Nanoflare statistics in an active region 3D MHD coronal model

Aims. We investigate the statistics for the spatial and temporal distribution of the energy input into the corona 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 that braid the magnetic field lines. This induces currents that are dissipated, thereby leading to transient heating of the coronal 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. Observed solar flares and other smaller transients cover a wide range of energies. The frequency distribution of energies follow a power law, the lower end of the distribution given by the detection limit of current instrumentation. One particular heating mechanism is based on the occurrence of so-called nanoflares, i.e. very low-energy deposition events. Methods. To conduct the numerical experiment we use a high-order finite-difference code that solves the partial differential equations for the conservation of mass, the momentum and energy balance, and the induction equation. The energy balance includes Spitzer heat conduction and optically thin radiative losses in the corona. Results. The temporal and spatial distribution of the Ohmic heating in the 3D MHD model follows a power law and can therefore be understood as a system in a self-organized critical state. The slopes of the power law are similar to the results based on observations of flares and smaller transients. We find that the coronal heating is dominated by events similar to the so-called nanoflares with energies on the order of 10(17) J or 10(24) erg.