The Heating of Coronal Loops in Solar Active Regions

The active region corona is believed to be heated by magnetic disturbances that propagate into the corona from the convection zone below. A reduced magnetohydrodynamic (MHD) model of Alfven waves in a coronal loop is presented. The waves are launched in the photosphere from a collection of kilogauss flux tubes, and they reflect at various positions along the loop, leading to counter-propagating waves and turbulence. It is found that turbulent Alfv en waves can produce only enough heat to maintain a peak temperature of about 2.5 MK, less than the temperatures typically observed in active regions (similar to 4 MK). We consider an alternative model in which the flux tubes are subject to slow random footpoint motions, but we find that such braiding motions produce less heating than the waves inside the flux tubes. Therefore, models of coronal heating based on small-scale random footpoint motions cannot readily explain the observed high temperatures loops; more energetic "nanoflare" heating events are required. We suggest that such strong heating events may be produced by disturbances associated with flux emergence and large-scale non-potential fields.