Energy transport in intense flux tubes on the sun. I - Equilibrium atmosphere

Abstract

Model calculations are performed to determine self-consistently the equilibrium atmosphere in an intense flux tube. The generalization of the Eddington approximation to three dimensions is used to develop a zeroth-order transfer equation valid for an axisymmetric thin flux tube. Convection is included by using a mixing length formalism and a parameter to incorporate its inhibition by the magnetic field. The results suggest that the temperature on the axis of a flux tube is lower than the ambient medium at the same geometric level. At equal optical depths, however, the temperature in the tube is higher. At an optical depth of unity, the temperature difference is typically about 500 K. In the optically thin layers, horizontal exchange of heat is efficient and the temperature inside the tube is insensitive to the magnetic field strength. The equilibrium stratification is almost independent of the degree of convective inhibition.