Mass-loss rates and the mass evolution of star clusters

We describe the interplay between stellar evolution and dynamical mass loss of evolving star clusters, based on the principles of stellar evolution and cluster dynamics and on the details of a grid of N-body simulations of Galactic cluster models. The cluster models have different initial masses, different orbits, including elliptical ones, and different initial density profiles. We use two sets of cluster models: one set of Roche lobe filling models and a new set of cluster models that are initially underfilling their tidal radius.

We identify four distinct mass-loss effects: (1) mass loss by stellar evolution, (2) loss of stars induced by stellar evolution and (3) relaxation-driven mass loss before and (4) after core collapse. At young ages the mass loss is dominated by stellar evolution, followed by the evolution-induced loss of stars. This evolution-induced mass loss is important if a cluster is immersed in the tidal field. Both the evolution-induced loss of stars and the relaxation-driven mass loss need time to build up. This is described by a delay function that has a characteristic time-scale of a few crossing times for Roche lobe filling clusters and a few half-mass relaxation times for initially Roche lobe underfilling clusters. The relaxation-driven mass loss (called `dissolution' in this paper) can be described by a simple power-law dependence of the mass d(M/M_solar)/dt = -(M/M_solar)^{1 - γ}/t₀, where t₀ depends on the orbit and environment of the cluster. The index γ is 0.65 for clusters with a King parameter W₀ = 5 for the initial density distribution, and 0.80 for more concentrated clusters with W₀ = 7. For initially Roche lobe underfilling clusters the dissolution is described by the same γ = 0.80, independent of the initial density distribution. The values of the constant t₀ are derived for the models and described by simple formulae that depend on the orbit of the cluster. The mass-loss rate increases by about a factor of 2 at core collapse and the mass dependence of the relaxation-driven mass loss changes to γ = 0.70 after core collapse.

We also present a simple recipe for predicting the mass evolution of individual star clusters with various metallicities and in different environments, with an accuracy of a few per cent in most cases. This can be used to predict the mass evolution of cluster systems.