Shapes and Probabilities of Galaxy Clusters
  We develop a general theory for estimating the probability that a galaxy
cluster of a given shape exists. The theory is based on the observed result
that the distribution of galaxies is very close to quasi-equilibrium, in both
its linear and nonlinear regimes. This places constraints on the spatial
configuration of a cluster of galaxies in quasi-equilibrium. In particular, we
show that that a cluster of galaxies may be described as a collection of nearly
virialized subclusters of approximately the same mass. Clusters that contain
more than 10 subclusters are very likely to be completely virialized. Using our
theory, we develop a method for comparing probabilities of different spatial
configurations of subclusters. As an illustrative example, we show that a
cluster of galaxies arranged in a line is more likely to occur than a cluster
of galaxies arranged in a ring.
