On the heat transport in a sunspot penumbra

The penumbra radiates an energy flux that is roughly 75% of the quiet-sun value. One mechanism proposed to bring this flux to the surface is interchange convection of magnetic flux tubes according to which hot flux tubes rise to the surface, cool off their heat by radiation and sink down again. Another way to deposit heat in the penumbral photosphere is by steady upflows along magnetic flux tubes. We discuss these two mechanisms and elaborate on consequences that can be compared with and constrained by observations. We estimate the time scales for variations of the intensity and the magnetic field pattern. By comparing them with the corresponding observed time scales, we find that pure interchange convection is unable to account for the observed penumbral heat flux. Heating the penumbra by steady upflows along magnetic flux tubes, however, turns out to be sufficient to explain the penumbral brightness, under the condition that significant magnetic return flux is present within the penumbra. Associated with the magnetic return flux, downflows within the penumbra should be present, in accordance with recent observational findings of such downflows. Exploring other possible heating mechanisms, we find that dissipation of magnetic energy is negligible, while dissipation of the kinetic energy of the Evershed flow could contribute significantly to the brightness of the penumbra.