Wavelength dependence of angular diameters of M giants: an observational perspective

We discuss the wavelength dependence of angular diameters of M giants from an observational perspective. Observers cannot directly measure an optical-depth radius for a star, despite this being a common theoretical definition. Instead, they can use an interferometer to measure the square of the fringe visibility. We present new plots of the wavelength-dependent centre-to-limb variation (CLV) of intensity of the stellar disk as well as visibility for Mira and non-Mira M giant models. We use the terms ``CLV spectra'' and ``visibility spectra'' for these plots. We discuss a model-predicted extreme limb-darkening effect (also called the narrow-bright-core effect) in very strong TiO bands which can lead to a misinterpretation of the size of a star in these bands. We find no evidence as yet that this effect occurs in real stars. Our CLV spectra can explain the similarity in visibilities of R Dor (M8IIIe) that have been observed recently despite the use of two different passbands. We compare several observations with models and find the models generally under-estimate the observed variation in visibility with wavelength. We present CLV and visibility spectra for a model that is applicable to the M supergiant alpha Ori.