Statistical Description of a Magnetized Corona above a Turbulent Accretion Disk

Abstract

We present a physics-based statistical theory of a force-free magnetic field in the corona above a turbulent accretion disk. The field is represented by a statistical ensemble of loops tied to the disk. Each loop evolves under several physical processes: Keplerian shear, turbulent random walk of the disk footpoints, and reconnection with other loops. To build a statistical description, we introduce the distribution function of loops over their sizes and construct a kinetic equation that governs its evolution. This loop kinetic equation is formally analogous to Boltzmann's kinetic equation, with loop-loop reconnection described by a binary collision integral. A dimensionless parameter is introduced to scale the (unknown) overall rate of reconnection relative to Keplerian shear. After solving for the loop distribution function numerically, we calculate self-consistently the distribution of the mean magnetic pressure and dissipation rate with height, and the equilibrium shapes of loops of different sizes. We also compute the energy and torque associated with a given loop, as well as the total magnetic energy and torque in the corona. We explore the dependence of these quantities on the reconnection parameter and find that they can be greatly enhanced if reconnection between loops is suppressed.