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We explore the occurrence of dust in M-type Mira atmospheres and its effect on limb darkening under schematic assumptions about dust temperatures and dust particle properties. Dust particles that are thermodynamically coupled to the surrounding gas may form and may affect limb darkening, though only by very little in infrared continuum bandpasses. Dust particles that assume the equilibrium temperature given by the mean intensity of the radiation field only form under rare circumstances. Unexpectedly large or wavelength-dependent infrared continuum radii observed by interferometry are unlikely to be caused by atmospheric dust, except possibly near 1 μm; however, radius measurements may be significantly affected by molecular band contamination. [ABSTRACT FROM AUTHOR]

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 disc 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 that the models generally underestimate the observed variation in visibility with wavelength. We present CLV and visibility spectra for a model that is applicable to the M supergiant α Ori. [ABSTRACT FROM AUTHOR]