Photometric metallicity of Galactic RR Lyrae stars in the Gaia DR3 era

TL;DR

This paper introduces a new calibrated G-band relation between pulsation period, Fourier parameter, and metallicity for galactic RR Lyrae stars from Gaia DR3, emphasizing calibration purity and validation against spectroscopic data.

Contribution

The study presents a high-reliability, purely calibrated G-band P-phi31-[Fe/H] relation for RR Lyrae stars, validated with spectroscopic metallicities and improved over previous Gaia-based relations.

Findings

Achieved a negligible bias of 0.00 dex in metallicity predictions.

Empirical RMS scatter of 0.26 dex in metallicity estimates.

The relation aligns well with other Gaia DR3 studies and improves upon older relations.

Abstract

We present a new, calibrated $G$-band relationship between pulsation period $P$, Fourier parameter $\phi_{31}$, 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 $\text{[Fe/H]} = (-6.93 \pm 0.58) - (6.04 \pm 0.37)P + (1.65 \pm 0.11)\phi_{31}$. 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 $P$-$\phi_{31}$-[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 $R_{21}$ 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.