The Infrared Ca II lines in Sunspot Umbrae

We present an empirical working model for sunspot umbrae which equally describes observed continuum intensities and line profiles. The wings of the infrared Ca II lines depend sensitively on the temperature gradient at -0.6 < log(tau-0.5) < +0.3 but not essentially on the absolute value of T. These lines are observed to remain almost unchanged from photosphere to umbra and are thus insensitive to parasitic light. It is also shown that the infrared K I 7699 line is suitable for umbral spectroscopy since it is not seriously blended, its continuum is well defined and it is less influenced by parasitic light as compared to lines in the visible spectrum, due to the smaller umbral contrast. Calculations show that the umbral gradient dT/d(tau), required to fit the Ca II triplet lines, strongly conflicts with the observed profiles of K I 7699, NaD2 and Fe I 5434 (g=0), even when assuming vanishing Fe II lines for a maximum correction of parasitic light. It is shown that this discrepancy from the different line profiles may be removed by adopting an opacity enhancement as introduced by Zwaan (1974) from a discussion of continuum contrasts alone. The finally proposed umbral working model is very close to a scaled model of the quiet sun with T(eff)= 4000 K thus resembling a M0 rather than a K5 stellar atmosphere