Converging on the Cepheid Metallicity Dependence: Implications of Non-Standard Gaia Parallax Recalibration on Distance Measures

TL;DR

The paper reassesses the claim by Madore & Freedman (2025) that there is no metallicity dependence in the Cepheid period–luminosity relation by contrasting MF25's multiplicative Gaia parallax correction with the Gaia collaboration's additive $\varpi_{\mathrm{L21}}$ calibration. Using updated Gaia EDR3 parallaxes, corrected Milky Way cluster Cepheid P--L relations, and improved LMC/SMC differential analyses, the authors find a persistent negative metallicity dependence, $\gamma$, near the canonical value of about $-0.2$ mag/dex (e.g., $\gamma_{[3.6]} \approx -0.16$ to $-0.3$ mag/dex depending on band and geometry corrections). They show that MF25’s approach would imply unphysical distances and parallaxes (e.g., the Pleiades near $120$ pc and nonzero quasar parallaxes) and would inflate $H_0$ to $\sim74.4$ km s$^{-1}$ Mpc$^{-1}$, in tension with other constraints. The discussion argues that the best available data support a nonzero negative Cepheid metallicity dependence, while MF25’s recalibration introduces inconsistencies; future Gaia DR4 should further stabilize parallax systematics and tighten constraints on $\gamma$.

Abstract

By comparing Cepheid brightnesses with geometric distance measures including Gaia EDR3 parallaxes, most recent analyses conclude metal-rich Cepheids are brighter, quantified as $γ\sim -0.2$ mag/dex. While the value of $γ$ has little impact on the determination of the Hubble constant in contemporary distance ladders (due to the similarity of metallicity across these ladders), $γ$ plays a role in gauging the distances to metal-poor dwarf galaxies like the Magellanic Clouds and is of considerable interest in testing stellar models. Recently, Madore & Freedman (2025, hereafter MF25) recalibrated Gaia EDR3 parallaxes by adding to them a magnitude offset to match certain historic Cepheid parallaxes which otherwise differ by $\sim1.6σ$. A calibration which adjusts Gaia parallaxes by applying a magnitude offset (i.e., a multiplicative correction in parallax) differs significantly from the Gaia Team's calibration (Lindegren et al. 2021), which is additive in parallax space - especially at distances much closer than 1 kpc or beyond 10 kpc, outside the $\sim$2-3 kpc range on which the MF25 calibration was based. The MF25 approach reduces $γ$ to zero. If extrapolated, it places nearby cluster distances like the Pleiades too close compared to independent measurements, while leaving distant quasars with negative parallaxes. We conclude that the MF25 proposal for Gaia calibration and $γ\sim 0$ produces farther-reaching consequences, many of which are strongly disfavored by the data.

Figures (5)

• Figure 1: Recent empirical and theoretical estimates of the Cepheid metallicity dependence $\gamma$ from the literature in the $m_H^W$ and $m_{VI}^W$ Wesenheit indices. A few analyses were excluded from this plot Freedman2011Wielgorski2017Owens2022 due to issues that were identified and discussed in Breuval2022. The blue band shows broad agreement between $\gamma \sim -0.15$ and $-0.30$ mag/dex. The methods labeled with different shapes include: comparison between P--L relations in different galaxies, metallicity gradients, Milky Way Cepheids with Gaia EDR3 parallaxes, Baade-Wesselink distances, and theoretical predictions. The red point indicates the $\gamma \sim 0$ multi-wavelength result by MF2025, based on a variety of methods. The metallicity dependence $\gamma$ in the $m_H^W$ Wesenheit magnitude and the Hubble constant $H_0$Riess2022a are related as follows: $\gamma$ shifts the luminosity of Cepheids which show the largest metallicity difference with respect to Cepheids in SNIa hosts (i.e. in the SH0ES distance ladder, the metal-poor LMC and SMC). This luminosity difference directly translates into a shift in $H_0$. We note that the $H_0$ values represented on the top $x$-axis are not actually measured in the quoted references but are derived from H0DN2025.
• Figure 2: P--L relation for Milky Way cluster Cepheids (blue) as selected by MF2025, after applying the corrections listed in Table \ref{['table:MF25_improvements_clusters']}, and for the HST FGS sample from Benedict2007 (yellow). The red point shows V367 Sct as plotted using MF2025's incorrect period. The blue version uses the correct $\log P = 0.799$ value.
• Figure 3: P--L intercept $\beta$, where $M = \alpha \, (\log P-1) + \beta$, in the [3.6 $\mu$m] filter for Milky Way cluster Cepheids (red), the sample of 10 bright Cepheids with HST FGS parallaxes from Benedict2007 (yellow), LMC Cepheids (blue) and Cepheids in different regions of the SMC (green). The red "X" shows the P--L intercept obtained after the MF2025 recalibration of Gaia EDR3 parallaxes. The metallicity on the horizontal axis is expressed in [O/H] for a direct comparison with abundances in SNIa host galaxies (grey histogram). The slope of the grey line represents a $\gamma \sim -0.23$ mag/dex metallicity dependence obtained by fitting a straight line through the MW, LMC and SMC. Conversely, the $\gamma \sim 0$ result by MF2025 is obtained from a comparison between the MW red "X" marker, the LMC, and the SMC dark green "X" marker, which align with a horizontal line.
• Figure 4: Distance estimates to the Pleiades open cluster. Light blue values are pre- Gaia measurements, orange is Hipparcos, dark blue are Gaia-based distances and the red point corresponds to Gaia EDR3 after applying the recalibration suggested by MF2025.
• Figure 5: Mean parallaxes of distant quasars as a function of Gaia$G$ magnitude from the Gaia EDR3 catalog without any correction (black), with the multiplicative correction proposed by MF2025 (red) and with the additive correction recommended by the Gaia team [][in blue]Lindegren2021_plx_bias. Quasar parallaxes are expected to be equal to zero. Figure adapted from Lindegren2021_plx_bias.