Formation of a Dynamically Contracting Protostellar Disk

We present similarity solutions that describe the runaway collapse of a rotating isothermal cloud and its subsequent inside-out collapse. 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. 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 similarity solution of the inside-out collapse explains the origin of disks around very young T Tauri stars.