The early evolution of protostellar disks

We consider the origin and intital growth of the disks that form around protostars during the collapse of rotating molecular cloud cores. These disks are assumed to be inviscid and pressure free, and to have masses small compared to those of their central stars. We find that there exist three distinct components-an outer disk, in which shocked gas moves with comparable azimuthal and radical velocities; and inner disk, where material follows nearly circular orbits, but spirals slowly toward the star because of the drag exerted by adjacent onfalling matter, and a turbulent ring adjoining the first two regions. Early in the evolution, i.e., soon after infalling matter begins to miss the star, only the outer disk is present, and the total mass acceration rate onto the protostar is undiminished. Once the outer disk boundary grows to more than 2.9 times the stellar radius, first the ring, and then the inner disk appear. Thereafter, the radii of all three components expand as t3. The mass of the ring increase with time and is always 13% of the total mass that has fallen from the cloud. Concurrently with the buildup of the inner disk and ring, the accretion rate onto the star falls off. However, the protostellar mass continue to rise, asymptotically as t1/4. We calculated the radiated flux from the inner and outer disk components due to the release of gravitational potential energy. The flux from the inner disk is dominant and rises steeply toward the stellar surface. We also determine the surface temperature of the inner disk as a function of radius. The total disk luminosity decreases slowly with time, while the contributions from the ring and inner disk both fall as t-2.