# 研究成果・発表論文

## Self-similar Collapse of a Self-gravitating Viscous Disk

### Mineshige, Shin,   & Umemura, Masayuki

##### 要旨
A self-similar solution for time evolution of isothermal, self- gravitating viscous disks is found under the condition that \ensuremathα' \ensuremath≡ \ensuremathα(H/r) is constant in space (where \ensuremathα is the viscosity parameter and H/r is the ratio of a half-thickness to the radius of the disk). This solution describes a homologous collapse of a disk via self- gravity and viscosity. The disk structure and evolution are distinct in the inner and outer parts. There is a constant mass inflow in the outer portions so that the disk has flat rotation velocity, constant accretion velocity, and surface density decreasing outward according to \ensuremathΣ åisebox-0.5ex~ r$^-1$. In the inner portions, in contrast, mass is accumulated near the center owing to the boundary condition of no radial velocity at the origin, a strong central concentration being thereby produced; surface density varies according to \ensuremathΣ \i̊sebox-0.5ex~ r$^-5/3$. Moreover, the transition radius separating the inner and outer portions increases linearly with time. The consequence of such a high condensation is briefly discussed in the context of formation of a quasar black hole.