A prescription and fast code for the long-term evolution of star clusters - II. Unbalanced and core evolution

We introduce version two of the fast star cluster evolution code Evolve Me A Cluster of StarS (emacss). The first version (Alexander and Gieles) assumed that cluster evolution is balanced for the majority of the life cycle, meaning that the rate of energy generation in the core of the cluster equals the diffusion rate of energy by two-body relaxation, which makes the code suitable for modelling clusters in weak tidal fields. In this new version, we extend the model to include an unbalanced phase of evolution to describe the pre-collapse evolution and the accompanying escape rate such that clusters in strong tidal fields can also be modelled. We also add a prescription for the evolution of the core radius and density and a related cluster concentration parameter. The model simultaneously solves a series of first-order ordinary differential equations for the rate of change of the core radius, half-mass radius and the number of member stars N. About two thousand integration steps in time are required to solve for the entire evolution of a star cluster and this number is approximately independent of N. We compare the model to the variation of these parameters following from a series of direct N-body calculations of single-mass clusters and find good agreement in the evolution of all parameters. Relevant time-scales, such as the total lifetimes and core collapse times, are reproduced with an accuracy of about 10 per cent for clusters with various initial half-mass radii (relative to their Jacobi radii) and a range of different initial N up to N = 65 536. The current version of emacss contains the basic physics that allows us to evolve several cluster properties for single-mass clusters in a simple and fast way. We intend to extend this framework to include more realistic initial conditions, such as a stellar mass spectrum and mass-loss from stars. The emacss code can be used in star cluster population studies and in models that consider the co-evolution of (globular) star clusters and large-scale structures

A prescription and fast code for the long-term evolution of star clusters - III. Unequal masses and stellar evolution

We present a new version of the fast star cluster evolution code Evolve Me A Cluster of StarS (emacss). While previous versions of emacss reproduced clusters of single-mass stars, this version models clusters with an evolving stellar content. Stellar evolution dominates early evolution, and leads to: (1) reduction of the mean mass of stars due to the mass loss of high-mass stars; (2) expansion of the half-mass radius; (3) for (nearly) Roche Volume filling clusters, the induced escape of stars. Once sufficient relaxation has occurred (≃10 relaxation times-scales), clusters reach a second, ‘balanced’ state whereby the core releases energy as required by the cluster as a whole. In this state: (1) stars escape due to tidal effects faster than before balanced evolution; (2) the half-mass radius expands or contracts depending on the Roche volume filling factor; and (3) the mean mass of stars increases due to the preferential ejection of low-mass stars. We compare the emacss results of several cluster properties against N-body simulations of clusters spanning a range of initial number of stars, mass, half-mass radius, and tidal environments, and show that our prescription accurately predicts cluster evolution for this data base. Finally, we consider applications for emacss, such as studies of galactic globular cluster populations in cosmological simulations