Nanoflare statistics in an active region 3D MHD coronal model

Abstract

Context. We investigate the statistics of the spatial and temporal distribution of the coronal heating in a three-dimensional magneto- hydrodynamical (3D MHD) model. The model describes the temporal evolution of the corona above an observed active region. The model is driven by photospheric granular motions which braid the magnetic field lines. This induces currents and their dissipation heats the plasma. We evaluate the transient heating as subsequent heating events and analyze their statistics. The results are then interpreted in the context of observed flare statistics and coronal heating mechanisms. Methods. To conduct the numerical experiment we use a high order finite difference code which solves the partial differential equations for the conservation of mass, the momentum and energy balance, and the induction equation. The energy balance includes the Spitzer heat conduction and the optical thin radiative loss in the corona. Results. The temporal and spatial distribution of the Ohmic heating in the 3D MHD model follow a power law and can therefore be explained by system in a self-organized critical state. The slopes of the power law are similar to the results based on flare observations. We find that the corona is heated foot point dominated and the coronal heating is dominated by events called nanoflares with energies on the order of 1017 J.