Formation of spiral structure from the violent relaxation of self-gravitating disks

We present the numerical study of the formation of a spiral structure in the context of violent relaxation. Initial conditions are the out-of-equilibrium disks of self-gravitating particles in rigid rotation. Using that mechanism, robust and nonstationary spiral arms can be formed within a few free-fall times through the shearing of 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 the disk surface is circular, both the 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 in thickness leads to a complicated outcome as the number of arms and winding degree are less effectively controlled. We speculate that this complexity is caused by a strong nonaxisymmetric field during the violent relaxation that disorganizes the precollapse motion and the concentration of particles.