## 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. |