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

TL;DR

This study systematically quantifies how physical and numerical choices in the MESA framework affect surface abundances of key elements in intermediate-mass stars, focusing on Cepheid-relevant tracks from $M=2$ to $8\,M_\odot$ across $Z=0.0014,0.004,0.014$. Using a fixed reference physics setup, the authors generate 22 variant models per mass/metallicity by varying mixtures, networks, atmospheres, convection criteria, resolutions, and boundary treatments, including canonical and overshooting cases, and track abundances at eight benchmark evolutionary points through the end of core He-burning. They find that surface abundances are mostly robust (differences typically <0.01–0.04 dex) with the notable exceptions arising from the depth of the first dredge-up and from convective boundary prescriptions or certain reaction-rate choices, while the central C/O ratio is highly sensitive to these factors, shifting by up to ~0.15–0.5 depending on model assumptions. The work provides online tables of surface and central abundances and highlights modeling inconsistencies in opacities and atmosphere treatments, underscoring the need for careful diagnostics and potential asteroseismic constraints to disentangle the physical drivers of abundance predictions in Cepheid progenitors.

Abstract

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.

Figures (10)

• Figure 1: Evolution of a 5 M⊙$_{\odot}$, $Z=0.014$ reference model on the HR diagram (left panel) and a corresponding Kippenhahn diagram (right panel). Left: Evolutionary track is shown with color-coded benchmark points. The black cross on the RGB marks the model investigated further with profiles in Fig. \ref{['fig:Tmix-profiles']}. With dash-dotted lines, we show the isoradial lines with $\log R$/ R⊙$_{\odot}$=0.4, 0.8, 1.2, 1.6, 2.0. Right: The corresponding Kippenhahn diagram, showing the interior structure of the model during evolution (time expressed in model number). The green hatched regions mark convection, and the blue-shaded ones mark regions of efficient nuclear burning. We indicate the location of the evolutionary benchmark points (and the model marked with a cross on the HR diagram) with vertical lines and labels. The radius, $\log R / \,{\rm R}_$_⊙$$, vs. model number is shown with a dash-dotted line with the same scale as the mass coordinate on the left axis. Surface (dashed lines) and central (solid lines) mass fractions of $^{12}$C, $^{14}$N, and $^{16}$O are shown with scales given on the right side of the figure. The dotted line marks temperature equal to $10^6$ K.
• Figure 2: Surface (top) and central (bottom) mass fractions relative to their initial values as a function of time for the $5\,{\rm M}_$_⊙$$, $Z=0.014$ canonical model. The top panel shows a zoom near the first dredge-up, while the bottom panel shows the whole evolution until AGB.
• Figure 3: Profiles of the 5 M⊙$_{\odot}$, $Z=0.014$ model marked on the HR diagram (Fig. \ref{['fig:kip0']}) with a cross. Left: temperature gradients (radiative, Ledoux, adiabatic), opacity and optical depth, as a function of zone (starting at one from the surface and increasing towards the center). Right: Mass fractions of the analysed isotopes as a function of zone number. The top panels show the profiles before removing the surface radiative shell, and the lower ones -- after. Green area marks the convective envelope.
• Figure 4: Maximum mass extent of the two largest convective regions: the envelope on the RGB (top panels) and the main sequence convective core (bottom panels), for the reference models. We plot $m_{\rm CE}/M_{\rm tot}$ and $m_{\rm core_{\rm MS}}/M_{\rm tot}$ vs. total stellar mass of a model, $M_{\rm tot}$, in the top and bottom panels, respectively. Results for different metallicities are plotted with different symbols/colors. On the left are the results for the canonical models, and on the right are the overshooting ones.
• Figure 5: Comparison of the reference model (top) and a modified model with the Ledoux criterion (bottom). Left: HRDs with a point marking tRGB, the point of maximal extent of the CE. Middle: profiles with all the isotopic abundances on early MS, when the convective core is the most massive. Right: profiles on tRGB.