Conditions for Photospherically Driven Alfvénic Oscillations to Heat the Solar Chromosphere by Pedersen Current Dissipation

A magnetohydrodynamic model that includes a complete electrical conductivity tensor is used to estimate conditions for photospherically driven, linear, non-plane Alfvénic oscillations extending from the photosphere to the lower corona to drive a chromospheric heating rate due to Pedersen current dissipation that is comparable to the observed net chromospheric radiative loss of ∼10 7 erg cm −2 s −1 . The heating rates due to electron current dissipation in the photosphere and corona are also computed. The wave amplitudes are computed self-consistently as functions of an inhomogeneous background (BG) atmosphere. The effects of the conductivity tensor are resolved numerically using a resolution of 3.33 m. The oscillations drive a chromospheric heating flux F Ch ∼ 10 7 –10 8 erg cm −2 s −1 at frequencies ν ∼ 10 2 –10 3 mHz for BG magnetic field strengths B ≳ 700 G and magnetic field perturbation amplitudes ∼0.01–0.1 B . The total resistive heating flux increases with ν. Most heating occurs in the photosphere. Thermalization of Poynting flux in the photosphere due to electron current dissipation regulates the Poynting flux into the chromosphere, limiting F Ch . F Ch initially increases with ν, reaches a maximum, and then decreases with increasing ν due to increasing electron current dissipation in the photosphere. The resolution needed to resolve the oscillations increases from ∼10 m in the photosphere to ∼10 km in the upper chromosphere and is ∝ν −1/2 . Estimates suggest that these oscillations are normal modes of photospheric flux tubes with diameters ∼10–20 km, excited by magnetic reconnection in current sheets with thicknesses ∼0.1 km.