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The structures of the outer atmospheres of red giants are very complex. Thenotion of large optically thick molecular spheres around the stars (MOLspheres)has been invoked in order to explain e.g. spectro-interferometric observations.However, high-resolution spectra in the mid-IR do not easily fit into thispicture. They rule out any large sphere of water vapour in LTE surrounding redgiants. Our aim here is to investigate high-resolution, mid-infrared spectrafor a range of red giants, from early-K to mid M. We have recorded 12 micronsspectra of 10 well-studied bright red giants, with TEXES on the IRTF. We findthat all giants in our study cooler than 4300 K, spanning a range of effectivetemperatures, show water absorption lines stronger than expected. The strengthsof the lines vary smoothly with spectral type. We identify several spectralfeatures in the wavelength region that undoubtedly are formed in thephotosphere. From a study of water-line ratios of the stars, we find that theexcitation temperatures, in the line-forming regions, are several hundredKelvin lower than expected from a classical photospheric model. This couldeither be due to an actually lower temperature structure in the outer regionsof the photospheres caused by, for example, extra cooling, or due to non-LTElevel populations, affecting the source function and line opacities. We havedemonstrated that these diagnostically interesting water lines are a generalfeature of red giants across spectral types, and we argue for a generalexplanation of their formation rather than explanations requiring specificproperties. Since the water lines are neither weak (filled in by emission) norappear in emission, as predicted by LTE MOLsphere models in their simplestforms, the evidence for the existence of such large optically-thick, molecularspheres enshrouding the stars is weakened. (abbreviated)

Systematic trend of water vapour absorption in red giant atmospheres revealed by high resolution TEXES 12 micron spectra