Alfvén waves in sunspots

The propagation of Alfvén waves in a simple model of a sunspot is considered. The vertical structure near the center of the umbra is modelled realistically, but the horizontal structure is not considered. The full wave equation is solved, without recourse to the WKB approximation. Only wave propagation in the vicinity of the central field line in an axially symmetric spot is examined, and it is assumed that this field line is open. By taking wave reflections into account, we find that the observations of non-thermal motions near the temperature minimum (Beckers, 1976) and in the corona (Beckers and Schneeberger, 1977) are both consistent with an upward-propagating Alfvénic energy flux density of a few times 10⁷ erg cm^–2 s^–1. This flux density is too small to cool the sunspot, but it is large enough to supply the energy requirements of the transition region and corona above a sunspot. This conclusion depends on the assumptions that the observed motions are indeed Alfvénic with periods near 180 s.The National Center for Atmospheric Research is sponsored by the National Science Foundation.