Homologous evolution in the post-collapse expansion of globular clusters

Abstract

We examine the evolution of globular star clusters, modelled as spherically symmetric stellar systems, using various techniques. Such clusters possess a central region of approximately uniform density which is referred to as the core. We concentrate our analysis on the evolution of the cluster after the core has undergone core collapse; a process where its radius decreases and its density increases. After this collapse, the system as a whole can expand in a self-similar fashion (homologous post-collapse evolution) which has long been thought to be due to gravitational interactions between different populations of single stars and binary stars in the core. We confirm this assumption by constructing a simple analytical model which combines much of the theoretical knowledge of previous research in the field. This model consists of two stellar populations, each defined by the mass of the individual stars, and a separate core. Our simple model is itself constructed from two simpler models – a twocomponent model without a core and a single mass model with a core – and takes into account the main gravitational interactions thought to drive the post-collapse evolution. To ensure that no important mechanisms have been neglected in our simple model, we will compare it with an N-body simulation. We compute our N-body models with NBODY6 (using a GPU version for large N). When we compare the N-body model with the simple model, we find qualitative agreement between them for most cases. Even though some mechanisms (e.g. escape of stars) are neglected in our simple model, we find that both models show homologous post-collapse evolution. We also review the homologous post-collapse Fokker-Planck model in the case of equal stellar masses derived by H´enon (1961) with the intention of extending this for the two-component case. We present our numerical solutions for H´enon’s model and find that our numerical solutions are in satisfactory agreement with the results shown in this paper. When we extend this work for a general two-component model (i.e. with no restriction on the number of heavier stars), we find that a homologous solution cannot be found with this approach. By contrast, we suggest that it would be possible to find a homologous two-component solution by extending the one-component solution published later by H´enon (1965), which differs from the earlier model by neglecting the external tidal field of the parent galaxy. Much of the work shown in this thesis would be relevant for such future study.