Viscous accretion discs around rotating black holes

Abstract

The stationary hydrodynamic equations for transonic viscous accretion discs in Kerr geometry are derived. The consistent formulation is given for the viscous angular momentum transport and the boundary conditions on the horizon of a central black hole. An expression for the thickness of the disc is obtained from the vertical Euler equation for general accretion flows with vanishing vertical velocity. Different solution topologies are identified, characterized by a sonic transition close to or far from the marginally stable orbit. A numerical method is presented that allows to integrate the structure equations of transonic accretion flows. Global polytropic solutions for the disc structure are calculated, covering each topology and a wide range of physical conditions. These solutions generally possess a sub-Keplerian angular momentum distribution and have maximum temperatures in the range $10^{11}-10^{12}$ K. Accretion discs around rotating black holes are hotter and deposit less angular momentum on the central object than accretion discs around Schwarzschild black holes.