Abstract:
RR Lyrae stars are pulsating variables crucial for distance determination and galactic structure studies. Metallicities of fundamental-mode (RRab) RR Lyrae stars are commonly derived from photometry using empirical relations involving the Fourier parameter ϕ31 and the pulsation period. We present a new, calibrated G-band relationship between pulsation period P, Fourier parameter ϕ31, and metallicity [Fe/H] for galactic RR Lyrae stars from the Gaia survey. A set of 72 fundamental mode RR Lyrae stars were identified for deriving the relation in the G-band after visual examination of their light curves. Unlike recent large-scale calibrations, our relation prioritizes calibration purity by anchoring exclusively to a homogeneously analyzed sample of high-resolution spectroscopic metallicities from the literature. Our best fit relation is [Fe/H] = (−6.93 ± 0.58) − (6.04 ± 0.37)P + (1.65 ± 0.11)ϕ31. We compare the [Fe/H] predicted by our relation for the stars in our calibration sample with that obtained from previously established relations in the G-band using different approaches. Our calibrated G-band P-ϕ31-[Fe/H] relationship demonstrates high reliability when validated against spectroscopic data, achieving a negligible bias of 0.00 dex and an empirical RMS scatter of 0.26 dex. Furthermore, by applying an Orthogonal Distance Regression (ODR) routine that fully propagates parameter covariance, we establish a mathematically strict empirical baseline whose theoretical uncertainties perfectly align with this observed dispersion. We find that the inclusion of the R21 Fourier parameter offers no significant improvement in metallicity estimation. Comparisons with literature confirm that our linear relation aligns closely with other Gaia DR3-based studies, while offering improved precision over older DR2-based relations.
