Nonaxisymmetric Evolution of Dynamically Contracting Disks and Its Implication for Binary Formation

Using the thin disk approximation we study nonaxisymmetric evolution of a rotating magnetized disk during its dynamic collapse. Since the disk shrinks in size and mass during the collapse, we introduce the zooming coordinates in which the length and timescales shorten with the time in accordance with the collapse. These coordinates enable us to follow the nonaxisymmetric evolution of the disk with high spatial resolution even for the late stage. Numerical simulations show the nonlinear evolution of a perturbation superimposed on a dynamically contracting disk. When a perturbation is absent, the disk is apparently stationary in the zooming coordinates and fits a similarity solution for a dynamically collapsing disk. The disk is unstable against the bar ( m = 2) mode; a perturbation grows to change the disk into a bar. In the early phase, the growth is proportional to ( t 0 - t ) -0.6 , where t 0 denotes an epoch. The length of the bar is about a hundredth of the initial disk diameter. The width of the bar is much shorter than the length. Then the bar is likely to be unstable against fragmentation and to fragment into many small, denser cores. We expect that the small denser cores evolve into binary or multiple stars after merger, scatter, and accretion.