Plane-parallel atmosphere in hydrostatic equilibrium published by Ding & Fang (1989, "A semi-empirical model of sunspots penumbra",
1989A&A...225..204D). Statistical equilibrium for hydrogen model-atom with 12 levels plus continuum. The model is produced by fitting observations of penumbra in 2 lines of H and 5 lines of Ca. The observations were carried out on McMath telescope at Kitt Peak National Observatory. The observed sunspot was small, rounded and close to the disk center. The field strength in the umbra was around 1.25 kG and 560 G in the penumbra.
It is interesting to note their Fig.2 (see it below). In the deep photosphere, the temperature in this model is similar to the temperature in the model of
Yun et al. (1981). However, between the optical depths -3 and -4 it becomes close to the VALC model (
Vernazza et al, 1981).
