Cepheid Metallicity in the Leavitt Law (C-MetaLL) survey: VII. Metallicity dependence of Period-Wesenheit relations based on a homogeneous spectroscopic sample

TL;DR

This work investigates how metallicity affects Cepheid PW relations by exploiting a large, homogeneous Galactic Cepheid sample with uniform abundances and extensive multi-band photometry. Using a robust photometric-parallax method and Bayesian MCMC, the authors derive PWZ relations across optical and NIR Wesenheit magnitudes, finding a strong metallicity term $\gamma$ (approximately $-0.5$ mag/dex in optical and HST-like Wesenheits bands, and about $-0.4$ mag/dex in the NIR) and a Gaia parallax zero-point offset $\epsilon$ around $10\ \mu$as. Applying these PWZ relations to ~4500 LMC Cepheids yields distances largely consistent with geometric estimates, supporting the validity of the method while highlighting the sensitivity of $\gamma$ to sample selection and metallicity range. The results imply a non-negligible metallicity impact on the Cepheid distance scale and hint at potential non-linear metallicity behavior at the metal-poor end, underscoring the need for more homogeneous data and improved Gaia DR4 parallaxes to robustly quantify $\gamma$.

Abstract

The C-MetaLL project has provided homogeneous spectroscopic abundances of 290 Classical Cepheids (DCEPs) for which we have the intensity-averaged magnitudes in multiple optical and near-infrared (NIR) bands, periods, pulsation modes, and Gaia parallaxes. Our goal is to derive updated period-Wesenheit-metallicity (PWZ) relations using the largest and most homogeneous metallicity sample ever used for such analyses, covering a range of $-1.3<$[Fe/H]$<+0.3$ dex. We computed several optical and NIR Wesenheit magnitudes using 275 DCEPs with reliable parallaxes, by applying a robust photometric parallax technique, which simultaneously fits all parameters -- including the global Gaia parallax counter-correction -- and handles outliers without data rejection. We find a stronger metallicity dependence ($γ\approx -0.5$ mag/dex in optical, $-0.4$ mag/dex in NIR) than recent literature reports. Gaia parallax zero-point conter-corrections ($ε$) vary smoothly across bands, with an average value of $\sim$10 $μ$as, aligning with previous determinations. Applying our PWZ relations to LMC Cepheids yields distances generally consistent within $1σ$ with geometric estimates. The choice of reddening law has a negligible impact, while using only fundamental-mode pulsators significantly increases the uncertainties. Including $α$-element corrections increases $|γ|$ and reduces $ε$. However, we find statistically consistent $γ$ values with the literature, particularly for the key Wesenheit magnitude in the HST bands, by restricting the sample to the brighter (i.e. closer) objects, or by including only pulsators with $-0.7<$[Fe/H]$<$0.2 dex. Our results hint at a large $γ$ or a non-linear dependence on metallicity of DCEP luminosities at the metal-poor end, which is difficult to quantify with the precision of parallaxes of the present dataset.

Figures (14)

• Figure 1: Periods and iron abundances spanned by the investigated sample. The different pulsation modes are labelled in the figure.
• Figure 2: Relative parallax error as a function of the $Gaia$ G magnitude. The points are colour-coded according to their iron abundance.
• Figure 3: Reliability of parallaxes based on the two parameters RUWE and astrometric_gof_al (in absolute value). For reference, the typical limits at 1.4 and 12.5 have been reported with dashed lines.
• Figure 4: Examples of corner plot with the posterior distributions for the output parameters and the best-fit solution obtained for the $WJK_S$ (top) and $WcHVI$ (bottom) Wesenheit magnitudes. The units of $\alpha,\, \beta,\, \gamma,\,\epsilon$ and of their uncertainties are mag, mag/dex, mag/dex and mas, respectively.
• Figure 5: Comparison between final photometric parallax (i.e. calculated with the final result of the fitting procedure) and that from $Gaia$. In blue and red are the objects not considered/considered as outliers by the Cauchy loss function. The top and bottom panels show the results for the $WJK_S$ and $WcHVI$ Wesenheit magnitudes, respectively. The units of $\alpha,\, \beta,\, \gamma,\,\epsilon$ and $\varpi$ are mag, mag/dex, mag/dex, mas and mas, respectively.