Reprocessing the Hipparcos data for 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 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 a little fainter than the expected AGB limit. We show that the stars with the longest periods (P>400d) have high mass loss rates and are almost all Mira variables.