On the luminosity criteria relative to late-type stars.

Summary. In this paper we study three luminosity criteria relating to late-type giants: those of Spite (1966), revised by da Silva and Grenier (1976), of Hansen and Kjaergaard (1971) and of Yoss and Lutz (1971). As an independent method of calibration, we used the method of statistical parallaxes as worked out by Heck (1975), using only positions, proper motions, radial velocities and apparent magnitudes. In this technique, the tests on the spatial velocities permit to constitute homogeneous samples according to the asymmetrical drift and the numerical experiments allow the estimation of the bias and precision of the results. We examined particularly a sample of stars measured in Spite's system which contains late-type stars and a 5 p of stars observed in the direction of the galactic rotation. For the giant stars, we found the following mean deviations (per unit of volume): AMv (Spite) -0.79 (+ 0.28), AMv (Hansen and Kjaergaard) = -0.72 (+- 0.28), AMv (Yoss and Lutz)=0.18 (10.27). The two first criteria underestimate significantly the luminosity. We showed that our result obtained for Yoss and Lutz's sample is not in contradiction with their discussion in Yoss and Lutz (1974) and that all results are coherent. A correlation between the individual calculated absolute magnitudes and the statistical ones was also searched for. Extrapolation effect and abundance effect are investigated as to their influence on Mv and on the kinematical properties. The influence of temperature and of age on the kinematical properties are also studied. The existence of the radial chemical gradient of the galaxy in the solar neighbourhood as described by Mayor (1976) is confirmed. Key words: late-type stars luminosity criteria stellar kinematics stellar age metallic abundance