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

Abstract

By comparing Cepheid brightnesses with geometric distance measures including Gaia EDR3 parallaxes, most recent analyses conclude metal-rich Cepheids are brighter, quantified as $\gamma \sim -0.2$ mag/dex. While the value of $\gamma$ has little impact on the determination of the Hubble constant in contemporary distance ladders (due to the similarity of metallicity across these ladders), $\gamma$ 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 $\sim1.6\sigma$. 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 $\gamma$ 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 $\gamma \sim 0$ produces farther-reaching consequences, many of which are strongly disfavored by the data.