7 Conclusion

Using available HIPPARCOS data we apply the LM algorithm to improve the luminosity calibrations in visible, near-infrared and infrared wavelength ranges and to get information about the star and the circumstellar envelope.

According to the galactic population - related to initial mass and metallicity of the stars - and to the circumstellar envelope thickness and expansion, several groups of LPVs are obtained: bright (BD) and disk (disk1) galactic population with bright and expanding envelope, not so young and massive disk population (disk2) divided into 2 groups: one with thin envelope (f) and the other with a bright and expanding envelope (b). A similar separation according to envelope properties is found for the old disk (OD) population. At least some LPVs are found to belong to extended disk (ED) population.

Our results deduced from kinematic properties confirm that the AGB evolution depends on the initial mass of the progenitor in the main sequence. This agrees with the comparison of color-magnitude diagrams using our estimated individual luminosities with theoretical evolutionary tracks. According to the assigned galactic population we can give ranges of age and of the lower limit main sequence mass for each star of our sample. The upper limit of the AGB also depends on ${\cal M}_{\rm ms}$. The difference of the values found in K luminosity limits are consistent with Willson's schematic model related to the mass loss rate and its acceleration by the pulsations: "Stars evolve up the AGB with only moderate mass loss; at $T_{\rm e} \sim 3000$ K Mira pulsation commences, driving the mass loss rate up by at least a factor 10''. The induced dust formation is followed by the stabilization of the K luminosity after the carbon enrichment.

The ultimate aim of this work is to estimate individual K, 12 and 25 absolute magnitudes given, in the annex (available as an electronic table at CDS and in the ASTRID database). This allows us to study simultaneously the stellar properties and the behavior of the circumstellar envelope. The results recalled in the previous paragraph are obtained thanks to the estimated individual luminosities and they mainly concern properties related to the assigned galactic populations. They will be systematically used in another paper (Mennessier et al. 2001) to study implications regarding the physics of LPVs, specifically the simultaneous stellar and circumstellar evolutions along the Asymptotic Giant Branch.

Acknowledgements

This work is supported by the PICASSO program PICS 348 and by the CICYT under contract ESP97-1803 and AYA2000-0937. We thank A. Gomez for fruitful discussions of our first results.