Astrophysics provides many examples of complex dynamical systems. This course covers the mathematical tools to describe Galaxies as well as reviewing their observational properties. The behaviour of these systems is controlled by Newton's laws of motion and Newton's law of gravity. Galaxies are dynamically very young, a typical star like the Sun having orbited only thirty or so times around the galaxy. The motions of stars in Galaxies are described using classical statistical mechanics, since the number of stars is so great. The study of large assemblies of stars interacting via long-range forces provides many unusual examples of cooperative phenomena, such as bars and spiral structure. The interplay between astrophysical dynamics and modern cosmology is also important -- much of the evidence for dark matter is dynamical in origin.
Observational overview. Stellar populations in galaxies, galaxy morphology and classification. Dust and gas in galaxies. Scaling Laws. Theory of the gravitational potential. Poisson's equation. The gravity field of spherical. elliptical and disk galaxies. Regular and chaotic orbits, the epicyclic approximation, surfaces of section, action-angle coordinates, adiabatic invariance. Collisionless stellar dynamics, the Boltzmann equation, the Jeans theorem, the Jeans equations, equilibrium models of spherical, elliptical and disk galaxies. Collisions, collisional dynamics, the Fokker-Planck equation. Globular cluster evolution, evaporation and ejection, the gravothermal catastrophe, hard and soft binaries. Galactic stability, The Jeans length, theories of spiral structure, the role of resonances. The Milky Way Galaxy, the thin disk, thick disk and halo, substructure and tidal streams
There will be four examples class associated with the course. Three are given this term given in the Hoyle Committee Room, Institute of Astronomy.