Spherical symmetry breaking in cold gravitational collapse of isolated
  systems
  We study, using $N$-body simulation, the shape evolution in gravitational
collapse of cold uniform spherical system. The central interest is on how the
deviation from spherical symmetry depends on particle number $N$. By revisit of
the spherical collapse model, we hypothesize that the departure from spherical
symmetry is regulated by the finite-$N$ density fluctuation. Following this
assumption, the estimate of the flattening of relaxed structures is derived to
be $N^{-1/3}$. In numerical part, we find that the virialized states can be
characterized by the core-halo structures and the flattenings of the cores fit
reasonably well with the prediction. Moreover the results from large $N$
systems suggest the divergence of relaxation time to the final shapes with
$N$.We also find that the intrinsic shapes of the cores are considerably
diverse as they vary from nearly spherical, prolate, oblate or completely
triaxial in each realization. When $N$ increases, this variation is suppressed
as the final shapes do not differ much from initial symmetry. In addition, we
observe the stable rotation of the virialized states. Further investigation
reveals that the origin of this rotation is related in some way to the initial
density fluctuation.
