Ml. Goodman, CONVECTION DRIVEN HEATING OF THE SOLAR MIDDLE CHROMOSPHERE BY RESISTIVE DISSIPATION OF LARGE-SCALE ELECTRIC CURRENTS .2., Astronomy and astrophysics, 325(1), 1997, pp. 341-351
A generalization of a recently developed MHD model of a proposed heati
ng mechanism for the middle chromosphere is presented. The generalizat
ion consists of including the ideal gas equation of state, allowing th
e temperature to vary with position, and allowing the hydrogen flow ve
locity to vary with height in a specified manner. These generalization
s allow for a self consistent calculation of a temperature profile. Th
e 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 l
ower temperature for a given number density. The solutions presented s
uggest that resistively heated magnetic loops embedded in a much stron
ger, larger scale potential field, and having horizontal spatial scale
s of several thousand kilometers provide the thermal energy necessary
to heat the middle chromosphere on these spatial scales. For these sol
utions the temperature is in the range of 6000 - 8700 K, consistent wi
th the temperature range in the middle chromosphere. The magnetic loop
s have one footpoint region where the field is strongest and directed
mainly upward, and where the heating rates per unit mass and volume ar
e small. The field lines extend upward from this region at the base of
the middle chromosphere, diverge horizontally, and return to a footpo
int region at the base of the middle chromosphere as a weaker, more di
ffuse, mainly downward directed field. In this footpoint region the he
ating rates are also small. The heating rates are largest in the middl
e of the loops. For the magnetic loops considered, the temperature sho
ws little horizontal variation between the footpoint region where the
field is strongest and the heating rates are small, and the region whe
re the heating rates are largest. This suggests that large horizontal
variations in the net radiative loss from heated magnetic loops may no
t always be associated with large horizontal variations in temperature
.