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Abstract Utilizing Zwicky Transient Facility (ZTF) data and existing RR Lyrae stars (RRLs) catalogs, this study achieves the first calibration of theP−ϕ₃₁−R₂₁− [Fe/H] andP−ϕ₃₁−A₂−A₁− [Fe/H] relations in the ZTF photometric system for RRab and RRc stars. We also recalibrate the period–absolute magnitude–metallicity (PMZ) and period–Wesenheit–metallicity (PWZ) relations in the ZTFgribands for RRab and RRc stars. Based on nearly 4100 stars with precise measurements ofP,ϕ₃₁,A₂, andA₁, and available spectroscopic metallicity estimates, the photometric metallicity relations exhibit strong internal consistency across different bands, supporting the use of a weighted averaging method for the final estimates. The photometric metallicity estimates of globular clusters based on RR Lyrae members also show excellent agreement with high-resolution spectroscopic measurements, with a typical scatter of 0.15 dex for RRab stars and 0.14 dex for RRc stars, respectively. Using hundreds of local RRLs with newly derived photometric metallicities and precise Gaia Data Release 3 parallaxes, we establish the PMZ and PWZ relations in multiple bands. Validation with globular cluster RR Lyrae members reveals typical distance errors of 3.1% and 3.0% for the PMZ relations, and 3.1% and 2.6% for the PWZ relations for RRab and RRc stars, respectively. Compared to PMZ relations, the PWZ relations are tighter and almost unbiased, making them the recommended choice for distance calculations. We present a catalog of 73,795 RRLs with precise photometric metallicities; over 95% of them have accurate distance measurements. Compared to Gaia DR3, approximately 25,000 RRLs have precise photometric metallicities and distances derived for the first time. 

ABSTRACT We employ a sample of 135 873 RR Lyrae stars (RRLs) with precise photometric-metallicity and distance estimates from the newly calibrated P–ϕ31–R21–[Fe/H] and Gaia G band P–R21–[Fe/H] absolute magnitude–metallicity relations of Li et al., combined with available proper motions from Gaia EDR3, and 6955 systemic radial velocities from Gaia DR3 and other sources, in order to explore the chemistry and kinematics of the halo of the Milky Way (MW). This sample is ideally suited for characterization of the inner- and outer-halo populations of the stellar halo, free from the bias associated with spectroscopically selected probes, and for estimation of their relative contributions as a function of Galactocentric distance. The results of a Gaussian mixture model analysis of these contributions are broadly consistent with other observational studies of the halo, and with expectations from recent MW simulation studies. We apply the hdbscan clustering method to the specific energies and cylindrical actions (E, Jr, Jϕ, Jz), identifying 97 dynamically tagged groups (DTGs) of RRLs, and explore their associations with recognized substructures of the MW. The precise photometric-distance determinations (relative distance errors on the order of 5 per cent or better), and the resulting high-quality determination of dynamical parameters, yield highly statistically significant (low) dispersions of [Fe/H] for the stellar members of the DTGs compared to random draws from the full sample, indicating that they share common star-formation and chemical histories, influenced by their birth environments.