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Abstract We present new period- ϕ 31 -[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-SN V band) and, inaugurally, in the infrared (WISE W1 and W2 bands). Our V -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 RR Lyrae stars have long been popular standard candles, but significant advances in methodology and technology have been made in recent years to increase their precision as distance indicators. We present multiwavelength (optical UBVRcIc and Gaia G, BP, RP; near-infrared JHKs; mid-infrared [3.6], [4.5]) period–luminosity–metallicity (PLZ), period–Wesenheit–metallicity (PWZ) relations, calibrated using photometry obtained from the Carnegie RR Lyrae Program and parallaxes from the Gaia second data release for 55 Galactic field RR Lyrae stars. The metallicity slope, which has long been predicted by theoretical relations, can now be measured in all passbands. The scatter in the PLZ relations is on the order of 0.2 mag, and is still dominated by uncertainties in the parallaxes. As a consistency check of our PLZ relations, we also measure the distance modulus to the globular cluster M4, the Large Magellanic Cloud and the Small Magellanic Cloud, and our results are in excellent agreement with estimates from previous studies.