Intermittent heating in the solar corona employing a 3D MHD model

Aims. We investigate the spatial and temporal evolution of the heating of the corona of a cool star such as our Sun in a three-dimensional magneto-hydrodynamic (3D MHD) model. Methods. We solve the 3D MHD problem numerically in a box representing part of the (solar) corona. The energy balance includes Spitzer heat conduction along the magnetic field and optically thin radiative losses. The self-consistent heating mechanism is based on the braiding of magnetic field lines rooted in the convective photosphere. Magnetic stress induced by photospheric motions leads to currents in the atmosphere that heat the corona through Ohmic dissipation. Results. While the horizontally averaged quantities, such as heating rate, temperature, or density, are relatively constant in time, the simulated corona is highly variable and dynamic, on average reaching the temperatures and densities found in observations. The strongest heating per particle is found in the transition region from the chromosphere to the corona. The heating is concentrated in current sheets roughly aligned with the magnetic field and is transient in time and space. This supports the idea that numerous small heating events heat the corona, often referred to as nanoflares.