In collaboration with Dr. Bonnie Steves of the Astrodynamics group of Glasgow Caledonian University, Prof. Archie Roy is engaged in a long-term exploration of the so-called Caledonian n-body dynamical models (with n equal 4 or greater). The studies already carried out have provided considerable insight into the stability of hierarchical dynamical configurations and their possible paths of evolution. This work is also important in placing limits on the theoretical possibility and stability of extra-solar planets in multiple star systems. The diagram on the right shows surfaces of zero velocity obtained from the energy integral in the Caledonian symmetrical equal mass 4-body problem.
Hendry
and Penny, in collaboration with El-Zant (Kentucky) and Gonzalez (Puebla), are
developing a powerful new numerical technique for building self-consistent density
potential pair galaxy models. The technique is based on the established Schwarszchild
method, whereby one builds a library of galaxy orbits integrated in a specified
model potential, from which a self-consistent solution for the stellar space
density (which satisfies Poisson's equation for the system) can be obtained
by standard optimisation techniques. The novel feature of our method is that
we treat the sampling of orbits as a Monte Carlo integration problem, with integral
equal to the Kolmogorov-Sinai entropy of the system. From dynamical systems
theory, this K-S entropy is simply the integral of the Liapunov exponents over
all initial conditions in the phase space of the system; hence our Monte-Carlo
algorithm will preferentially sample those orbits with non-zero Liapunov exponents
- i.e. the orbits which are stochastic, or chaotic. We are using this
new approach to investigate the stability of galactic disk models, embedded
in triaxial dark matter haloes, with and without the presence of a central black
hole mass. The speed and efficiency of our numerical algorithm has allowed us
to explore a wide range of model parameters, and evaluate the relevance of chaotic
orbits to the phase space structure of different models. Shown on the left are
some examples of the phase portraits of orbits sampled in our Monte Carlo procedure
for a disk+halo model.
Studying the dynamics of the Universe is one of the primary motivations of
our cosmology research, on the statistical
analysis of galaxy distance and redshift-distance surveys. Comparison of the
predicted large scale velocity field and redshift-independent peculiar velocity
estimates is a powerful method for constraining the linear
bias parameter and dimensionless matter density parameter. With Simmons,
Newsam, Rauzy and Schumacher (all formerly Glasgow) we have developed various
techniques for eliminating systematic
biases from the reconstructed dynamical fields, with applications to e.g.
the POTENT
and VELMOD reconstruction methods. Recently Hendry wrote an invited
review of this topic.