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

Wepresent new empirical infrared period–luminosity–metallicity (PLZ) and period–Wesenheit–metallicity (PWZ) relations for RR Lyae based on the latest Gaia Early Data Release 3 (EDR3) parallaxes. The relations are provided in the Wide-field Infrared Survey Explorer (WISE) W1 and W2 bands, as well as in the W(W1, V−W1) and W(W2, V−W2) Wesenheit magnitudes. The relations are calibrated using a very large sample of Galactic halo f ield RRLyrae stars with homogeneous spectroscopic [Fe/H] abundances (over 1000 stars in the W1 band), covering a broad range of metallicities (−2.5  [Fe/H] 0.0). We test the performance of our PLZ and PWZ relations by determining the distance moduli of both galactic and extragalactic stellar associations: the Sculptor dwarf spheroidal galaxy in the Local Group (finding m =  ¯ ¯ 0 11.16 (m =  0.05 0 19.47 0.06 ), the Galactic globular clusters M4 ), and the Reticulum globular cluster in the Large Magellanic Cloud (m =  ¯ 0 18.23 ). The distance moduli determined through all our relations are internally self-consistent (within 0.05 mag) but are systematically smaller (by ∼2–3σ) than previous literature measurements taken from a variety of methods/ anchors. However, a comparison with similar recent RR Lyrae empirical relations anchored with EDR3 likewise shows, to varying extents, a systematically smaller distance modulus for PLZ/PWZ RR Lyrae relations.