Reprocessing the Hipparcos data of evolved 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 measurements 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 different variability types have different P–L distributions. Both the Mira variables and the SRb variables have reasonably well-defined period–luminosity relationships, but with very different 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 relationships 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