Tests of stellar model atmospheres by optical interferometry III: NPOI and VINCI interferometry of

Aims: We present a comparison of the visual and NIR intensity profile of the M0 giant gamma Sagittae to plane-parallel ATLAS 9 as well as to plane-parallel & spherical PHOENIX model atmospheres. Methods: We use previously described visual interferometric data obtained with the NPOI in July 2000. We apply the recently developed technique of coherent integration, and thereby obtain visibility data of more spectral channels and with higher precision than before. In addition, we employ new measurements of the K-band diameter of gamma Sagittae obtained with the instrument VINCI at the VLTI in 2002. Results: The spherical PHOENIX model leads to a precise definition of the Rosseland angular diameter and a consistent high-precision diameter value for our NPOI and VLTI/VINCI data sets of Theta_Ross=6.06 pm 0.02 mas, with the Hipparcos parallax corresponding to R_Ross=55 pm 4 R_sun, and with the bolometric flux corresponding to an effective temperature T_eff=3805 pm 55 K. Our visual visibility data close to the first minimum and in the second lobe constrain the limb-darkening effect and are generally consistent with the model atmosphere predictions. The visual closure phases exhibit a smooth transition between 0 and pi. Conclusions: The agreement between the NPOI and VINCI diameter values increases the confidence in the model atmosphere predictions from optical to NIR wavelengths as well as in the calibration and accuracy of both interferometric facilities. The consistent night-by-night diameter values of VINCI give additional confidence in the given uncertainties. The closure phases suggest a slight deviation from circular symmetry, which may be due to surface features, an asymmetric extended layer, or a faint unknown companion.