Star cluster evolution, dynamical age estimation and the kinematical signature of star formation

Abstract

We use N-body integration to follow the evolution of clusters of 200 binary systems with different initial half mass radii $R_{0.5}$. We also simulate single-star clusters. All clusters evolve according to the same $n(t)$ curve, where $n(t)$ is the number density of stars in the central 2~pc sphere at time $t$. $n(t)$ and the lifetime are independent of (i) the inital proportion of binaries and (ii) the initial $R_{0.5}$. Mass segregation measures the dynamical age of the cluster. The proportion of binaries in the central cluster region is a sensitive indicator of the initial cluster concentration. If most stars form in binaries in a typical embedded cluster which is located at the edge of a giant molecular cloud, then we estimate that at most about 10~per cent of all pre-main sequence stars achieve near escape velocities from the molecular cloud. The large ejection velocities resulting from close encounters between binary systems imply a `halo' distribution of young stars over large areas surrounding star forming sites which is expected to have a significantly reduced binary proportion and a significantly increased proportion of stars with depleted circumstellar disks. We compare the time dependent model single star and system luminosity function in the central cluster region with the observational Hyades and Pleiades luminosity functions and find no evidence for different dynamical properties of stellar systems at birth in the Hyades, Pleiades and Galactic field stellar samples. The observed proportion of binary stars in the very young Trapezium Cluster is consistent with the early dynamical evolution of a cluster with a very high initial stellar number density.