare in the Milky
Way. Our models indicate a distinct evolutionary path from molecular clouds to
open clusters and associations or to massive star clusters. The mass-radius
relation for both types of evolutionary tracks excellently matches the
observations. According to our calculations the time evolution of the half-mass
radius for open clusters and associations follows $r_{\rm h}/{\rm
pc}=2.7(t_{\rm age}/{\rm pc})^{2/3}$, whereas for massive star clusters $r_{\rm
h}/{\rm pc}=0.34(t_{\rm age}/{\rm Myr})^{2/3}$. Both trends are consistent with
the observed age-mass-radius relation for clusters in the Milky Way.
