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We report the observations in the K band of the red supergiant star alphaOrionis and of the bright giant star alpha Herculis with the FLUOR beamcombinerat the IOTA interferometer. The high quality of the data allows us to estimatelimb-darkening and derive precise diameters in the K band which combined withbolometric fluxes yield effective temperatures. In the case of Betelgeuse, datacollected at high spatial frequency although sparse are compatible withcircular symmetry and there is no clear evidence for departure from circularsymmetry. We have combined the K band data with interferometric measurements inthe L band and at 11.15 micron. The full set of data can be explained if a 2055K layer with optical depths $\tau_{K}=0.060\pm0.003$, $\tau_{L}=0.026\pm0.002$and $\tau_{11.15\mu m}=2.33\pm0.23$ is added 0.33 $R_{\star}$ above thephotosphere providing a first consistent view of the star in this range ofwavelengths. This layer provides a consistent explanation for at least threeotherwise puzzling observations: the wavelength variation of apparent diameter,the dramatic difference in limb darkening between the two supergiant stars, andthe previously noted reduced effective temperature of supergiants with respectto giants of the same spectral type. Each of these may be simply understood asan artifact due to not accounting for the presence of the upper layer in thedata analysis. This consistent picture can be considered strong support for thepresence of a sphere of warm water vapor, proposed by Tsuji (2000) wheninterpreting the spectra of strong molecular lines.Comment: Accepter for publication by Astronomy and Astrophysic

Interferometric observations of the supergiant starsα Orionis andα Herculis with FLUOR at IOTA