Equilibrium phase-space density distribution in numerical dynamical models of open clusters

Abstract

In dynamical models for open clusters, virial equilibrium is not achieved over the violent relaxation time scale τvr. The stars form an equilibrium distribution in (ɛ, ɛζ, l) space, where ɛ and l are the energy and angular momentum per unit stellar mass in the combined field of the Galaxy and cluster and ɛζ is the energy of motion perpendicular to the Galactic plane per unit mass of cluster stars in the gravitational field of the Galaxy. This distribution of stars changes little when t>τvr. The stellar phase-space distribution corresponding to this type of equilibrium and the regular cluster potential vary periodically (or quasi-periodically) with time. This phase-space equilibrium is probably possible due to an approximate balance in the stellar transitions between phase-space cells over times equal to the oscillation period for the regular cluster field.