Measuring galactic distances and metallicity through RR Lyrae optical and infrared light curves

Abstract

RR Lyrae stars (RRLs) are radially pulsating stars that are widely used tracers of old (age $> 10$~Gyr) stellar populations in the Milky Way and Local Group galaxies. The number of known RRLs has significantly increased with the advent of large-area photometric surveys (e.g., ASAS-SN, Catalina Sky Survey, PanSTARRS, DES, Gaia, TESS). RRLs with known metal abundances remain limited due to the reliance on spectra, which require large amounts of telescope/analysis time and are difficult to obtain at large distances or in high extinction environments. Reliable metallicity measurements are pivotal in utilizing RRLs as distance indicators through standard candle (Period-Luminosity-Metallicity) relations.

Properties of RRL light curves, such as shape (described via Fourier decomposition parameters, e.g., $\phi_{31}$), are inherently linked to fundamental parameters such as metallicity. In this work, to derive accurate metallicities from readily available photometry, I present newly-calibrated period-$\phi_{31}$-[Fe/H] relations for RRLs in the fundamental (RRab) and first overtone (RRc) mode in the optical (ASAS-SN $V$-band) and, inaugurally, in the mid-infrared (WISE $W1$ and $W2$ bands). I further present new empirical infrared Period-Luminosity-Metallicity (PLZ) and Period-Wesenheit-Metallicity (PWZ) relations for RRLs based on the latest Gaia EDR3 parallaxes, in the $W1$ and $W2$ bands, as well as in the $W(W1, V - W1)$ and $W(W2, V - W2)$ Wesenheit magnitudes. These works rely upon the same calibration dataset, which provides the largest and most comprehensive span of parameter space to date, with homogeneous spectroscopic metallicities from $\sim$9000 Galactic halo field RR Lyrae spanning $-3<\textrm{[Fe/H]}\lessapprox 0.0$. Using the same calibration set and parameter extraction techniques ensures a homogeneous and straightforward application of photometric metallicities to PLZ/PWZ distances.

The optical period-$\phi_{31}$-[Fe/H] relations are compared with those available in the literature and are demonstrated to minimize systematic trends in the lower and higher metallicity range. The relations are directly tested by measuring both the metallicity of the Sculptor dSph and a sample of Galactic globular clusters rich in both RRab and RRc stars. The average metallicity obtained for the combined RRab+RRc sample in each cluster is consistent within $\pm 0.08$~dex of their spectroscopic metallicities, supporting the good performance of this work's optical relations. The infrared relations are shown to possess a similar dispersion to the optical relations. The metallicity error is shown to decrease further when optical and infrared relations are used together.

Finally, the performance of the PLZ and PWZ relations are tested by determining the distance moduli of both galactic and extragalactic stellar associations, including: the Sculptor dwarf spheroidal galaxy in the Local Group (finding $\bar{\mu}_{0}=19.47 \pm 0.06$), the Galactic globular clusters M4 ($\bar{\mu}_{0}=11.16 \pm 0.05$) and the Reticulum globular cluster in the Large Magellanic Cloud ($\bar{\mu}_{0}=18.23 \pm 0.06$). The distance moduli determined through all PLZ/PWZ relations are internally self-consistent (within $\lesssim$ 0.05 mag) but are systematically smaller (by $\sim$ 2-3$\sigma$) than previous literature measurements taken from a variety of methods/anchors. We link this systematic effect to literature relations based on different parallax anchors (from HST, Gaia DR2, and the newest Gaia DR3) leading to slight differences in zero-points and, in turn, distance. A comparison with recent RRL PLZ/PWZ empirical relations similarly anchored with Gaia EDR3 likewise shows a systematically smaller distance modulus.

The relations obtained in this work greatly impact future studies (such as the Vera Rubin LSST survey and the Roman Space telescope), where we will reach across the Local Group to larger distances and into higher-extinction domains where spectroscopic observations will not be feasible. Knowing the chemical and structural distribution of RRLs, corresponding to some of our galaxy's oldest stellar populations, will better constrain the mechanisms behind galactic formation and evolution.