Globular clusters are found in the halos of all types of galaxies, and have been shown to play major roles in the formation of stars and galaxies. The purpose of this thesis is to advance our level of understanding of the dynamical evolution of globular clusters through N-body simulations of clusters with a range of circular, eccentric, and inclined orbits. Theoretical studies have historically assumed that globular clusters experience a static tidal field, however the orbits of globular clusters are all non-circular and the tidal field of most galaxies is not symmetric. Understanding how clusters evolve in realistic potentials allows for them to be used to constrain the formation, merger history, and evolution of a host galaxy and even map out the current size, shape, and strength of a galaxy's gravitational field. We find that dense and compact clusters evolve as if they are in isolation, despite being subject to a non-static tidal field. For larger clusters, tidal shocks and heating inject energy into the cluster and significantly alter its evolution compared to previous studies. We describe how a non-static field alters the mass loss rate and relaxation time of a cluster, and propose methods for calculating a cluster's size and orbit. We then apply our work to clusters in the giant galaxies M87, NGC 1399, and NGC 5128. We consider each cluster population to be a collection of metal poor and metal rich clusters and generate models with a range of orbital distributions. From our models we constrain the orbital anisotropy profile of each galaxy, place constraints on their formation and merger histories, and explore the effects of nearby galaxies on cluster evolution. By advancing studies of globular cluster evolution to include the effects of a non-static tidal field, we have made an important step towards accurately modelling globular clusters from birth to dissolution. Our work opens the door for globular clusters to be used as tools to study galaxy formation, evolution, and structure. Future studies will explore how galaxy formation and growth via the hierarchical merger of smaller galaxies will affect cluster evolution. / Thesis / Doctor of Philosophy (PhD)

<p>Globular clusters have linear sizes (tidal radii) which are theoretically de- termined by their mass and by the gravitational potential of their host galaxy. However observationally, cluster sizes are simply a determination of where the cluster’s surface brightness profile becomes zero. This distance is also known as the limiting radius. While it is commonly assumed that the tidal radius and the limiting radius of a globular cluster are the same thing, it has yet to be validated. The purpose of this thesis is to explore the assumption that cluster tidal radii and limiting radii are equal by comparing the tidal radii of an observed and simulated globular cluster population.</p> <p>An established link between cluster tidal radii and limiting radii will yield new methods of utilizing globular clusters as tools for studying galaxies. If cluster sizes are truly imposed by the tidal field of the host galaxy, then tidal radii measurements can be used to trace the mass distribution within a galaxy, including the dark matter halo. Additionally, as we will demonstrate in this thesis, cluster sizes can also be used a tracer for the orbital anisotropy profile of a galaxy.</p> <p>To explore the assumption that tidal radii and limiting radii are equal, we utilize the globular cluster population of the Virgo giant M87. Unusually deep, high signal-to-noise images of M87 are used to determine the radius for approximately 2000 globular clusters. To compare with these observations, we simulate a globular cluster population that has the same characteristics to the observed M87 cluster population. These characteristics include cluster radial distribution, mass distribution, central concentration distribution and line of sight velocity dispersion. Placing these simulated clusters in the well-studied tidal field of M87, the orbit of each cluster is solved and the theoretical tidal radius of each cluster is determined. We compare the predicted relationship between cluster size and projected galactocentric distance found in our sim- ulation to observations in order to test whether a cluster’s tidal radius and limiting radius are equal. We find that for an isotropic distribution of cluster velocities, theoretical tidal radii are approximately equal to observed limiting radii. The simulation predicts the observed increase in cluster size with galac- tocentric distance, which is expected if tidal radii are dependent on the tidal field. Additionally, simulated cluster sizes are of the same order of magnitude as observed cluster sizes. However the simulation does underestimate cluster sizes in the inner regions of M87. To minimize the discrepancy between theory and observations, we further explore the effects of orbital anisotropy on cluster sizes, and suggest a possible orbital anisotropy profile for M87 which yields the best fit between theory and observations. Finally, we suggest multiple future studies which will aid in our understanding of tidal theory and in establishing a stronger link between tidal radii and limiting radii.</p> / Master of Science (MSc)