RR Lyrae Mid-infrared Period–Luminosity–Metallicity and Period–Wesenheit–Metallicity Relations Based on Gaia DR3 Parallaxes

We present new empirical infrared Period-Luminosity-Metallicity (PLZ) and Period-Wesenheit-Metallicity (PWZ) relations for RR Lyrae based on the latest Gaia EDR3 parallaxes. The are provided in WISE $W1$ $W2$ bands, as well $W(W1, V - W1)$ $W(W2, W2)$ Wesenheit magnitudes. calibrated using a very large sample of Galactic halo field stars with homogeneous spectroscopic [Fe/H] abundances (over 1,000 band), covering broad range metallicities ($-2.5 \lesssim \textrm{[Fe/H]} 0.0$). test performance our PLZ PWZ by determining distance moduli both galactic extragalactic stellar associations: Sculptor dwarf spheroidal galaxy Local Group (finding $\bar{\mu}_{0}=19.47 \pm 0.06$), globular clusters M4 ($\bar{\mu}_{0}=11.16 0.05$) Reticulum cluster Large Magellanic Cloud ($\bar{\mu}_{0}=18.23 0.06$). determined through all internally self-consistent (within $\lesssim$ 0.05 mag) but systematically smaller (by $\sim$ 2-3$\sigma$) than previous literature measurements taken from variety methods/anchors. However, comparison similar recent anchored likewise shows to varying extents modulus PLZ/PWZ relations.