On the Relationship Between Photospheric Footpoint Motions and Coronal Heating in Solar Active Regions

Abstract

Coronal heating theories can be classified as either direct current (DC) or alternating current (AC) mechanisms, depending on whether the coronal magnetic field responds quasi-statically or dynamically to the photospheric footpoint motions. In this paper we investigate whether photospheric footpoint motions with velocities of 1-2 km s–1 can heat the corona in active regions, and whether the corona responds quasi-statically or dynamically to such motions (DC versus AC heating). We construct three-dimensional magnetohydrodynamic models for the Alfvén waves and quasi-static perturbations generated within a coronal loop. We find that in models where the effects of the lower atmosphere are neglected, the corona responds quasi-statically to the footpoint motions (DC heating), but the energy flux into the corona is too low compared to observational requirements. In more realistic models that include the lower atmosphere, the corona responds more dynamically to the footpoint motions (AC heating) and the predicted heating rates due to Alfvén wave turbulence are sufficient to explain the observed hot loops. The higher heating rates are due to the amplification of Alfvén waves in the lower atmosphere. We conclude that magnetic braiding is a highly dynamic process.