The Mira-based distance to the Galactic centre

Mira variables are useful distance indicators, due to their high luminosities and well-defined period-luminosity relation. We select 1863 Miras from SAAO and MACHO observations to examine their use as distance estimators in the Milky Way. We measure a distance to the Galactic centre of $R_0 = 7.9 \pm 0.3$ kpc, which is in good agreement with other literature values. The uncertainty has two components of $\sim$0.2 kpc each: the first is from our analysis and predominantly due to interstellar extinction, the second is due to zero-point uncertainties extrinsic to our investigation, such as the distance to the Large Magellanic Cloud (LMC). In an attempt to improve existing period-luminosity calibrations, we use theoretical models of Miras to determine the dependence of the period-luminosity relation on age, metallicity, and helium abundance, under the assumption that Miras trace the bulk stellar population. We find that at a fixed period of $\log P = 2.4$, changes in the predicted $K_s$ magnitudes can be approximated by $\Delta M_{Ks} \approx -0.109(\Delta \rm{[Fe/H]}) + 0.033( {\Delta}t/\rm{Gyr}) + 0.021 ({\Delta}Y/0.01)$, and these coefficients are nearly independent of period. The expected overestimate in the Galactic centre distance from using an LMC-calibrated relation is $\sim$0.3 kpc. This prediction is not validated by our analysis; a few possible reasons are discussed. We separately show that while the predicted color-color diagrams of solar-neighbourhood Miras work well in the near-infrared, though there are offsets from the model predictions in the optical and mid-infrared.