Self‐similar Collapse of a Self‐gravitating Viscous Disk

A self-similar solution for time evolution of isothermal, self-gravitatingviscous disks is found under the condition that $\alpha' \equiv \alpha (H/r)$is constant in space (where $\alpha$ is the viscosity parameter and $H/r$ isthe ratio of a half-thickness to radius of the disk). This solution describes ahomologous collapse of a disk via self-gravity and viscosity. The diskstructure and evolution is distinct in the inner and outer parts. There is aconstant mass inflow in the outer portions so that the disk has flat rotationvelocity, constant accretion velocity, and surface density decreasing outwardas $\Sigma \propto r^{-1}$. In the inner portions, in contrast, mass isaccumulated near the center owing to the boundary condition of no radialvelocity at the origin, thereby a strong central concentration being produced;surface density varies as $\Sigma \propto r^{-5/3}$. Moreover, the transitionradius separating the inner and outer portions increases linearly with time.The consequence of such a high condensation is briefly discussed in the contextof formation of a quasar black hole.Comment: 6 pages without figures. The paper has 3 figures (if you need figures, please send email to minesige@kusastro.kyoto-u.ac.jp). To appear in ApJ, 1997 May 1 issu