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 & 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% for clusters with various initial half-mass radii (relative to their Jacobi radii) and a range of different initial N up to N = 65536. 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.