  Several recent papers have argued for warm, semi-detached, molecular layers
surrounding red giant and supergiant stars, a concept known as a MOLsphere.
Spectroscopic and interferometric analyses have often corroborated this general
picture. Here, we present high-resolution spectroscopic data of pure rotational
lines of water vapor at 12 microns for the supergiant mu Cephei. This star has
often been used to test the concept of molecular layers around supergiants.
Given the prediction of an isothermal, optically thick water-vapor layer in
Local Thermodynamic Equilibrium around the star (MOLsphere), we expected the 12
micron lines to be in emission or at least in absorption but filled in by
emission from the molecular layer around the star. Our data, however, show the
contrary; we find definite absorption. Thus, our data do not easily fit into
the suggested isothermal MOLsphere scenario. The 12 micron lines, therefore,
put new, strong constraints on the MOLsphere concept and on the nature of water
seen in signatures across the spectra of early M supergiants. We also find that
the absorption is even stronger than that calculated from a standard,
spherically symmetric model photosphere without any surrounding layers. A cool
model photosphere, representing cool outer layers is, however, able to
reproduce the lines, but this model does not account for water vapor emission
at 6 microns. Thus, a unified model for water vapor on mu Cephei appears to be
lacking. It does seem necessary to model the underlying photospheres of these
supergiants in their whole complexity. The strong water vapor lines clearly
reveal inadequacies of classical model atmospheres.
