A Random Walk Model for Halo Triaxiality
  We describe a semi-analytic model to predict the triaxial shapes of dark
matter halos utilizing the sequences of random merging events captured in
merger trees to follow the evolution of each halo's energy tensor. When coupled
with a simple model for relaxation toward a spherical shape, we find that this
model predicts distributions of halo axis length ratios which approximately
agree with those measured from cosmological N-body simulations in their medians
and inter-quartile ranges. We demonstrate the predictive and explanatory power
of this model by considering conditioned distributions of axis length, and the
mass-dependence of halo shapes, finding these to be in excellent agreement with
N-body results. This model provides both insight into the physics driving the
evolution of halo triaxial shapes, and rapid quantitative predictions for the
statistics of triaxiality connected directly to the formation history of the
halo.
