An Exact Equilibrium Model of an Unbound Stellar System in a Tidal Field

Abstract

Star clusters and dwarf galaxies gradually dissolve as they move in the potential of their host galaxy. Once their density falls below a certain critical density (which is comparable with the background density of the galaxy) it is often assumed that their evolution is completed. In fact the remnant of such a system forms a distribution of stars which are unbound to each other and which move on similar orbits in their host potential. With this motivation we study the evolution of an idealised unbound system and follow its expansion and dissolution in the tidal field of a model galaxy. Initially the stars are uniformly distributed (with a density below the critical density) within an ellipsoidal volume. The system itself travels on a circular orbit within a galaxy modelled as an isothermal sphere. The initial velocities of the stars are chosen by assuming that they move on (three-dimensional) epicycles with guiding centre at the centre of the ellipsoid, though the usual epicyclic theory is altered to account for the self-gravity of the system. This is believed to be the first exact equilibrium model of a stellar system in a tidal field. Our main task is to study the stability of such configurations and the time-scale of their dissolution, as a function of the initial density and size of the ellipsoid. If the time of dissolution is measured by an increase of the half-mass radius of 50 %, we find that systems of low density (about 1 % of the background density) and small radius (50 pc on an orbit of radius 10 kpc) can survive for about 20 galactic orbits. For small systems we show that the lifetime is approximately proportional to the inverse square root of the density.