A new sunspot umbral model and its variation with the solar cycle

Semiempirical model atmospheres are presented for the darkest parts of large sunspot umbrae, regions have called umbral cores. The approach is based on general-purpose computational procedures that are applicable to different types of stellar atmospheres. It is shown that recent umbral intensity measurements of the spectral energy distribution may be accounted for by an umbral core atmospheric model that varies with time during the solar cycle; the observed center-limb variation can be accounted for by the properties of the model. Three umbral core models are presented, corresponding to the early, middle, and late phases of the solar cycle. These three models also may be regarded as having the properties of dark, average, and bright umbral cores respectively. The effects of atomic, opacity, and abundance data uncertainties on the model calculations are briefly discussed. For comparison, a new reference model for the average quiet solar photosphere is given.