Alfven wave trapping, network microflaring, and heating in solar coronal holes

Abstract

We present new evidence that much of the heating in coronal holes is provided by Alfven waves. This evidence comes from examining the reflection of Alfven waves in an isothermal hydrostatic model coronal hole with open magnetic field. Reflection occurs if the wavelength is as long as of the order of the scale height of the Alfven velocity. For Alfven waves with periods of about 5 minutes, and for realistic density, magnetic field strength, and magnetic field spreading in the model, the waves are reflected back down (trapped) within the model hole if the coronal temperature is only slightly less than 1.0 x 10(6) K, but are not reflected and escape out the top of the model (which escape corresponds to the escape of the Alfven waves into the solar wind) if the coronal temperature is only slightly greater than 1.0 x 10(6) K. Because the spectrum of Alfven waves in real coronal holes is expected to peak around 5 minutes and the temperature is observed to be close to 1.0 x 10(6) K, the sensitive temperature dependence of the trapping suggests that the temperature in coronal holes is regulated by heating by the trapped Alfven waves. In addition, the dependence of the trapping on the spreading rate and leaning of the open magnetic field suggests that polar coronal holes should be cooler at their edges than in their centers, in agreement with the observation in thermal radio emission that polar coronal holes are dimmer at their edges and brighter in their centers. In light of our findings in favor Alfven wave heating in coronal holes, we discuss the heating of the quiet corona in general and the possible role of network microflares in particular. We point out that the network microflares might be the source of the Alfven waves that heat coronal holes.