Mathematical Modeling of Discs at the centre of Galaxies - Kaur, Amanpreet (My University, 2018)
The galactic system can be mathematically modeled as Ellipsoidals (elliptical galaxies) or thin (zero thickness) axisymmetric discs. To study the dynamical evolution of galactic discs we can model the system in different ways depending upon the physical process we wish to study. In some cases disc is assumed to be continum and the fluid equations are used to study the evolution of such systems. In some other cases, the continuum approximation doesnot hold and we need to go to particle description, for such cases we use collisionless Boltzmann equation, as the galactic systems can be safely assumed to be collisionless. In this thesis, we first discuss the approximations under which continuum behaviour of fluid is valid. Next we move on to discuss various types of galactic system and their components. Some observational features that we aim to explain by the means of studying the dynamical evolution of the systems using perturbation analysis are also discussed. The centres of some galaxies exhibit a counter-intuitive lopsided distribution of stars. In the last part of this thesis we give a dynamical model to explain such features as a part of time evolution of gas and star discs at the centres of galaxies. The gravitationally coupled gas and stellar discs turns out to be stable to non-axisymmetric perturbations. The observed lopsided distribution of stars will only be long lived if there is a continuous source of trigger for such perturbations.
Keywords: Mathematical Modeling; Fluids; Gravitational Dynamics; Galaxies