Convection driven heating of the solar middle chromosphere by resistive dissipation of large scale electric currents .2.

A generalization of a recently developed MHD model of a proposed heating mechanism for the middle chromosphere is presented. The generalization consists of including the ideal gas equation of state, allowing the temperature to vary with position, and allowing the hydrogen flow velocity to vary with height in a specified manner. These generalizations allow for a self consistent calculation of a temperature profile. The variation of the flow velocity with height generates a component of the inertial force which adds to the vertical gradient of the thermal pressure in supporting the plasma against gravity. This allows for a lower temperature for a given number density. The solutions presented suggest that resistively heated magnetic loops embedded in a much stronger, larger scale potential field, and having horizontal spatial scales of several thousand kilometers provide the thermal energy necessary to heat the middle chromosphere on these spatial scales. For these solutions the temperature is in the range of 6000 - 8700 K, consistent with the temperature range in the middle chromosphere. The magnetic loops have one footpoint region where the field is strongest and directed mainly upward, and where the heating rates per unit mass and volume are small. The field lines extend upward from this region at the base of the middle chromosphere, diverge horizontally, and return to a footpoint region at the base of the middle chromosphere as a weaker, more diffuse, mainly downward directed field. In this footpoint region the heating rates are also small. The heating rates are largest in the middle of the loops. For the magnetic loops considered, the temperature shows little horizontal variation between the footpoint region where the field is strongest and the heating rates are small, and the region where the heating rates are largest. This suggests that large horizontal variations in the net radiative loss from heated magnetic loops may not always be associated with large horizontal variations in temperature.