Small-scale Flux Emergence, Coronal Hole Heating, and Flux-tube Expansion: A Hybrid Solar Wind Model

Extreme-ultraviolet images from the Solar Dynamics Observatory often show looplike fine structure to be present where no minority-polarity flux is visible in magnetograms, suggesting that the rate of ephemeral region (ER) emergence inside "unipolar" regions has been underestimated. Assuming that this rate is the same inside coronal holes as in the quiet Sun, we show that interchange reconnection between ERs and open field lines gives rise to a solar wind energy flux that exceeds 10$^5$ erg cm$^{-2}$ s$^{-1}$ and that scales as the field strength at the coronal base, consistent with observations. In addition to providing Ohmic heating in the low corona, these reconnection events may be a source of Alfv{\'e}n waves with periods ranging from the granular timescale of $\sim$10 minutes to the supergranular/plume timescale of many hours, with some of the longer-period waves being reflected and dissipated in the outer corona. The asymptotic wind speed depends on the radial distribution of the heating, which is largely controlled by the rate of flux-tube expansion. Along the rapidly diverging flux tubes associated with slow wind, heating is concentrated well inside the sonic point (1) because the outward conductive heat-flux density and thus the outer coronal temperatures are reduced, and (2) because the net wave energy flux is dissipated at a rate proportional to the local Alfv{\'e}n speed. In this "hybrid" solar wind model, reconnection heats the lower corona and drives the mass flux, whereas waves impart energy and momentum to the outflow at greater distances.