Distribution of coronal heating in a solar active region

Abstract

Aims. We investigate the distribution of heating of coronal loops in a non-flaring solar active region, using a simple electrodynamic model: the random displacements of the loop footpoints, caused by photospheric plasma motions, generate electric potential differences between the footpoints and, as a result, electric currents flow along the loops, producing Ohmic heating. Methods. We implement our model on the closed magnetic field lines in the potential magnetic field extrapolation of an MDI active region magnetogram. For each one of the magnetic field lines, we compute the heating function and obtain the hydrostatic distribution of temperature and pressure. We find that coronal heating is stronger close to the footpoints of the loops and asymmetric along them. We obtain scaling laws that relate both the mean volumetric heating to the loop length, and the heating flux through the loop footpoints to the magnetic field strength at the footpoints. Our results agree with observational data. Results. According to our model, we attribute the observed small coronal-loop width expansion to both the preferential heating of coronal loops of small cross-section variation, and the cross-section confinement due to the random electric currents flowing along the loops. Conclusions. We conclude that our model can be used as a simple working tool in the study of solar active regions.