The Deep Layers of Sunspot Umbrae
  We model the deepest observable layers of dark sunspot umbral atmospheres in terms of an empirical model which equally describes observed near infrared continuum intensities and line profiles. We use the umbral continuum intensity at 1.67 nm and the three C I lines at 1,6888, 1,7449 and 1,7456 nm to model the deep layers near the minimum of H- absorption. We find that a radiative equilibrium stratification yields the best compromise between continuum and C I line observations. We determine the effective temperature from the umbral and photospheric flux ratio by down-scaling the monochromatic photospheric flux with the umbral contrast for each frequency. The thus obtained monochromatic umbral flux and the photospheric one are integratied over the whole frequency range, yielding the ratio of total umbral and photospheric flux, which gives 3560 K < T_eff < 3780 K. We assume for our model M3 T_eff=3750 K and fit M3 to the theoretical model by Meyer et al. (1974). Comparison of the model's 'nabla' gradient with the adiabatic one shows that umbral convection, if existing at all, can only occur at considerably deeper layers than in the photosphere. 
Goetz Stellmacher and Eberhard Wiehr
astro-ph.SR