Formation of spiral structure from the violent relaxation of
  self-gravitating disks
  We present the numerical study of the formation of spiral structure in the
context of violent relaxation. Initial conditions are the out-of-equilibrium
disks of self-gravitating particles in rigid rotation. By that mechanism,
robust and non-stationary spiral arms can be formed within a few free-fall
times by the shearing of the mass ejection following the collapse. With a
closer look, we find different properties of the arms in connection with the
initial configuration. The winding degree tends to increase with initial
angular speed provided that a disk is thin. If disk surface is circular, both
number and position of arms are governed by the Poissonian density fluctuations
that produce more arms as more particles are introduced. On the contrary, if
the surface ellipticity is imposed, the number of arms and their placement are
effectively controlled. Otherwise, the increase of thickness leads to a
complicated outcome since the number of arms and winding degree are less
effectively controlled. We speculate that this complexity is caused by a strong
non-axisymmetric field during the violent relaxation that disorganizes the
pre-collapse motion and the concentration of particles.
