A homogeneous temperature calibration for K and M giants with an extension to the coolest stars

In this paper we present a new estimate of the effective temperatures of 32 giant stars in the spectral range K0 to M10. The sample includes also 4 Mira stars. The temperatures are based on a homogeneous set of angular diameters obtained by our group by the technique of lunar occultations, and using a photometric and spectroscopic coverage with a combination of original measurements and literature data. Most of this basic material had been presented in previous papers, but in the present work we derive improved effective temperatures by using for the first time a grid of numerical center-to-limb darkening models. We use this revision to derive a new calibration of the effective temperature of K and M giant stars, which has the advantage of being based on only one, highly homogeneous set of data (while previous calibrations often used mixed data sets). The resulting calibration is extended to the coolest stars, reaching for the first time M9 for the non-Mira stars, and M10 for the Mira stars. In this latter case the calibration does not account for pulsation phase variations and is only tentative. In the region of overlap with previously existing calibrations, we find a largely satisfactory agreement, although some differences exist and are discussed. In particular, it appears that the calibration of the effective temperature of cool Mira stars requires additional observational as well as theoretical effort. Seven of the stars in our sample appear to exhibit an effective temperature that departs significantly from the mean relation (≈ 900K cooler between K1 and M8), and no simple explanation in terms of possible bias or experimental error could be found.