Mathematical Sciences: The Dynamical Structure and Stabilityof Galaxies

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The principal investigator is proposing theoretical studies into some aspects of the dynamics of galaxies. One objective of this research is to build self-consistent equilibrium stellar dynamic models of elliptical galaxies, with special emphasis on galaxies in which orbits of more than one basic family are present. For self-consistency, the different orbits that are dynamically possible must be populated in such a way that the resulting gravitational field is exactly that needed to hold the galaxy together. The second aim of the work is to understand the kinematic properties of the stellar dynamic models, and to relate them to observations. Projections of the kinematic properties of real galaxies on the plane of the sky can be observed, and provide only indirect information from which to determine the true intrinsic motions. A third aim of the work is to study the oscillations and stability of disk-like galaxies. A typical galaxy is composed of hundreds of billions of stars, each of which moves on its own individual orbit according to well-known physical laws of dynamics. Galaxies are also interesting examples of complex systems, whose behavior comes from the combined effects of much simpler components. This project aims to build mathematical models that incorporate the basic characteristics of real galaxies, matching observations as far as possible, which is not simple because only flat pictures of the truly three-dimensional galaxies are ever observed. The work will use a combination of both mathematical analysis and computation to elucidate the present day dynamical structure of galaxies, which should contain significant information about their past history, including that of their formation.