Self-similar viscous accretion and growth of the central core in self-gravitating disks

Unsteady viscous accretion in self-gravitating disks is investigated. Taking into account the growth of the central point mass, a series of self-similar solutions is derived for rotating isothermal disks. These solutions represent the inside-out evolution after central core formation. Solutions are specified by the nondimensional parameters alpha and Q, where alpha is the Shakura and Sunyaev viscous parameter and Q is the Toomre stability parameter. As a core mass increases, the rotation law changes from flat rotation to Keplerian rotation in the inner disk. In addition to the central point mass, the inner disk grows by mass accumulation due to the differing mass accretion rates in the inner and outer radii. The mass accretion rate onto the central core is found to be 3 alpha c(s)(3)/QG for a variety of outer flows. We show that possibly stable solutions with Q greater than or similar to 1 exist for a wide range of alpha.