  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
