AGB variables and the Mira period-luminosity relation

Published data for large-amplitude asymptotic giant branch variables in the Large Magellanic Cloud (LMC) are re-analysed to establish the constants for an infrared (K) period-luminosity relation of the form M-K = 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 very long baseline interferometry (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.