Magnetohydrodynamic Turbulence of Coronal Active Regions and the Distribution of Nanoflares

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Abstract
We present results from numerical simulations of an externally driven two-dimensional magnetohydrodynamic system over extended periods of time, used to model the dynamics of a transverse section of a solar coronal loop. A stationary forcing was imposed to model the photospheric motions at the loop footpoints. After several photospheric turnover times, a turbulent stationary regime is reached that has an energy dissipation rate consistent with the heating requirements of coronal loops. The turbulent velocities obtained in our simulations are consistent with those derived from the nonthermal broadening of coronal spectral lines. We also show the development of small scales in the spatial distribution of electric currents, which are responsible for most of the energy dissipation. The energy dissipation rate as a function of time displays an intermittent behavior, in the form of impulsive events, that is a direct consequence of the strong nonlinearity of the system. We associate these impulsive events of magnetic energy dissipation with the so-called nanoflares. A statistical analysis of these events yields a power-law distribution as a function of their energies with a negative slope of 1.5, consistent with those obtained for flare energy distributions reported from X-ray observations. A simple model of dissipative structures, based on Kraichnan's theory for MHD turbulence, is also presented.