9704615 Hunter The principal investigator is proposing to investigate two classes of phenomena that are relevant to the dynamics of galaxies. One is that of instabilities and modes, and the other is that of bifurcations of orbits. The work is analytical and is based on the approximation that galaxies are collisionless stellar systems. That approximation is based on the belief that most of the mass of galaxies is in the form of stars and dark matter, which move, without mutual collisions, on orbits whose form is determined by the total gravity field of the galaxy. N-body simulations of galaxies have shown that both instabilities and large-scale modes of oscillation do occur, and that their occurrence depends on the orbital population of the galaxy. Modes occur when all the orbits pulsate in a coherent manner, while instability occurs when the collective response of the orbital population to a disturbance is to reinforce it and make it grow. The principal investigator will seek detailed descriptions of these possibilities to help explain the underlying dynamics. He has developed a new technique for the accurate location and tracking of modes and instabilities. The bifurcations to be investigated are those at which the form and stability of orbits change. The nature of the orbits is crucial to the structure of a galaxy. Though the two classes of phenomena are to be investigated separately, they are likely interrelated. Galaxies are of interest because they are the fundamental building blocks of the Universe. 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. The primary interest of the principal investigator is in the stability of such systems, and a secondary interest is in the nature of the orbits and the ways in which they can change. One determines whether or not a system is stable by studying how it responds when it is pertur bed. The response may be a mode in which all the orbits manage to pulsate regularly in unison. Alternatively, disturbances dissipate and decay when there is stability, or reinforce and grow when there is instability. Each type of behavior has been observed in computer experiments. What this work seeks is theoretical understanding of underlying causes. It will be carried out using mathematical models, which are of necessity statistical because of the large number of stars to be represented, and a combination of mathematical analysis and computation. Galaxies are known to have existed over a large fraction of the age of the Universe, and hence should be free of all but the mildest instabilities. Hence any findings concerning the requirements for stability is in principle testable against observations of the present day dynamical structure of galaxies.
