Title:

Dynamical evolution of idealised star cluster models

This thesis is concerned with the dynamical evolution of globular star clusters modelled as the classical gravitational Nbody problem. The models in this thesis are idealised in order to allow the detailed study of particular dynamical aspects of the cluster evolution. Examples of properties which tend to be omitted are stellar evolution, primordial binaries and the effect of an external tidal gravitational field. The methods used in this thesis are gas models, Nbody models and physical arguments. One of the main topics in this thesis is gravothermal oscillations in multicomponent star clusters. The evolution of onecomponent globular clusters, systems with equal particle masses, is quite well understood. However, the evolution of more realistic globular clusters, with a range of particle masses, is a much more complicated matter. The condition for the onset of gravothermal oscillations in a onecomponent system is simply that the number of stars is greater than a certain number ( ≈7000). In a multicomponent system the relationship between the number of stars at which the gravothermal oscillations first appear and the stellar mass distribution of a cluster is a complex one. In order to investigate this phenomenon two different types of multicomponent systems were studied: twocomponent systems (the simplest approximation of a mass spectrum, Chapter 2) and tencomponent systems (which were realisations of continuous power law IMFs, Chapter 3). In both cases the critical number of stars at which gravothermal oscillations first appear are found empirically for a range of stellar mass distributions. The nature of the oscillations themselves are investigated and it is shown that the oscillations can be understood by focusing on the behaviour of the heavier stars within the cluster. A parameter Nef (de nined Mtot/mmax where Mtot is the total mass and mmax is the maximum stellar mass) acts as an approximate stability boundary for multicomponent systems.The stability boundary was found to be at Nef ~ 12000. In this Chapter 4, globular star clusters which contain a subsystem of stellarmass black holes (BH) are investigated. This is done by considering twocomponent models, as these are the simplest approximation of more realistic multimass systems, where one component represents the BH population and the other represents all the other stars. These systems are found to undergo a long phase of evolution where the centre of the system is dominated by a BH subsystem. After mass segregation has driven most of the BH into a compact subsystem, the evolution of the BH subsystem is found to be in uenced by the cluster in which it is contained. The BH subsystem evolves in such a way as to satisfy the energy demands of the whole cluster, just as the core of a one component system must satisfies the energy demands of the whole cluster. The BH subsystem is found to exist for a significant amount of time. It takes approximately 10trh;i, where trh;i is the initial halfmass relaxation time, from the formation of the compact BH subsystem up until the time when 90% of the subsystem total mass is lost (which is of order 103 times the halfmass relaxation time of the BH subsystem at its time of formation). Based on theoretical arguments the rate of mass loss from the BH subsystem (M2) is predicted to be (βζM)/(αtrh): where M is the total mass, trh is the halfmass relaxation time, and α, β, ζ are three dimensionless parameters. (see Section 4.3 for details). An interesting consequence of this is that the rate of mass loss from the BH subsystem is approximately independent of the stellar mass ratio (m2/m1) and the total mass ratio (M2/M1) (in the range m2/m1 ≥ 10 and M2/M1 ≈ 102, where m1, m2 are the masses of individual lowmass and highmass particles respectively, and M1, M2 are the corresponding total mass). The theory is found to be in reasonable agreement with most of the results of a series of Nbody simulations, and all of the models if the value of ζ is suitable adjusted. Predictions based on theoretical arguments are also made about the structure of BH subsystems. Other aspects of the evolution are also considered such as the conditions for the onset of gravothermal oscillation. The final chapter (Chapter 5) of the thesis contains some concluding comments as well as a discussion on some possible future projects, for which the results in this thesis would be useful.
