Gravitational Collapse of Isothermal Magnetized Clouds: Universality of Self-similar Collapse

We study dynamical collapse of isothermal magnetized clouds with two-dimensional axisymmetric numerical simulations. As a model of the cloud, we consider an innnitely long lamentary cloud with longitudinal magnetic eld. An initial model is constructed by adding an axisymmetric perturbation on an equilibrium model. Because of gravitational instability, it fragments into magnetically supercritical cloud cores, which collapse to form dynamically-contracting disks keeping nearly quasistatic equilibrium in the vertical direction. The disk contraction is followed until the central density increases by a factor of more than 10 7. The disk collapses self-similarly while oscillating with appreciable amplitude; the structures of the disk at the diierent times are similar to each other, except 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 eld strength. The disk evolution depends only weakly on the initial condition. Taking account of the magnetic pressure and tension, we reened the similarity solution for a magnetized thin disk obtained by Nakamura, Hanawa, & Nakano (1995). We nd that the reened 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 connrm that also the dynamical collapse phase of the subcritical cloud can be well approximated by the similarity solution. The structure of a dynamically collapsing magnetized disk is essentially similar irrespectively 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.