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

Between the base of the solar corona at r = r(b) and the Alfven critical point at r = r(A), where r is heliocentric distance, the solar-wind density decreases by a factor greater than or similar to 10(5), but the plasma temperature varies by a factor of only a few. In this paper, I show that such quasi-isothermal evolution out to r = r(A) 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 brief, simplified calculation showing that in a solar or stellar wind powered by AW turbulence with minimal conductive losses, (M) over dot similar or equal to P-AW(r(b))/v(esc)(2), U-infinity similar or equal to v(esc), and T similar or equal to m(p)v(esc)(2)/[8k(B) ln(v(esc)/delta v(b))], where (M) over dot is the mass outflow rate, U-infinity is the asymptotic wind speed, T is the coronal temperature, v(esc) is the escape velocity of the Sun, delta v(b) is the fluctuating velocity at r(b), P-AW is the power carried by outward-propagating AWs, k(B) is the Boltzmann constant, and m(p) is the proton mass. I then develop a more detailed model of the transition region, corona, and solar wind that accounts for the heat flux q(b) from the coronal base into the transition region and momentum deposition by AWs. I solve analytically for q(b) by balancing conductive heating against internal-energy losses from radiation, p dV work, and advection within the transition region. The density at r(b) is determined by balancing turbulent heating and radiative cooling at r(b). I solve the equations of the model analytically in two different parameter regimes. In one of these regimes, the leading-order analytic solution reproduces the results of the aforementioned simplified calculation of (M) over dot, U-infinity, and T. Analytic and numerical solutions to the model equations match a number of observations.

Automated summary

This paper demonstrates that quasi-isothermal evolution in the solar wind, powered by reflection-driven Alfven-wave turbulence, is a common feature from the base of the solar corona to the Alfven critical point. The mass outflow rate, wind speed, and coronal temperature can be calculated with minimal conductive losses.