Modeling APOKASC-3 red giants: I. The first dredge-up and red giant branch bump

TL;DR

This study rigorously tests the predictions for two key red-giant diagnostics—the first dredge-up (FDU) and the red giant branch bump (RGBB)—by comparing APOKASC-3 asteroseismic-spectroscopic data to MESA models across a broad mass and birth composition range. Using extensive model grids that vary chemical composition, reaction rates, opacities, boundary conditions, and convection, the authors find that the qualitative mass- and composition-trends are reproduced, but the observed magnitude of surface abundance changes, particularly for $[\mathrm{C}/\mathrm{N}]$, is smaller than theory by about $0.16$ dex, with systematics around $0.01$ dex. The empirical RGBB locus is well defined and captured in its mass/metallicity trends, yet the observed RGBB occurs at lower luminosity (higher $\log g$) than predicted by roughly $0.15$ dex in $\log g$, mirroring similar tensions reported in prior work. Enveloping undershoot can shift the RGBB to align with data but aggravates lithium depletion predictions, conflicting with observed post-FDU Li in the APOKASC-3 and GALAH samples. The authors conclude that envelope undershooting as a fix is problematic and propose Li in the FDU as a sensitive test of the RGBB and FDU, while suggesting other interior-structure modifications or physics may be needed; they also promote self-consistent, publicly available MESA-based RGB tracks for the community.

Abstract

We focus on two key diagnostics of stellar physics in red giant branch (RGB) stars: the first dredge-up (FDU) of nuclear processed material and the location of the red giant branch bump (RGBB). We compare asteroseismic and spectroscopic APOKASC-3 data with theoretical MESA models. Our FDU predictions have similar mass and metallicity trends to the data, but the observed magnitude of the change in $[{\rm C}/{\rm N}]$ in data is smaller than theoretical predictions by $[0.1615 \pm 0.0760 \,({\rm obs}) \pm 0.0108 \,({\rm sys})] \,{\rm dex}$. These results are insensitive to the input physics, but they are at a level consistent with systematic uncertainties in the abundance measurements. When we include observed trends in birth $[{\rm C}/{\rm Fe}]$ and $[{\rm N}/{\rm Fe}]$ in our models, it modestly increases the metallicity dependent difference relative to the data. We find a well-defined empirical RGBB locus: $\log g = 2.6604 - 0.1832 (M/{\rm M}_\odot-1) + 0.2824 \,[{\rm Fe}/{\rm H}]$. Our model RGBB loci have mass and composition trends that mirror the data, but we find that the observed RGBB is $[0.1509 \pm 0.0017 \,({\rm obs}) \pm 0.0182 \,({\rm sys})] \,{\rm dex}$ higher than predicted across the board, similar to prior literature results. We find that envelope undershooting, proposed solution to reconcile theory with data, increases ${\rm Li}$ destruction during the FDU at higher metallicities, creating tension with depletion observed in GALAH data. We propose ${\rm Li}$ in the FDU as a sensitive test of the RGBB and FDU, and discuss other potential solutions.

Figures (22)

• Figure 1: Observational sample of RGB stars used in this work. The cuts we apply, shown as red or blue dashed lines, are explained in the text. Top panel: $[\alpha/{\rm Fe}]$ versus $[{\rm Fe}/{\rm H}]$, color-coded by mass; we select the $3801$$\alpha$-poor stars from the $4997$ "gold" RGB stars. Middle panel: $[{\rm Fe}/{\rm H}]$ versus mass, color-coded by $[\alpha/{\rm Fe}]$; we use the $3513$ stars within the metallicity range $-0.45 < [{\rm Fe}/{\rm H}] < 0.45$ and the mass range $0.9 \,{\rm M}_\odot < M < 1.8 \,{\rm M}_\odot$. The green dotted lines show the $5^{\rm th}$ and $95^{\rm th}$ percentiles in mass at each metallicity within the $3513$ selected stars. Bottom panel: Kiel diagram ($\log g$ versus $T_{\rm eff}$) of selected stars, color-coded by metallicity; we select the $1261$ lower RGB stars (well below the RGBB) for RGB mixing length calibration purposes and FDU comparisons.
• Figure 2: Predicted $\Delta[{\rm C}/{\rm N}]$ (change from birth value) as a function of $\log g$ according to our benchmark models. Left panel: tracks at and stars near $M = 1.10 \,{\rm M}_\odot$, color-coded by metallicity; right panel: tracks at and stars near $[{\rm Fe}/{\rm H}] = 0.00$, color-coded by mass. End of FDU and center of RGBB are marked with red crosses and orange plus signs, respectively. Note that the curves begin where $\Delta[{\rm C}/{\rm N}]$ values start to change; in other words, $\Delta[{\rm C}/{\rm N}]$ values are constantly zero at higher $\log g$.
• Figure 3: Gravity dependence of observed $\Delta[{\rm C}/{\rm N}]$ (RGB value minus birth value, which is assumed to be Equation (\ref{['eq:Roberts24']})). In each panel, lower RGB stars used in FDU comparisons are shown in pink, while other RGB stars are shown in gray; blue points and error bars are medians and dispersions in $10$ bins of equal widths. Upper panel: observed $\Delta[{\rm C}/{\rm N}]$ values as a function of $\log g$; middle panel: we fit observed $\Delta[{\rm C}/{\rm N}]$ as a function of mass and metallicity, but not gravity, and plot the residuals as a function of $\log g$; lower panel: we subtract benchmark predictions in the middle of RGBB at given masses and metallicities from observed values, and again plot the residuals as a function of $\log g$.
• Figure 4: Comparisons between the APOKASC-3 lower RGB sample (black dots) and theoretical predictions (curves) regarding FDU at solar metallicity. Changes in three abundance ratios from birth values (Equation (\ref{['eq:Roberts24']}) assumed for observational data) to RGB, $\Delta[{\rm C}/{\rm N}]$, $\Delta[{\rm C}/{\rm Fe}]$, and $\Delta[{\rm N}/{\rm Fe}]$ are shown in the upper, middle, and lower panels, respectively. Solid blue curves present our benchmark predictions, and dashed curves are variations (see Section \ref{['ss:fdu_var']}).
• Figure 5: Comparisons between different observational samples regarding FDU at solar metallicity. APOKASC-3 lower RGB, APOKASC-3 RC, and APO-K2 lower RGB samples are shown in blue, orange, and green, respectively. We subtract predicted $\Delta[{\rm C}/{\rm N}]$, $\Delta[{\rm C}/{\rm Fe}]$, and $\Delta[{\rm N}/{\rm Fe}]$ values as functions of mass and metallicity from individual observations, fit the residuals, and visualize the results based on our benchmark grid (other grids) as solid (dashed) curves. The curves start (end) at the $5^{\rm th}$ ($95^{\rm th}$) mass percentile of each sample. In addition, we plot medians and dispersions in several (depending on the number of stars) bins of equal sizes as points and error bars.