Quantitative Magnetohydrodynamic Modeling of the Solar Transition Region

Abstract

The transition region (TR) is assumed to be a collision-dominated plasma. The dissipation and transport of energy in such a plasma is accurately described by the classical transport coefficients, which include the electrical and thermal conductivity, viscosity, and thermoelectric tensors. These tensors are anisotropic and are functions of local values of temperature, density, and magnetic field strength. The transport coefficients are valid for all magnetic field strengths and so may be used to study the physics of weakly as well as strongly magnetized regions of the TR. They may be used in an MHD model to obtain a self-consistent, realistic description of the TR. The physics of kinetic processes is included in the MHD model through the transport coefficients. As a first step in studying heating and cooling processes in the TR in a realistic, quantitative manner, a 1.5 dimensional, steady state MHD model with a specified temperature profile is developed. The momentum equation includes the inertial, pressure, magnetic, and gravitational forces. Ohm's law includes the exact expressions for the electrical conductivity and thermoelectric tensors. It is found that the contribution of the dissipation of large-scale electric currents to in situ heating of the TR is negligible, but that thermal energy flowing into the TR from the corona can provide the energy required to heat the TR. The possibility that significant in situ heating of the TR takes place through viscous dissipation or small-scale electric current dissipation such as may occur in current sheets or filaments is discussed, although these processes are not described by the model. The importance of thermoelectric and electron pressure gradient effects in Ohm's law, and in determining the electron heat flux, is demonstrated. Results of the model suggest that the force-free approximation is not valid over most of the TR. Justification for assuming that the TR is collision dominated is presented. In particular, a self-consistent calculation of the ratio of the electric field parallel to the magnetic field to the Dreicer electric field yields a value 10-3, which suggests that anomalous transport processes are not important. The necessity of using a realistic description of transport processes in modeling heating mechanisms in the solar atmosphere is stressed.