[Paper Review] Cepheid Metallicity in the Leavitt Law (C- MetaLL) survey: IV. The metallicity dependence of Cepheid Period-Luminosity relations

E. Trentin, V. Ripepi+11 more|arXiv (Cornell University)|Oct 5, 2023

Astronomy and Astrophysical ResearchPhysics and Astronomy3 citations

TL;DR

This study investigates the metallicity dependence of Cepheid Period-Luminosity (PL) and Wesenheit (PW) relations across optical to near-infrared bands using a sample of 910 Galactic classical Cepheids with precise [Fe/H] and Gaia DR3 astrometry. It finds a strong negative metallicity effect on the PL/PW intercepts (γ ≈ −0.4 to −0.5 mag/dex), significantly larger than most prior estimates, while the slope’s metallicity dependence remains unconstrained.

ABSTRACT

Classical Cepheids (DCEPs) play a fundamental role in the calibration of the extra-galactic distance ladder which eventually leads to the determination of the Hubble constant($H_0$) thanks to the period-luminosity ($PL$) and period-Wesenheit ($PW$) relations exhibited by these pulsating variables. Therefore, it is of great importance to establish the dependence of $PL/PW$ relations on metallicity. We aim at quantifying the metallicity dependence of the Galactic DCEPs' $PL/PW$ relations for a variety of photometric bands ranging from optical to near-infrared. We gathered a literature sample of 910 DCEPs with available [Fe/H] values from high-resolution spectroscopy or metallicities from \gaia\ Radial Velocity Spectrometer. For all these stars, we collected photometry in the $G_{BP},G_{RP},G,I,V,J,H,K_S$ bands and astrometry from the \gaia\ DR3. These data have been used to investigate the metal dependence of both intercepts and slopes of a variety of $PL/PW$ relations at multiple wavelengths. We find a large negative metallicity effect on the intercept ($γ$ coefficient) of all the $PL/PW$ relations investigated in this work, while present data still do not allow us to draw firm conclusions regarding the metal dependence of the slope ($δ$ coefficient). The typical values of $γ$ are around $-0.4:-0.5$ mag/dex, i.e. larger than most of the recent determinations present in the literature. We carried out several tests which confirm the robustness of our results. As in our previous works, we find that the inclusion of global zero point offset of \gaia\ parallaxes provides smaller values of $γ$ (in an absolute sense). However, the assumption of the geometric distance of the LMC seems to indicate that larger values of $γ$ (in an absolute sense) would be preferred.

Motivation & Objective

• Quantify the metallicity dependence of Cepheid Period-Luminosity (PL) and Wesenheit (PW) relations across multiple photometric bands.
• Address the unresolved tension in Hubble constant measurements by refining the metallicity correction in the cosmic distance ladder.
• Assess the impact of parallax zero-point offsets and LMC distance assumptions on metallicity calibration.
• Investigate whether sample metallicity imbalance affects the robustness of the derived metallicity dependence.
• Provide improved constraints on the intercept (γ) and slope (δ) coefficients of PL/PW relations for future H₀ calibration.

Proposed method

• Compiled a sample of 910 Galactic classical Cepheids with [Fe/H] from high-resolution spectroscopy or Gaia RVS, and photometry in G, G_BP, G_RP, V, I, J, H, K_S bands from Gaia DR3 and literature.
• Applied Gaia DR3 astrometry and parallaxes, including corrections from L21 (Luri et al. 2021) for zero-point offsets.
• Fitted three- and four-parameter PL and PW relations (PL, PW, PWZ) with period, metallicity, and band-dependent terms.
• Used a robust fitting procedure with bootstrapping and resampling to test for bias due to uneven metallicity distribution.
• Compared results under different assumptions: global parallax offset (−14, −22 μas), LMC geometric distance (Pietrzyński et al. 2019), and sample subsets (F vs. F+1O).
• Validated consistency via comparison of Gaia and literature photometry, and [Fe/H] from HiRes vs. Gaia RVS.

Experimental results

Research questions

• RQ1 What is the metallicity dependence of the PL and PW relation intercepts (γ) across optical to near-infrared bands?
• RQ2 Does the slope of the PL and PW relations (δ) depend on metallicity, and if so, how?
• RQ3 How do global parallax zero-point offsets (e.g., −14 or −22 μas) affect the derived metallicity dependence?
• RQ4 Is the observed metallicity dependence robust against sample bias due to uneven metallicity distribution?
• RQ5 Does assuming the geometric distance to the LMC as a reference favor larger or smaller absolute values of γ?

Key findings

• A strong negative metallicity dependence on the PL and PW relation intercepts is found, with γ ≈ −0.4 to −0.5 mag/dex across all bands, significantly larger than most prior literature estimates.
• The inclusion of a global parallax zero-point offset (e.g., −14 or −22 μas) reduces the absolute value of γ, bringing it into better agreement with recent literature.
• However, assuming the geometric distance to the LMC (Pietrzyński et al. 2019) as a reference favors larger absolute values of γ, suggesting that the true value may be closer to −0.5 mag/dex.
• The metallicity dependence of the slope (δ) remains unconstrained: in most cases, δ is consistent with zero within 1σ, and in the literature-only sample, it is often positive (0 to +0.5).
• Resampling the data to balance metallicity distribution confirms that the results are robust and not driven by sample bias, as median coefficients from 10,000 resampled sets match the full-sample results.
• The F+1O sample (including stars with uncertain Fe/H) shows larger error bars on γ and δ, but does not alter the overall conclusions.