Tests of stellar model atmospheres by optical interferometry. IV. VINCI interferometry and UVES spectroscopy of Menkar

Aims. We present coordinated near-infrared K-band interferometric and optical spectroscopic observations of the M 1.5 giant α Cet (Menkar) obtained with the instruments VINCI and UVES at the Paranal Observatory. Spherically symmetric PHOENIX stellar model atmospheres are constrained by comparison to our interferometric and spectroscopic data, and high-precision fundamental parameters of Menkar are obtained. Methods. Our high-precision VLTI/VINCI observations in the first and second lobes of the visibility function directly probe the model-predicted strength of the limb darkening effect in the K-band and the stellar angular diameter. The high spectral resolution of UVES of R = 80 000–110 000 allows us to confront in detail observed and model-predicted profiles of atomic lines and molecular bands. Results. We show that our derived PHOENIX model atmosphere for Menkar is consistent with both the measured strength of the limbdarkening in the near-infrared K-band and the profiles of spectral bands around selected atomic lines and TiO bandheads from 370 nm to 1000 nm. At the detailed level of our high spectral resolution, however, noticeable discrepancies between observed and synthetic spectra exist. We obtain a high-precision Rosseland angular diameter of ΘRoss = 12.20 mas ± 0.04 mas. Together with the Hipparcos parallax of 14.82 mas ± 0.83 mas, it corresponds to a Rosseland radius of RRoss = 89 ± 5R� , and together with the bolometric flux based on available spectrophotometry, to an effective temperature of Teff = 3795 K ± 70 K. The luminosity based on these values is