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

ABSTRACTWe discuss the wavelength dependence of angular diameters of M giants from an observationalperspective. Observers cannot directly measure an optical-depth radius for a star, despite thisbeing a common theoretical definition. Instead, they can use an interferometer to measure thesquare 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-MiraM giant models. We use the terms “CLV spectra” and “visibilit y spectra” for these plots. Wediscuss a model-predicted extreme limb-darkening effect (also called the narrow-bright-coreeffect) in very strong TiO bands which can lead to a misinterpretation of the size of a star inthese bands. We find no evidence as yet that this effect occurs in real stars. Our CLV spectracan explain the similarity in visibilities of R Dor (M8IIIe) that have been observed recentlydespite the use of two different passbands. We compare several observations with models andfind 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 α Ori.Key words: techniques:interferometric,stars: fundamentalparameters, stars: variables: Miras,stars: individual: R Dor, α Ori1 INTRODUCTIONThe radius of a star is considered to be one of its fundamen-tal properties. Stellar radii may be determined from interfer-ometric observations of stellar angular diameters, but starsdo not necessarily appear to us as sharp-edged disks of uni-formbrightness and size. Rather, two effects may be present:limb-darkeningwhich tapers the surface brightness down to-wards the star’s edge and line absorption which changes thestar’s apparent size. Both effects depend on the wavelengthof the observation and are particularly significant in M gi-ants.To determine the radii of M giants from interferomet-ric data, observers have relied upon comparisons with mod-els of the centre-to-limb variation (CLV) of the intensity ofthe stellar disk. The simplest CLV, a uniform disk, is oftenused for this. Alternatively we can use CLVs derived fromappropriate model photospheres of late M giants, since thisprocedure can lead to improvements in these models and agreater understandingof these stars. The model-photosphereCLVs are defined for a particular filter or spectral passband