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

Academic Article

Abstract

  • Between the base of the solar corona at$r=r_\textrm {b}$and the Alfvén critical point at$r=r_\textrm {A}$, where$r$is heliocentric distance, the solar-wind density decreases by a factor$ \mathop > \limits_\sim 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_\textrm {A}$is a generic property of outflows powered by reflection-driven Alfvén-wave (AW) turbulence, in which outward-propagating AWs partially reflect, and counter-propagating AWs interact to produce a cascade of fluctuation energy to small scales, which leads to turbulent heating. Approximating the sub-Alfvénic region as isothermal, I first present a brief, simplified calculation showing that in a solar or stellar wind powered by AW turbulence with minimal conductive losses,$\dot {M} \simeq P_\textrm {AW}(r_\textrm {b})/v_\textrm {esc}^2$,$U_{\infty } \simeq v_\textrm {esc}$, and$T\simeq m_\textrm {p} v_\textrm {esc}^2/[8 k_\textrm {B} \ln (v_\textrm {esc}/\delta v_\textrm {b})]$, where$\dot {M}$is the mass outflow rate,$U_{\infty }$is the asymptotic wind speed,$T$is the coronal temperature,$v_\textrm {esc}$is the escape velocity of the Sun,$\delta v_\textrm {b}$is the fluctuating velocity at$r_\textrm {b}$,$P_\textrm {AW}$is the power carried by outward-propagating AWs,$k_\textrm {B}$is the Boltzmann constant, and$m_\textrm {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_\textrm {b}$from the coronal base into the transition region and momentum deposition by AWs. I solve analytically for$q_\textrm {b}$by balancing conductive heating against internal-energy losses from radiation,$p\,\textrm {d} V$work, and advection within the transition region. The density at$r_\textrm {b}$is determined by balancing turbulent heating and radiative cooling at$r_\textrm {b}$. I solve the equations of the model analytically in two different parameter regimes. In one of these regimes, the leading-order analytic solution reproduces the results of the aforementioned simplified calculation of$\dot {M}$,$U_\infty$, and$T$. Analytic and numerical solutions to the model equations match a number of observations.
  • Status

    Publication Date

  • May 21, 2021
  • Has Subject Area

    Published In

    Keywords

  • astrophysical plasmas
  • space plasma physics
  • Digital Object Identifier (doi)

    Start Page

  • 905870304
  • End Page

  • 905870304
  • Volume

  • 87
  • Issue

  • 3