Self-Similar Viscous Collapse of a Self-Gravitating, Polytropic Gas Disk

Abstract

Self-similar solutions for the time evolution of polytropic, self-gravitating viscous disks is found on the condition that the kinematic viscosity is v ∝ rl and the gas pressure is P ∝ ρΓ, where l and Γ are free parameters, r is radius, and ρ is density. This solution describes a self-similar collapse of a rotating gas disk via self-gravity and viscosity. For Γ < Γc = (3 + 2l)/(3 + l) global accretion solutions exist, provided that 0 < l ≤ 1. Owing to the boundary condition of no radial velocity at the origin, mass is accumulated near to the center, giving rise to a strong central concentration; the surface density varies as Σ ∝ r−1−⅔l. In the outer portions, in contrast, the surface density more slowly decreases outward as Σ ∝ r−Γ/(2-Γ). For Γ > Γc, conversely, no global accretion solution is found.