Similarity Solution for Formation of Circumstellar Disk through the Collapse of a Rotating Cloud

We present similarity solutions which describe the runaway collapse of a rotating isothermal cloud and its subsequent inside-out collapse. The similarity solutions contain the sound speed, c s , and the ratio of the speci c angular momentum to the mass, !, as model parameters. During the runaway collapse, the surface density of the disk is nearly constant in the central part and inversely proportional to the radius in the tail. As the central surface density increases by collapse, the central high surface density part shrinks in mass and in the linear dimension. In the subsequent inside-out collapse phase, the disk has two parts: an inner rotating disk in quasi-equilibrium and an outer dynamically infalling envelope. The inner disk and outer envelope are bounded by a shock wave. The mass and outer edge of the inner disk grows at a constant rate. The accretion rate is proportional to the cubic of the sound speed, i.e., _ M / c s =G, where G denotes and gravitational constanty. The similarity solution of the runaway collapse can reproduce numerical simulations of dynamical collapse of either rotating or magnetized disks. The similarity solution of the inside-out collapse explains the origin of disks around very young T Tauri stars. Subject headings: accretion | hydrodynamics | ISM:clouds | stars:circumstellar matter | stars:formation