A Unified Model for Chromospheric and Coronal Heating Driven by Small-Scale Random Footpoint Motions

The solar corona is thought to be heated by dissipation of magnetic disturbances that propagate up from the Sun's convection zone. We propose that a major contribution to the heating comes from disturbances that originate on small spatial scales inside the kilogauss magnetic flux elements in the photosphere. Interactions of convective flows with such flux elements produce Alfven waves that travel upward along the magnetic field lines. When they reach the chromosphere and transition region, the waves reflect, producing counter-propagating waves in the chromosphere. Such counter-propagating waves are subject to well-known nonlinear wave-wave interactions that can lead to the development of turbulence. We simulate the dynamics of Alfven waves using a 3D MHD model of a coronal loop (including the lower atmospheres at the two ends of the loop) and we find that strong turbulence does indeed develop in the lower parts of the flux tube. Some of the wave energy is transmitted into the corona and produces turbulence there. We find that the hot coronal loops typically found in active regions can be explained in terms of Alfven wave turbulence, provided the photospheric footpoint motions have a velocity of 1 - 2 km/s and a correlation time of about 60 seconds. The heating rate in the chromosphere is 2 to 3 orders of magnitude larger than that in the corona, consistent with empirical models of facular regions. We conclude that coronal loops and the underlying chromosphere may both be heated by Alfven wave turbulence.