HEATING OF THE SOLAR MIDDLE CHROMOSPHERIC NETWORK AND INTERNETWORK BYLARGE-SCALE ELECTRIC CURRENTS IN WEAKLY IONIZED MAGNETIC ELEMENTS

A two-dimensional, dissipative magnetohydrodynamic model is used to ar gue that a major source of in situ heating for the solar middle chromo sphere is the resistive dissipation of large-scale electric currents f lowing in magnetic elements. A magnetic element is an arch-shaped magn etic field configuration consisting of a central region of horizontall y localized, mainly vertical magnetic field based in the photosphere, with field lines that diverge horizontally with increasing height, ext end into the middle chromosphere, and then return to the photosphere a s a relatively diffuse, weaker field. The currents that flow in these elements are carried by protons, and are large scale in that their sca le height is hundreds of kilometers in the network and thousands of ki lometers in the internetwork. Solutions to the model demonstrate that the resistive dissipation of large-scale electric currents flowing ort hogonal to the magnetic held in magnetic elements embedded in a weakly ionized, strongly magnetized hydrogen gas may generate all of the the rmal energy necessary to heat the middle chromosphere. The magnetic fi eld is computed self-consistently with the electric field, pressure, a nd hydrogen and proton densities. Solutions to the model suggest that magnetic elements with horizontal extents up to several arcseconds may be confined to, and heat, the chromospheric network, while elements w ith the largest horizontal extents may span and heat the internetwork and be the building blocks of the chromospheric magnetic canopy. The m odel predicts that the heating rate per unit mass (q) is independent o f height, peaked near but horizontally displaced from the center of a magnetic element, and for realistic model input parameters has an aver age value computed over the base area of the element close to the valu e 4.5 x 10(9) ergs g(-1) s(-1) predicted by semiempirical models of th e chromosphere that also predict that q is independent of height in th e middle chromosphere. The model predicts that the heating rate per un it volume is peaked near the horizontal midpoint of a magnetic element where the field is mainly horizontal. The model predicts that both he ating rates are zero at the center and outer boundary of a magnetic el ement where the field is vertical. These model predictions for the spa tial localization of the heating rates are consistent with observation s that regions of enhanced emission are near but horizontally displace d from regions of vertical, high-magnitude magnetic field.