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) periodluminosity relation of the form: MK = ρ[logP − 2.38]+ δ. A slope of ρ = −3.51± 0.20 and a zero point of δ = −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 δ = −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.