Quantitative spectral classification of galactic disc K-M stars from spectrophotometric measurements

New spectral observations for 47 southern galactic red supergiants obtained with the new RUBIKON spectrophotometer at the Bochum 61-cm telescope on La Silla are presented. The spectra range from 4800 to 7700 A, and their resolution is 10 A. The mean error of absolute fluxes is 0.028 mag and that of relative fluxes 0.021 mag. For stars from K4 to M7, a strong temperature dependence is found for all spectral indices. For the Fe I + TiO and especially the Mgb + TiO features, a strong dependence on luminosity has also been observed. These indices therefore have been combined to form a luminosity index, while the others together form a spectral index. The combined indices have been calibrated in terms of MK data using the stepwise linear regression technique, and may be used for quantitative 2D spectral classification of late K- and M-type stars. The mean error of the classification is 0.6 of spectral subtype and 0.8 of luminosity class, which is much higher than would be expected from the uncertainty of the indices alone. This may be explained by the uncertainty of the original MK classifications and the variability of some program stars. (Author)