The stellar evolution perspective on the metallicity dependence of classical Cepheid Leavitt laws

¹ Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
² Department of Astronomy, University of Geneva, Chemin Pegasi 51b, 1290 Versoix, Switzerland
³ European Space Agency (ESA), ESA Office, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA

^⋆ Corresponding authors: saniya.khan@epfl.ch; richard.anderson@epfl.ch

Received: 28 May 2025
Accepted: 6 August 2025

Abstract

Metallicity is a key parameter in stellar evolution and it significantly affects measurements of the mass-luminosity relation of classical Cepheids (henceforth, Cepheids). The impact of metallicity on the Cepheid Leavitt law (period-luminosity relation; henceforth, LL) and, in turn, the Hubble constant (H₀), has been the subject of much recent debate. While recent observational results have generally shown a negative intercept-metallicity effect at all wavelengths and for Wesenheit magnitudes, predictions based on different stellar evolution models have differed even in terms of sign. Here, we present a comprehensive analysis of metallicity effects on Cepheid LLs based on synthetic Cepheid populations computed using Geneva stellar evolution models and the SYCLIST tool. We computed 296 co-eval populations in the age range of 5 − 300 Myr for metallicities representative of the Sun, the LMC, and the SMC (Z ∈ [0.014, 0.006, 0.002]). We computed LLs in fourteen optical-to-infrared passbands spanning from GaiaG_BP to JWST’s F444W and five reddening-free Wesenheit magnitudes. All Cepheid populations take into account distributions of rotation rates and companion stars. We found an excellent agreement between the predicted populations and key observational constraints from the literature, such as a) instability strip (IS) boundaries, b) period distributions, c) LL slopes, and d) intrinsic LL dispersion as a function of wavelength and metallicity (match within 0.01 mag). This is further strengthened by the previously demonstrated excellent agreement between the same models and observed mass-luminosity relations, period-radius relations, and rates of period changes. Our simulations predict a significant LL slope-metallicity dependence (β_M > 0) that renders LLs steeper at lower metallicity at all wavelengths. This effect is strongest for shorter passbands where LL slopes are shallower. We point out that observational studies generally support β_M ≠ 0, albeit with varying degrees of significance. Importantly, β_M ≠ 0 implies that the intercept-metallicity dependence, α_M, depends on pivot period, which was not previously considered in the literature. Our comparison with α_M measurements in individual passbands reported in the literature yields an acceptable agreement of the order of agreement typically found among different observational studies. The wavelength dependence and magnitude of the disagreement suggests a possible origin rooted in reddening-related systematics. Conversely, we report excellent agreement between our α_M = −0.20 ± 0.03 mag dex⁻¹ and the value determined by the SH0ES distance ladder in the reddening-free H-band Wesenheit magnitude ( − 0.217 ± 0.046), the currently tightest and conceptually simplest empirical constraint. In summary, we show that Geneva stellar evolution models have high predictive power for Cepheid properties and the predicted metallicity effects on the Cepheid LL match the results obtained in parallel with the measurement of the Hubble constant. New evolutionary models extending to super-Solar metallicity and improved astrometry from the fourth Gaia data release will enable further probes of these effects.