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Abstract We present new period-ϕ₃₁-[Fe/H] relations for first-overtone RRL stars (RRc), calibrated over a broad range of metallicities (−2.5 ≲ [Fe/H] ≲ 0.0) using the largest currently available set of Galactic halo field RRL with homogeneous spectroscopic metallicities. Our relations are defined in the optical (ASAS-SNVband) and, inaugurally, in the infrared (WISEW1andW2bands). OurV-band relation can reproduce individual RRc spectroscopic metallicities with a dispersion of 0.30 dex over the entire metallicity range of our calibrator sample (an rms smaller than what we found for other relations in literature including nonlinear terms). Our infrared relation has a similar dispersion in the low- and intermediate-metallicity range ([Fe/H] ≲ −0.5), but tends to underestimate the [Fe/H] abundance around solar metallicity. We tested our relations by measuring both the metallicity of the Sculptor dSph and a sample of Galactic globular clusters, rich in both RRc and RRab stars. The average metallicity we obtain for the combined RRL sample in each cluster is within ±0.08 dex of their spectroscopic metallicities. The infrared and optical relations presented in this work will enable deriving reliable photometric RRL metallicities in conditions where spectroscopic measurements are not feasible; e.g., in distant galaxies or reddened regions (observed with upcoming Extremely Large Telescopes and the James Webb Space Telescope), or in the large sample of new RRL that will be discovered in large-area time-domain photometric surveys (such as the LSST and the Roman space telescope). 

ABSTRACT Accurate metallicities of RR Lyrae are extremely important in constraining period–luminosity–metallicity (PLZ) relationships, particularly in the near-infrared. We analyse 69 high-resolution spectra of Galactic RR Lyrae stars from the Southern African Large Telescope. We measure metallicities of 58 of these RR Lyrae stars with typical uncertainties of 0.15 dex. All but one RR Lyrae in this sample has accurate ($$\sigma _{\varpi }\lesssim 10{{\ \rm per\ cent}}$$) parallax from Gaia. Combining these new high-resolution spectroscopic abundances with similar determinations from the literature for 93 stars, we present new PLZ relationships in WISE W1 and W2 magnitudes, and the Wesenheit magnitudes W(W1, V − W1) and W(W2, V − W2).