Joint Calibration of RR Lyrae and Type-II Cepheids in Galactic Globular Clusters

RR Lyrae stars (RRL) and type-II Cepheids (T2Cep) are Population-II standard candles, well suited for measuring distances to old, metal-poor stellar populations. We present a joint calibration of their Leavitt laws (period–luminosity–metallicity relations) using Gaia DR3 parallaxes for 93 Galactic globular clusters (GC), based on a sample of 1168 pulsating stars: 802 RRab, 345 RRc, and 21 T2Cep.Our methodology models the period–luminosity relations in Wesenheit magnitude space within a distance-ladder-inspired framework, validated through Markov Chain Monte Carlo (MCMC) sampling. For RRab, we determine the absolute magnitude scale to an accuracy of 0.02 mag (including systematics), corresponding to ~1% in distance. The joint fit also provides highly precise relative calibrations for RRc and T2Cep.In parallel, we derive homogeneous distance estimates for all 93 GC. Clusters hosting multiple types of pulsators offer strong internal consistency checks, enabling robust constraints on both individual and relative Leavitt laws. We find no evidence of parallax bias with distance, confirming that even low signal-to-noise GC parallaxes remain unbiased on average. We further assess model stability across a wide range of assumptions, including photometric, metallicity, and parallax selection variants.This work lays the foundation for incorporating Population-II pulsators as high-accuracy standard candles within the extragalactic distance scale.