Self-Similar Collapse of a Self-Gravitating Viscous Disk

Abstract

A self-similar solution for time evolution of isothermal, self-gravitating viscous disks is found under the condition that ${\alpha }^{\prime }\equiv \alpha (H/r)$ is constant in space (where $\alpha$ is the viscosity parameter and $H/r$ is the ratio of a half-thickness to radius of the disk). This solution describes a homologous collapse of a disk via self-gravity and viscosity. The disk structure and evolution is 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 as $\Sigma \propto r^{-1}$. In the inner portions, in contrast, mass is accumulated near the center owing to the boundary condition of no radial velocity at the origin, thereby a strong central concentration being produced; surface density varies as $\Sigma \propto r^{-5/3}$. 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.

6 pages without figures. The paper has 3 figures (if you need figures, please send email to [email protected]). To appear in ApJ, 1997 May 1 issue

References in corpus (1)

• Black Holes

Cited by in corpus (23)

• Formation of Supermassive Black Holes by Direct Collapse in Pregalactic Halos
• Formation of the first nuclear clusters and massive black holes at high redshift
• Massive black hole seeds from low angular momentum material
• Self-similar Collapse of Rotating Magnetic Molecular Cloud Cores
• Gravitating discs around black holes
• High redshift formation and evolution of central massive objects I: model description
• Self-Similar Collapse of Nonrotating Magnetic Molecular Cloud Cores
• Direct collapse of exceptionally heavy black holes in the merger-driven scenario
• A Model for Quasi-Spherical Magnetized Accretion Flow
• Formation of Massive Black Holes in Globular Clusters
• Viscous accretion of a polytropic self-gravitating disk in the presence of wind
• New Analytical Formulae for Optically-Thin Accretion Flows
• Cosmological magnetic braking and the formation of high-redshift, super-massive black holes
• The influence of winds on the time-dependent behavior of self-gravitating accretion discs
• A Gravitational Instability-Driven Viscosity in Self-Gravitating Accretion Disks
• Self-similar Evolution of Self-Gravitating Viscous Accretion Discs
• Time-dependent evolution of quasi-spherical, self-gravitating accretion flow
• Numerical study of self-gravitating protoplanetary discs
• Self-Similar Evolutionary Solutions of Self-Gravitating, Polytropic $\beta$-Viscous Disks
• Self-gravity in thin discs and edge effects: an extension of Paczynski's approximation
• Stationary Axisymmetric Configuration of the Resistive Thick Accretion Tori around a Schwarzschild Black Hole
• Turbulent viscosity by convection in accretion discs - a self-consistent approach
• Accretion disk dynamics: α-viscosity in self-similar self-gravitating models