EMPIRICAL EFFECTIVE TEMPERATURES AND ANGULAR DIAMETERS OF STARS COOLER THAN THE SUN

Empirical correlations of stellar surface brightness F(v) as a function of the Johnson's broad-band (V-K)-colour have been investigated by using a selected sample of 44 stars cooler than the Sun with most of angular diameters accurately measured by modern Michelson interferometry. A linear correlation is found to well represent the brightness of G-K stars almost independently of their luminosity class. But the function is split in two fairly different branches of the giants and supergiants in the M spectral range. The calibration of supergiants enhances a tighter linear correlation which also spans the M-type stars. It appears unaffected by interstellar extinction and closely represents the behaviour of several other cool objects such as M-dwarfs, carbon stars and Mira-variables at their maximum phase. The photometric (F(v), V-K)-calibration is applied for inferring stellar angular dimensions and effective temperatures. The major achievement is an effective temperature scale of G through M-type supergiants. The empirical (T(e), V-K)-relationship of such stars is found to be in excellent agreement with the previous (T(e), V-K) calibration for giants in the G-K spectral range and with the narrow-band colour-temperature calibration in the M range. A reliable effective temperature of 3620 +/- 90 K is derived for the well-studied M-supergiant alpha Ori by careful discussion of the actual temperature scale.