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

TL;DR

This work uses synthetic Cepheid populations built from Geneva stellar evolution tracks and the SYCLIST tool to quantify how metallicity influences the Leavitt law across multiple photometric bands and Wesenheit indices. It predicts a slope–metallicity dependence ($\beta_{\mathrm{M}} > 0$) leading to steeper LLs at lower metallicity and a pivot‑period–dependent intercept ($\alpha_{\mathrm{M}}$), with $\alpha_{\mathrm{M}}\approx -0.20$ mag dex$^{-1}$ for $\log P_0=1.0$ in many bands, aligning with SH0ES constraints in the reddening-free $W_H$ magnitude. The model accurately reproduces IS boundaries, Cepheid period distributions, and LL scatter, while highlighting potential reddening systematics as a source of inter-band discrepancies. Overall, the results imply metallicity corrections in Cepheid distances can be modeled consistently with current H0 measurements, providing a solid theoretical underpinning for Riess 2022 and guiding future refinements with expanded metallicity coverage and improved observational data.

Abstract

The impact of metallicity on the Cepheid Leavitt law (LL) and, in turn, the Hubble constant, has been the subject of much recent debate. Here, we present a comprehensive analysis of metallicity effects on Cepheid LLs based on synthetic Cepheid populations computed using Geneva 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 ($Z \in [0.014, 0.006, 0.002]$). We computed LLs in fourteen optical-to-infrared passbands and five reddening-free Wesenheit magnitudes. All Cepheid populations take into account distributions of rotation rates and companion stars. We show excellent agreement between the predicted populations and key observational constraints from the literature. Our simulations predict a significant LL slope-metallicity dependence ($β_{\rm M} > 0$) that renders LLs steeper at lower metallicity at all wavelengths. Importantly, $β_{\rm M} \ne 0$ implies that the intercept-metallicity dependence, $α_{\rm M}$, depends on pivot period; an issue not previously considered. Comparison with $α_{\rm M}$ measurements in individual passbands reported in the literature yields acceptable agreement on the order of agreement found among different observational studies. The wavelength dependence and magnitude of the disagreement suggests a possible origin in reddening-related systematics. Conversely, we report excellent agreement between our $α_{\rm M} = -0.20 \pm 0.03$ mag dex$^{-1}$ and the value determined by the SH0ES distance ladder in the reddening-free H-band Wesenheit magnitude ($-0.217 \pm 0.046$), the currently tightest and conceptually simplest empirical constraint.

Figures (11)

• Figure 1: Hertzsprung-Russell diagrams for metallicities $Z=0.014$ (Solar, left), $Z=0.006$ (LMC, middle), and $Z=0.002$ (SMC, right). Solid black lines show predicted IS boundaries from Anderson2016 for the second and third crossings averaged together; dashed black lines show the first crossing. Solid and dashed cyan lines illustrate predicted boundaries from DeSomma2020DeSomma2022, for $\alpha_{\rm ML}=1.7$ and 1.5, respectively. Solid and dashed pink lines show predicted sets A (simple convective model) and D (added radiative cooling, turbulent pressure & flux) from Deka2024, which estimate the envelopes of instability strips across a large range of metallicities ($\rm{[M/H]}$$\in$ {0.00, $-$0.34, $-$0.75}, i.e., $Z \in$ {0.013, 0.006, 0.002}) and are shown in all panels. Observational estimates of 265 fundamental-mode Galactic classical Cepheids from Groenewegen2020 are shown in the left panel. Empirically-derived IS boundaries for the LMC from Espinoza-Arancibia2024 are shown as grey regions in the middle panel.
• Figure 2: Hertzsprung-Russell diagrams for all 296 SYCLIST cluster simulations at each metallicity considered: $Z=0.014$ (left), $Z=0.006$ (middle), and $Z=0.002$ (right). The colour scale indicates the initial mass of the star, from the least (blue) to the most massive ones (yellow). Overlaid in black are the IS boundaries determined by Anderson2016 for second and third crossings averaged together (solid), and first crossing (dashed). The red dashed lines show the cut applied to exclude most of the first crossing stars.
• Figure 3: Distribution of $\log P$ for $Z=0.014$ (left), 0.006 (middle), and 0.002 (right panel). The SYCLIST populations appear in red, while observations are shown as black histograms. Observations come from Pietrukowicz2021 and Soszynski2015Soszynski2017 for Classical Cepheids in the Milky Way and Magellanic Clouds, respectively. Observational counts have been rescaled in order to match the numbers we have in SYCLIST simulations, by a factor 3.4, 5.9, and 7.5 for $Z=0.014$, 0.006, and 0.002, respectively. The age limit applied ($< 300$ Myr) to the synthetic populations leads to mismatches at the shortest periods, particularly at $Z=0.002$.
• Figure 4: Distribution of $\log \hbox{$T_{\rm eff}$}\xspace-\log T_{\rm eff, mid}$ for our selection of IS stars in SYCLIST simulations, where $\log T_{\rm eff, mid}$ corresponds to the effective temperature at the mid-IS line right in the middle between the blue and red edges of the IS, for $Z=0.014$ (left), 0.006 (middle), and 0.002 (right panel). The vertical lines indicate the $1\sigma$ dispersion that would correspond to a uniform distribution of stars within the IS.
• Figure 5: Top: LLs in the $V$ band, for $Z=0.014$ (left), 0.006 (middle), and 0.002 (right panel). IS stars from SYCLIST are shown as grey points. The blue and red lines correspond to the IS boundaries from Anderson2016. The black solid line is the LL fit to the SYCLIST population, for $\log P_{\rm 0} = 0.0$. The corresponding slope value, $\beta$, is annotated on the bottom right of each panel. The black dashed line shows the mid-IS fit, obtained by averaging the magnitude values for the blue and red boundaries at a given period. It shows a break in slope where the transition between the red edges for first crossing and second+third crossings occurs. Note the different axis ranges. Bottom: Residuals computed as the difference in magnitude between the individual SYCLIST stars and that of the SYCLIST LL fit at the same period.