Beyond MESA Defaults: The Impact of Structural Resolution Uncertainty in p-mode Asteroseismology

TL;DR

This paper demonstrates that structural-resolution uncertainty in 1D stellar evolution calculations materially biases predicted $p$-mode frequencies across the HR diagram, at times surpassing observational errors by several orders of magnitude. By comparing two resolutions (default $\delta_{\text{mesh}}=1.0$ vs $0.1$) with a rigorous Equivalent Evolutionary Point framework, the authors quantify $\varepsilon_{\text{dmesh}}$ and $\zeta_{\text{dmesh}}$ for solar-like, upper-main-sequence, and Mira oscillators, revealing that high-mass, high-metallicity, and late-evolution models are most affected. They show that the impact propagates to seismic diagnostics ($\Delta\nu$, $\Delta\Pi_1$, $r_{02}$, $r_{13}$, $\epsilon_p$) and to fundamental parameters (age, mass, radius, density), and they compare these numerical uncertainties to synthetic TESS observational errors. The work advocates incorporating mesh-resolution uncertainties into model fitting, proposes best practices for convergence testing and reporting, and discusses the development of model-emulators that duly account for numerical errors, ultimately improving the reliability of asteroseismic inferences.

Abstract

Observations of pressure modes ($p$-modes) in stars have enabled profound insights into stellar properties, and theoretical stellar evolution and oscillation models are integral to these inferences. However, modeling uncertainties are often overlooked, even as they can rival or exceed observational uncertainties. In this study, we quantify, for the first time, the impact of structural resolution choices in 1D stellar evolution calculations on predicted $p$-mode frequencies across the HR diagram, using \texttt{MESA} and \texttt{GYRE}. We present demonstrative measurements of resolution-based modeling uncertainty for a range of solar-like, upper main-sequence, and Mira oscillators and compare these directly to \TESS{} observational uncertainties. We demonstrate that resolution-driven uncertainties can significantly influence theoretical predictions and in some cases overwhelm observational uncertainties by orders of magnitude. For the illustrative case considered -- an order-of-magnitude variation in mesh resolution -- solar-like oscillators typically have fractional, resolution-based uncertainties at or below 1\% of the test frequency. Fractional uncertainties in Miras, however, are as large as 20\%. We also find that the location and morphology of the RGB bump and red clump are impacted substantially by resolution uncertainty. Stellar ages are impacted at the 10\% level for young main-sequence stars, and the model-based correction factor for the $\Dnu{}$--$\sqrtρ$ scaling relation is impacted at the 2\% level. Our results underscore the need to incorporate modeling uncertainties into asteroseismic analyses and provide a reference framework for observers evaluating the reliability of theoretical models.

Figures (11)

• Figure 1: H--R diagram showing the three types of p-mode pulsators investigated in this study. Tracks shown have solar metallicity and masses of 1.0, 1.4, 2.0, and 5.0$M_\odot$, from lower right to upper left.
• Figure 2: Panels 1 through 7 show the locations and indices of Equal Evolutionary Points (EEPs) for each model class, with the class indicated in the upper left. The ages and other fundamental parameters measured at these EEPs are summarized in Table \ref{['table:overview']}.
• Figure 3: HR diagram color-coded by $\varepsilon_{\texttt{dmesh}}{$ɛ_dmesh$}$ ($\zeta_{\texttt{dmesh}}$), the degree of discrepancy in representative test frequency $\nu_\text{test}$ ($P_\text{test}$). The left panel shows all models with solar metallicity but different masses, and the right panel with solar mass but different metallicites.
• Figure 4: H--R diagram color-coded by the ratio of $\varepsilon_{\texttt{dmesh}}$ ($\zeta_{\texttt{dmesh}}$) to the typical observational uncertainties $\sigma_\text{obs}$ (or $\sigma_\text{obs, P}$), assuming the worst-case observing scenario (T=1 month, $\sigma_\text{noise}=197$ ppm/hr). The left panel shows all models with solar metallicity but different masses, and the right panel with solar mass but different metallicites.
• Figure 5: Seimic H--R diagram ($\nu_\text{max}$ vs. $T_\text{eff}$) around the RGB bump (top panel) and the CHeB phase (bottom panel).