HEATING OF THE SOLAR MIDDLE CHROMOSPHERE BY LARGE-SCALE ELECTRIC CURRENTS

A global resistive, two-dimensional, time-dependent magnetohydrodynami c (MHD) model is used to introduce and support the hypothesis that the quiet solar middle chromosphere is heated by resistive dissipation of large-scale electric currents which flu most of its volume. The scale height and maximum magnitude of the current density are 400 km and 31 .3 mA m(-2), respectively. The associated magnetic field is almost hor izontal, has the same scale height as the current density, and has a m aximum magnitude of 153 G. The current is carried by electrons flowing across magnetic field lines at 1 m s(-1). The resistivity is the elec tron contribution to the Pedersen resistivity for a weakly ionized, st rongly magnetized, hydrogen gas. The model does not include a driving mechanism. Most of the physical quantities in the model decrease expon entially with time on a resistive timescale of 41.3 minutes. However, the initial values and spatial dependence of these quantities are expe cted to be essentially the same as they would be if the correct drivin g mechanism were included in a more general model. The heating rate pe r unit mass is found to be 4.5 x 10(9) ergs g(-1) s(-1), independent o f height and latitude. The electron density scale height is found to b e 800 km. The model predicts that 90% of the thermal energy required t o heat the middle chromosphere is deposited in the height range 300-76 0 km above the temperature minimum. It is shown to be consistent to as sume that the radiation rate per unit volume is proportional to the ma gnetic energy density, and it then follows that the heating rate per u nit volume is also proportional to the magnetic energy density. MHD wa ves, bulk flow normal the magnetic field, and magnetic flux tubes emer ging from the photosphere into the overlying chromosphere are briefly discussed as possible driving mechanisms for establishing and maintain ing the current system. The case in which part or all of the current i s carried by protons and metal ions, and the contribution of electron- proton scattering to the current are also considered, with the conclus ion that these effects do not change the qualitative predictions of th e model, but probably change the quantitative predictions slightly, ma inly by increasing the maximum magnitude of the current density and ma gnetic held to at most similar to 100 mA m(-2) and similar to 484 G, r espectively. The heating rate per unit mass, current density scale hei ght, magnetic held scale height, temperatures, and pressures are uncha nged or are only slightly changed by including these additional effect s due to protons and ions.