On the dynamics of spherically symmetric self gravitating systems

Abstract

This thesis focuses on the investigation of the dark matter content of spherically symmetric self gravitating systems. The first system under investigation is the Galactic globular cluster NGC 6809; we use a variety of dynamical models and Bayesian inference in order to conclusively identify the presence of dark matter. Our findings exclude the hypothesis of a surrounding dark matter halo, and we predict to a 95% confidence interval there exists no significant amount of dark matter in the cluster. Pushing further the limits of theoretical modelling in the first two of a series of three papers we attack the problem of the mass-anisotropy degeneracy of the spherically symmetric Jeans equation. At the heart of our method lies the representation of the radial second order velocity moment with flexible B-splines. In the first of the papers we set the framework for the theoretical foundation of the method and we present a simple example. In the second paper, we define an optimum smoothing algorithm for the flexible B-spline and we validate our method through a series of examples. The overall result of these two papers is that for an assumed free functional form of the potential and mass density we identify a unique anisotropy profile (within statistical uncertainties) as this is described from the radial and tangential second order velocity moments. This is both for a constant or variable mass-to-light ratio. The third paper is currently a project under development. In this we perform the full mass-anisotropy resolution, i.e. the reconstruction from data of the stellar mass profile, the dark matter mass profile, and of the second order velocity moments of the radial and tangential components. In Chapter 5 I describe the basic mathematical framework for the full resolution of the mass-anisotropy resolution and I present a simple example