Magnetohydrodynamic Shock Heating of the Solar Corona

Coronal MHD waves excited by perturbations of magnetic field lines propagate upward, carrying with them the energy from the excitation. Under favorable conditions shocks form, and part of the wave energy is converted to plasma heating and motion. We use numerical simulations to accurately follow the shock formation and subsequent energy release. The model includes an adiabatic energy equation for the explicit evaluation of temperature increases and energy fluxes contributed by the shocks. Transverse, plane-polarized excitations are considered; they can be periodic, as in Alfvén wave trains, or pulsed, as might result from nanoflares. The model is tested with a set of validation runs that produce good agreement with theoretical predictions. Our results show that nonlinear waves moving along large magnetic fields with low plasma β, with field amplitudes comparable to the background field, develop shocks that form important amounts of plasma heating and that mass outflow may occur. Fast and slow magnetoacoustic shocks are generated, each one making its own contribution. Most of the heating takes place in the low corona, but long-range distributed heating still occurs up to heights of several solar radii. The energy fluxes for the stronger cases are sufficient to compensate for thermal and convective losses, consistent with observations. We conclude that large-amplitude MHD shocks in low-β regions could be a viable mechanism for coronal heating and wind acceleration in regions of open magnetic field lines.