AGB Variables and the Mira Period-Luminosity Relation
  Published data for large amplitude asymptotic giant branch variables in the Large Magellanic Cloud are re-analysed to establish the constants for an infrared (K) period-luminosity relation of the form: Mk=rho[log P-2.38] + delta. A slope of rho=-3.51+/-0.20 and a zero point of delta=-7.15+/-0.06 are found for oxygen-rich Miras (if a distance modulus of 18.39+/-0.05 is used for the LMC). Assuming this slope is applicable to Galactic Miras we discuss the zero-point for these stars using the revised Hipparcos parallaxes together with published VLBI parallaxes for OH Masers and Miras in Globular Clusters. These result in a mean zero-point of delta=-7.25+/-0.07 for O-rich Galactic Miras. The zero-point for Miras in the Galactic Bulge is not significantly different from this value.   Carbon-rich stars are also discussed and provide results that are consistent with the above numbers, but with higher uncertainties. Within the uncertainties there is no evidence for a significant difference between the period-luminosity relation zero-points for systems with different metallicity. 
Patricia A. Whitelock, Michael W. Feast and Floor van Leeuwen