Mathematical Modelling of Lopsided Features at the Centre of Galaxies

Abstract

In this thesis, we first introduce what are galaxies and types of galaxies. Then we discuss the observations of lopsided structures seen at the centers of galaxies. A brief review of literature on the mathematical modeling of center of galaxies in last few years and the dispersion relations derived by various authors by approximating galaxy disk as fluid, softened gravity and stellar disc is then discussed. The major limitation of these models is the treatment of components of galaxies. The galaxies are a combination of gas and stars however none of the discussed model consider the dynamics of the combined disc. We propose a model for eccentric modes, appropriate to the system which have both particle and gas disc coupled together. WKB (Wentzel-Kramers- Brillouin) dispersion relation is derived in which the star and gas disc are considered as a coupled system. The perturbation occurs in both star and gas disc. We have studied the nature of perturbations. The disc are found to be stable if they satisfy the Toomre’s stability criteria. We give the plot for stability region for different amount of gas content in the disc and also give the phase plots describing the nature of wave solution.