Coronal energy input and dissipation in a solar active region 3D MHD model

Context. We have conducted a 3D MHD simulation of the solar corona above an active region (AR) in full scale and high resolution, which shows coronal loops, and plasma flows within them, similar to observations. Aims. We want to find the connection between the photospheric energy input by field-line braiding with the coronal energy conversion by Ohmic dissipation of induced currents. Methods. To this end we compare the coronal energy input and dissipation within our simulation domain above different fields of view, e.g. for a small loops system in the AR core. We also choose an ensemble of field lines to compare, e.g., the magnetic energy input to the heating per particle along these field lines. Results. We find an enhanced Ohmic dissipation of currents in the corona above areas that also have enhanced upwards-directed Poynting flux. These regions coincide with the regions where hot coronal loops within the AR core are observed. The coronal density plays a role in estimating the coronal temperature due to the generated heat input. A minimum flux density of about 200 Gauss is needed in the photosphere to heat a field line to coronal temperatures of about 1 MK. Conclusions. This suggests that the field-line braiding mechanism provides the coronal energy input and that the Ohmic dissipation of induced currents dominates the coronal heating mechanism