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

TL;DR

This paper presents an approximate analytic solution to the coupled problems of coronal heating and solar-wind acceleration, showing that quasi-isothermal outflows driven by Alfvén wave turbulence are a generic property, and matches several observations.

Contribution

It develops an analytical model for coronal heating and solar wind acceleration incorporating wave reflection, turbulence, and heat flux, providing insights into the quasi-isothermal nature of the outflows.

Findings

Model agrees with observed solar wind properties

Analytical solutions match numerical simulations

Highlights the role of Alfvén wave turbulence in heating

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.