An approximate analytic solution to the coupled problems of coronal heating and solar-wind acceleration

Abstract

Between the base of the solar corona and the Alfven critical point, the solar-wind density decreases by approximately five orders of magnitude, but the temperature varies by a factor of only a few. In this paper, I show that such quasi-isothermal evolution out to the Alfven critical point is a generic property 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, which leads to turbulent heating. Approximating the sub-Alfvenic region as isothermal, I first present a simplified calculation of the mass outflow rate, asymptotic wind speed, and coronal temperature that neglects conductive losses and the wave pressure force. I then develop a more detailed model of the transition region, corona, and solar wind that accounts for the heat flux from the coronal base into the transition region and momentum deposition by AWs. I solve analytically for this heat flux by balancing, within the transition region, conductive heating against internal-energy losses from radiation, pdV work, and advection. The density at the coronal base is determined by locally balancing turbulent heating and radiative cooling. I solve the equations of the model analytically in two different parameter regimes. Analytic and numerical solutions to the model equations agree with a number of observations.