Magnetic viscosity in Keplerian accretion disks

A model for the anomalous viscosity in accretion disks is developed which is based on the hypothesis that the hydromagnetic turbulence within the disk takes the form of spatially localized magnetic flux cells. The analysis focuses on the dynamics of a single flux cell. The local shear flow due to the Keplerian differential rotation distorts the flux cell topology, thus converting shear flow energy into magnetic energy. The time scale for the enhanced magnetic Maxwell stresses to stop the shear flow and establish local corotation within the flux cell is estimated. A maximum scale size for dynamically active flux cells is set by magnetic buoyancy. The shear-distorted flux cell is driven to reconnect, thus dissipating the stored magnetic energy and splitting the initial cell into two disconnected cells. The time scale for reconnection is greatly reduced by the shear distortion of the flux cell. After disconnection, the altered momentum distribution within the flux cell results in a radial displacement to a new Keplerian equilibrium. The coalescence and the scale length spectrum of flux cells is discussed qualitatively. In the radial diffusion approximation, the kinematic viscosity is estimated from the radial displacement, and is shown to maximize at flux cell scale lengths for which the shear flow stopping and reconnection times are equal. Assuming that the flux cells are densely packed and that the scale length spectrum peaks at the largest cell size allowed by buoyancy, the maximum kinematic viscosity establishes an upper limit to the magnetic viscous stress which scales as the gas pressure