Absolute calibration of near-infrared Period-Luminosity-Metallicity relations for RR Lyrae variables using Gaia EDR3

RR Lyrae stars are sensitive probe for the precision stellar astrophysics and also for the cosmic distance scale thanks to their well-defined near-infrared Period-Luminosity relations (PLRs). These horizontal branch variables can be used for primary calibration of the first-rung of population II distance ladder providing an evaluation of the ongoing tension between Cepheid-Supernovae based Hubble constant and the Planck results. Therefore, absolute calibration of RR Lyrae PLRs is now crucial to complement or test the tip of the red giant branch based distances, and in turn, population II star based Hubble constant measurements. While the pulsation models of RR Lyrae can reproduce most observables, they predict a significant metallicity effect on their JHKs-band PLRs that is inconsistent with so-far limited observational studies. We remedy this inconsistency of metallicity dependence in RR Lyrae PLRs by combining their near-infrared observations in the globular clusters of different mean-metallicities with the new parallaxes from the Gaia early data release 3 (EDR3). Our empirical results on Period-Luminosity-Metallicity (PLZ)relations are consistent with theoretical predictions but the precision of absolute calibrations is still affected by the parallax uncertainties and the systematic zero-point offset present in the Gaia EDR3.