QUANTITATIVE SPECTRAL CLASSIFICATION OF GALACTIC DISC K-M STARS FROM SPECTROPHOTOMETRIC MEASUREMENTS

New spectral observations for 47 southern galactic red supergiants obt ained with the new RUBIKON spectrophotometer (developed at the Astrono misches Institut der Ruhr-Universitat Bochum) at the Bochum 61-cm tele scope on La Silla are presented. The spectra range from 4800 to 7700 A ngstrom and their resolution is 10 Angstrom. The mean error of absolut e fluxes is 0.028 mag and that of relative fluxes 0.021 mag. The spect ra will be available at the Strasbourg Stellar Database (CDS). Togethe r with data taken from recently published spectral catalogues, the new observations have been used to define spectral indices as measures of the strengths of the following features: Fe I + TiO alpha(1), Mgb + T iO alpha(0), NaD + TiO gamma'(1), TiO gamma'(0) and TiO gamma(1) syste ms. The indices have been checked against errors introduced by reducti ons, interstellar reddening and different resolutions of different spe ctral catalogues, and have been found to be very insensitive to all th ese effects. Therefore, different catalogues may be combined without a ny loss of accuracy and homogeneity. The mean error of a single index has been found to be 0.011 mag. For stars from K4 to M7, a strong temp erature dependence is found for all indices. For the Fe I + TiO and es pecially the Mgb + TiO features, a strong dependence on luminosity has also been observed. These indices therefore have been combined to for m a luminosity index, while the others together form a spectral index. The combined indices have been calibrated in terms of MK data using t he stepwise linear regression technique, and may be used for quantitat ive two-dimensional spectral classification of late K- and M-type star s. 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 (which, e.g., for an M4 gian t correspond to an uncertainty of 0.1 of spectral subtype and 0.3 of l uminosity class). This may be explained by the uncertainty of the orig inal MK classifications and the variability of some programme stars.