Heating of the solar chromosphere and corona by Alfvén wave turbulence

Abstract

A three-dimensional magnetohydrodynamic (MHD) model for the propagation and dissipation of Alfvén waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfvén waves using the reduced MHD approximation. The increase of Alfvén speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheric and chromospheric parts of the flux tube. Part of the wave energy is transmitted through the TR and produces turbulence in the corona. We find that the hot coronal loops typically found in active regions can be explained in terms of Alfvén wave turbulence, provided that the small-scale footpoint motions have velocities of 1-2kms-1 and timescales of 60-200s. The heating rate per unit volume in the chromosphere is two to three orders of magnitude larger than that in the corona. We construct a series of models with different values of the model parameters, and find that the coronal heating rate increases with coronal field strength and decreases with loop length. We conclude that coronal loops and the underlying chromosphere may both be heated by Alfvénic turbulence. © 2011. The American Astronomical Society. All rights reserved.