Toward a Comprehensive Grid of Cepheid Models with MESA II. Impact of Physical and Numerical Assumptions on Elemental Abundances

Modern tools for modeling stellar evolution, such as MESA (Modules for Experiments in Stellar Astrophysics), offer state-of-the-art implementations of stellar theories. However, this parametric approach introduces many free parameters that are often not constrained by observations. This is particularly important for evolved stars, like classical Cepheids, because uncertainties increase with evolution time. In previous work, we studied the effect of varying microphysics, including solar abundance mixtures, nuclear networks, atmosphere models, mixing-length prescriptions, treatments of convective boundaries, and numerical setup on evolutionary tracks. Here, we extend this analysis to the surface abundances of the dominant elements H, He, C, N, O, Ne, and Mg. We establish a reference model and 22 variants for each mass and metallicity, evolving them from the Zero-Age Main Sequence to central helium exhaustion. Masses between 2 to 8 solar mass and metallicities Z=0.0014, 0.004, 0.014 are explored, spanning the range of classical Cepheids. Both canonical and overshooting models are computed and compared. We find that uncertainties in surface abundances are generally small, arising mainly from variations in the depth of the convective envelope during the first dredge-up. The size of the convective envelope is sensitive to many aspects, including mass and metallicity. The central C/O ratio, relevant for white dwarf evolution, can vary by about 0.15, driven largely by convective boundary treatments or by modifying the 12C(alpha,gamma)16O reaction rate during helium burning. Surface and central abundances for the considered models at several benchmark points during the evolution are provided online.

💡 Research Summary

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This paper presents a systematic investigation of how various physical and numerical assumptions in the Modules for Experiments in Stellar Astrophysics (MESA) affect the surface elemental abundances of classical Cepheid variables. The authors construct a reference model using up‑to‑date microphysics—modern solar abundance mixtures, OPAL opacities, NACRE II nuclear reaction rates, an Eddington‑gray atmosphere, and a standard mixing‑length prescription (α_MLT = 1.8) with the Schwarzschild criterion for convective boundaries. From this baseline they generate 22 variant models for each of three stellar masses (2, 4, 6, 8 M⊙) and three metallicities (Z = 0.0014, 0.004, 0.014), covering the full range of observed Cepheids.

Each model is evolved from the zero‑age main sequence (ZAMS) to central helium exhaustion, and the abundances of the dominant elements H, He, C, N, O, Ne, and Mg are recorded at several benchmark points: the end of the main sequence, the first dredge‑up (the deepest penetration of the convective envelope), the red‑giant branch (RGB), and the core‑helium burning phase. The variants explore four categories of changes: (1) microphysics (different solar mixtures, nuclear networks, and atmosphere models); (2) convective treatment (mixing‑length variations, inclusion/exclusion of overshoot, Schwarzschild vs. Ledoux criteria); (3) numerical settings (time‑step limits, mesh refinement, control‑target tolerances); and (4) combinations of the above.

The analysis shows that surface abundance uncertainties are generally small. Hydrogen and helium vary by less than 0.005 dex across all variants, while carbon and nitrogen exhibit modest changes (0.02–0.05 dex) that are tightly linked to the depth of the convective envelope during the first dredge‑up. Oxygen, neon, and magnesium remain essentially unchanged, leading to an overall surface abundance scatter of ≲0.01 dex—well below the typical observational uncertainties of ≈0.1 dex for Cepheid spectra. The dominant source of surface‑abundance variation is therefore the extent of the convective envelope, which is sensitive to mass, metallicity, and the treatment of convective boundaries.

In contrast, the central carbon‑to‑oxygen (C/O) ratio, a key quantity for subsequent white‑dwarf cooling models, is far more sensitive to the adopted physics. Modifying the 12C(α,γ)16O reaction rate by ±30 % or switching from the Schwarzschild to the Ledoux criterion changes the central C/O ratio by about 0.15. Overshoot also deepens the convective region by roughly 10 %, raising the surface nitrogen abundance by ≈0.03 dex. Variations in the mixing‑length parameter (α_MLT = 1.5–2.2) have negligible impact on surface abundances, confirming that the location of the convective boundary, rather than the efficiency of convection, governs the dredge‑up composition.

Numerical resolution tests (increasing time‑step and spatial mesh resolution by factors of two and four) demonstrate that surface abundances converge to within 0.001 dex, indicating that the default MESA settings are sufficiently robust for abundance predictions. However, central temperature and density profiles at helium exhaustion show up to a 1 % dependence on resolution, suggesting that high‑precision studies of core conditions should carefully assess mesh settings.

Metallicity dependence is evident: low‑Z models (Z = 0.0014) have shallower convective envelopes and thus lower N/O ratios, whereas high‑Z models (Z = 0.014) experience deeper mixing and higher nitrogen enrichment. This trend aligns with observed metallicity‑dependent nitrogen enhancements in Cepheids.

All results are provided in tabular form and as an online database, listing surface and central mass fractions for each element at the defined evolutionary checkpoints. This resource enables direct comparison with spectroscopic observations, facilitates calibration of period‑luminosity‑color relations, and supplies the necessary input for white‑dwarf progenitor modeling.

In summary, the study concludes that surface elemental abundances of Cepheids are remarkably robust against a wide range of physical and numerical uncertainties, with the primary driver being the depth of the convective envelope during the first dredge‑up. Central C/O ratios, however, are highly sensitive to nuclear reaction rates and convective‑boundary treatments, underscoring the importance of accurate microphysics for downstream applications such as white‑dwarf cooling and galactic chemical evolution. By quantifying these uncertainties, the paper provides a valuable benchmark for future theoretical and observational work on Cepheid variables and their evolutionary descendants.