1999ApJ...510..274N

We study the dynamical collapse of isothermal magnetized clouds with two-dimensional axisymmetric numerical simulations. As a model of a cloud, we consider an infinitely long filamentary cloud with a longitudinal magnetic field. An initial model is constructed by adding an axisymmetric perturbation to an equilibrium model. Because of gravitational instability, it fragments into magnetically supercritical cloud cores, which collapse to form dynamically contracting disks keeping nearly quasi-static equilibrium in the vertical direction. The disk contraction is followed until the central density increases by a factor of more than 10⁷. The disk collapses self-similarly while oscillating with appreciable amplitude; the structure of the disk at the different times is similar, except for the scale. In each cycle of the oscillation, MHD fast and slow shock waves form. This oscillation is essentially the same as that during the collapse of an isothermal rotating cloud. We also follow the evolution of various models, changing the cloud mass and magnetic field strength. The disk evolution depends only weakly on the initial condition. Taking account of the magnetic pressure and tension, we refine the similarity solution for a magnetized thin disk obtained by Nakamura, Hanawa, & Nakano. We find that the refined similarity solution can reproduce the main features of our simulations. We also apply the similarity solution to the collapse of a magnetically subcritical cloud. We confirm that the dynamical collapse phase of the subcritical cloud can also be well approximated by the similarity solution. The structure of a dynamically collapsing magnetized disk is essentially similar irrespective of whether the initial cloud is supercritical or subcritical. It indicates that the similarity collapse is a universal characteristic of the dynamical collapse of magnetized clouds.