Metallicity of Galactic RR Lyrae from Optical and Infrared Light Curves: I. Period-Fourier-Metallicity Relations for Fundamental Mode RR Lyrae

We present newly-calibrated period-$\phi_{31}$-[Fe/H] relations for fundamental mode RR Lyrae stars in the optical and, for the first time, mid-infrared. This work's calibration dataset provides the largest and most comprehensive span of parameter space to date with homogeneous metallicities from $-3<\textrm{[Fe/H]}<0.4$ and accurate Fourier parameters derived from 1980 ASAS-SN ($V$-band) and 1083 WISE (NEOWISE extension, $W1$ and $W2$ bands) RR Lyrae stars with well-sampled light curves. We compare our optical period-$\phi_{31}$-[Fe/H] with those available in the literature and demonstrate that our relation minimizes systematic trends in the lower and higher metallicity range. Moreover, a direct comparison shows that our optical photometric metallicities are consistent with both those from high-resolution spectroscopy and globular clusters, supporting the good performance of our relation. We found an intrinsic scatter in the photometric metallicities (0.41 dex in the $V$-band and 0.50 dex in the infrared) by utilizing large calibration datasets covering a broad metallicity range. This scatter becomes smaller when optical and infrared bands are used together (0.37 dex). Overall, the relations derived in this work have many potential applications, including large-area photometric surveys with JWST in the infrared and LSST in the optical.