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Christopher Hunter's Math Page

Christopher Hunter
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McKenzie Professor of Mathematics
Ph.D., Cambridge, UK, 1960

Detailed description of research

Galactic Dynamics

I am working on several problems that are related to the internal dynamics of galaxies. Galaxies are composed primarily of stars, and so the nature of the orbits of those stars is of fundamental importance for the issue of which forms of galaxies can be sustained. Some of my work is directed toward constructing self-consistent models of elliptical galaxies. Here one needs to find out which combinations of stars in orbit reproduce the density that is needed to cause the gravitational field that one assumed in the first place when computing the orbits. The problems are complicated by the fact that the three-dimensional shapes of most elliptical galaxies, which are seen only in projection on the sky, may well be triaxial. A further challenge is to build models which are consistent with observations of line-of-sight velocities. Like the distribution of light, the kinematics of a galaxy is also observed only in projection on the plane of the sky.

I have recently developed some simple and direct algorithms for deriving the Fourier series which describe the quasi-periodic motion of regular orbits from numerical integrations of those orbits. These algorithms are based entirely on discrete Fourier transforms. They reproduce test orbits accurately, satisfy constraints which are consequences of Hamiltonian theory, and are faster than other methods currently in use. They were developed because galactic models require the use of large numbers of orbits. Hence efficient methods of representing orbits are needed for modeling, and my student Balsa Terzic is now using the new algorithms to construct triaxial galactic models.

Stability of Stellar Systems

Another current interest is that of the stability of stellar systems such as galaxies. Stability is a fundamental requirement of any galactic model, but much more theoretical understanding of this stability is still needed. Stellar dynamic stability problems are harder than those of hydrodynamic stability because they arise in a phase space with twice as many dimensions as physical space. Some results on the stability of particular models have come from numerical N-body simulations, which can act as a guide to theoretical understanding, but cannot replace it. For instance, it was N-body simulations that first showed how prone flat stellar disks are to bar-like instabilities and many galaxies do, indeed, have bar-like features. I am working to obtain a dynamical understanding of bar-like instabilities and what it takes to overcome them.

Gravitational Lensing

Gravitational lensing provides another way of investigating galaxies. Light and other rays are bent when they pass close to a massive object like a galaxy, and the light is slowed down. Consequently a galaxy which happens to lie between us and a distant quasar can cause us to see multiple images of that quasar. This phenomenon is known as gravitational lensing. It provides a tool for investigating the combined effects of the visible and dark matter content of a galaxy because both contribute to the lensing. There are many instances of galaxies which produce four images of the same distant quasar. Wyn Evans (Oxford) and I have developed ways for deducing what those image systems, their configurations and their relative strengths, tell us about mass content of those galaxies. It is that mass which produces the gravitational forces which control the orbits of the stars of the galaxy, and hence which is responsible for the dynamical structure. Hence dynamics and lensing give us two complementary means of studying galaxies; two means which we have been trying to interrelate.