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Reprocessing the Hipparcos data of evolved stars - III. Revised Hipparcos period–luminosity relationship for galactic long-period variable stars

We analyze the K band luminosities of a sample of galactic long-period variables using parallaxes measured by the Hipparcos mission. The parallaxes are in most cases re-computed from the Hipparcos Intermediate Astrometric Data using improved astrometric fits and chromaticity corrections. The K band magnitudes are taken from the literature and from measure- ments by COBE, and are corrected for interstellar and circumstellar extinction. The sample contains stars of several spectral types: M, S and C, and of several variability classes: Mira, semiregular SRa, and SRb. We find that the distribution of stars in the period-luminosity plane is independent of circumstellar chemistry, but that the dierent variability types have dierent P-L distributions. Both the Mira variables and the SRb variables have reasonably well-defined period-luminosity relationships, but with very dierent slopes. The SRa variables are distributed between the two classes, suggesting that they are a mixture of Miras and SRb, rather than a separate class of stars. New period-luminosity re- lationships are derived based on our revised Hipparcos parallaxes. The Miras show a similar period-luminosity relationship to that found for Large Magellanic Cloud Miras by Feast et al. (1989). The maximum absolute K magnitude of the sample is about 8:2 for both Miras and semi-regular stars, only slightly fainter than the expected AGB limit. We show that the stars with the longest periods (P> 400 d) have high mass loss rates and are almost all Mira variables.