SELF-SIMILAR VISCOUS COLLAPSE OF A SELF-GRAVITATING, POLYTROPIC GAS DISK

Self-similar solutions for the time evolution of polytropic, self-grav itating viscous disks is found on the condition that the kinematic vis cosity is nu alpha tau(l) and the gas pressure is Rho alpha rho(Gamma) , where l and Gamma are free parameters, tau is radius, and rho is den sity. This solution describes a self-similar collapse of a rotating ga s disk via self-gravity and viscosity. For Gamma < Gamma(c) = (3 + 2l) /(3 + l) global accretion solutions exist, provided that 0 < l less th an or equal to 1. owing to the boundary condition of no radial velocit y at the origin, mass is accumulated near to the center, giving rise t o a strong central concentration; the surface density varies as Sigma alpha tau(-1-2/3l) In the outer portions, in contrast, the surface den sity more slowly decreases outward as Sigma alpha tau(-Gamma/(2-Gamma) ). For Gamma > Gamma(c), conversely, no global accretion solution is f ound.