The effect of transition region heating on the solar wind from coronal holes

Using a 16 moment solar wind model extending from the chromosphere to 1 AU, we study how the solar wind is affected by direct deposition of energy in the transition region, in both radially expanding geometries and rapidly expanding coronal holes. Energy is required in the transition region to lift the plasma up to the corona, where additional coronal heating takes place. The amount of energy deposited determines the transition region pressure and the number of particles reaching the corona and, hence, how the solar wind energy flux is divided between gravitational potential and kinetic energy. We find that when only protons are heated perpendicularly to the magnetic field in a rapidly expanding coronal hole, the protons quickly become collisionless and therefore conduct very little energy into the transition region, leading to a wind much faster than what is observed. Only by additional deposition of energy in the transition region can a reasonable mass flux and flow speed at 1 AU be obtained. Radiative loss in the transition region is negligible in these low-mass flux solutions. In a radially expanding geometry the same form of coronal heating results in a downward heat flux to the transition region substantially larger than what is needed to heat the upwelling plasma, resulting in a higher transition region pressure, a slow, massive solar wind, and radiative loss playing a dominant role in the transition region energy budget. No additional energy input is needed in the transition region in this case. In the coronal hole geometry the solar wind response to transition region heating is highly nonlinear, and even a tiny input of energy can have a very large influence on the asymptotic properties of the wind. By contrast, the radially expanding wind is quite insensitive to additional deposition of energy in the transition region.