An Analytic Solar-Wind Model Including Alfven-Wave Turbulence and Heat Conduction into a Radiative Lower Solar Atmosphere

Abstract:

Between the base of the solar corona and the Alfven critical point, the solar-wind density decreases by a factor of approximately one hundred thousand, but the plasma temperature varies by a factor of only a few. In this work, it is shown that such quasi-isothermal behavior is a generic property of the sub-Alfvenic regions of outflows powered by reflection-driven Alfven-wave (AW) turbulence, in which outward-propagating AWs partially reflect, and counter-propagating AWs interact to produce a cascade of fluctuation energy to small scales. Building upon this result, I develop an analytic solar-wind model that accounts for turbulent heating, the wave-pressure force, heat conduction from the corona into the transition region, and radiative cooling from the lower solar atmosphere. The underlying differential equations are integrated analytically, yielding transcendental equations. Approximate analytic solutions to these transcendental equations are obtained in two different limits (weak and strong wave driving), and these solutions are compared with numerical solutions. The model does not assume values for the density or temperature at the coronal base, but determines these quantities self-consistently. The model results agree with some but not all of the observational constraints on the solar-wind mass flux and outflow velocity. The model can be adapted to different magnetic-field models (e.g., the Banaszkiewicz global solar magnetic-field model, or a source-surface model), and it offers a means of quickly predicting the solar-wind mass flux and outflow velocity based solely on the super-radial expansion factor of the magnetic field at the coronal base. The model may also be of use for constructing models of wave-driven outflows from other astrophysical objects.