Period–Luminosity–Colour distribution and classification of Galactic oxygen–rich LPVs

The absolute K magnitudes and kinematic parameters of about 350 oxygen–rich Long–Period Variable stars are calibrated, by means of an up–to–date maxi mum–likelihood method, using Hipparcos parallaxes and proper motions together with radial velocities and, as additional data, periods and colour indices. Four groups, differing by their kinematics and mean magnitudes, are found. For each of them, we also obtain the distributions of magnitude, period and de-reddened colour of the base population, as well as de-biased period–lumi nosity–colour relations and their two–dimensional projections. The SRa semiregulars do not seem to constitute a separate class of LPVs. The SRb appear to belong to two populations of different ages. In a PL diagram, they constitute two evolutionary sequences towards the Mira stage. The Miras of the disk appear to pulsate on a lower–order mode. The slopes of their de-biased PL and PC relations are found to be very different from the ones of the Oxygen Miras of the LMC. This suggests that a significant number of so–called Miras of the LMC are misclassified. This also suggests that the Miras of the LMC do not constitute a homogeneous group, but include a significant proportion of metal–deficient stars, suggesting a relatively smooth star formation history. As a consequence, one may not trivially transpose the LMC period–luminosity relation from one galaxy to the other.