[C/N] Ages and Extra-Mixing for [Fe/H] <- 0.5: Insights from the LMC and SMC

TL;DR

This work tackles how extra mixing alters the [C/N]-age relation at low metallicity, which complicates stellar age dating. By exploiting the Magellanic Clouds, it disentangles mass, age, and metallicity effects and tests both an empirical MW-based extra-mixing correction and Lagarde2012 thermohaline models. The study finds a mass-dependent mixing pattern with a threshold near $M \sim 1.8\,M_{\odot}$ at $[\mathrm{Fe/H}] \sim -0.7$, and shows that MW-derived corrections work well for $M<1.25\,M_{\odot}$ while thermohaline models reproduce the trend for $M>1.25\,M_{\odot}$ but over-predict mixing at lower masses. These results demonstrate the feasibility of deriving [C/N]-based ages for individual stars in external galaxies and outline concrete steps (denser metallicity grids, higher-$\log g$ observations, cluster benchmarks) to refine the calibration for low-metallicity populations.

Abstract

The [C/N]-age relation has become a powerful tool for reconstructing the formation history of the Milky Way (MW), providing the largest age sample for field giant stars. However, at metallicities below [Fe/H] $< -0.5$, stellar surfaces are altered by a poorly understood process known as extra mixing, which modifies [C/N] in a mass- and metallicity-dependent manner. This effect complicates the application of the traditional [C/N]-age relation in metal-poor regimes. Within the MW, constraining the mass dependence of extra mixing is particularly challenging because stars at [Fe/H] $< -0.5$ are predominantly old and therefore low-mass, leading to strong degeneracies between mass and metallicity. In this work, we explore the potential of the Magellanic Clouds (MCs) to disentangle these effects and constrain extra mixing as a function of age and metallicity. By comparing empirical corrections calibrated in the MW with predictions from thermohaline mixing models, we isolate the mass dependence of extra mixing in the MCs down to [Fe/H] $\sim-0.7$. We find that the empirical calibration performs well for lower-mass stars ($< 1.25$ $M_{\odot}$), while theoretical models successfully reproduce the observed mass dependence down to $\sim$ 1.25 $M_{\odot}$. We further present the first observational evidence that extra mixing becomes ineffective above $\sim$ 1.8 $M_{\odot}$ at [Fe/H] $\sim -0.7$. Our results demonstrate the feasibility of deriving [C/N]-based ages for individual stars in external galaxies. Future observations targeting higher-$\log g$ or fainter stars in the MCs will provide stronger constraints on extra-mixing processes and enable the calibration of [C/N]-age relation that can be applied to low-metallicity individual stars in the MW or external galaxies.

Figures (4)

• Figure 1: The age-metallicity (left), mass-metallicity (middle), and [(C+N)/Fe]-[Fe/H] relations for the APOKASC--3 sample Pinsonneault2025 in gray, the LMC sample in blue abdurrouf2022Povick2024, and the SMC sample in red abdurrouf2022Povick2024. The LMC and SMC harbor massive, metal-poor stars that can be used to understand and test extra-mixing correction as a function of mass at [Fe/H]$< -$0.5. The strong correlation between [Fe/H] and [(C+N)/Fe] suggests [Fe/H] should be a good proxy for the birth mixture for stars in the MW and the MCs. The two sequences observed in [(C+N)/Fe]–[Fe/H] space in the MW correspond to the high- and low-$\alpha$ disk populations. At a fixed [Fe/H], stars belonging to the high-$\alpha$ disk exhibit systematically higher [(C+N)/Fe] than those in the low-$\alpha$ disk.
• Figure 2: The top row shows the observed [C/N] and the bottom row shows the [C/N] after correcting for extra-mixing following Shetrone2019. The points are colored by their metallicity. The gray points in the middle and right columns show the [C/N]-mass relation for the MW (same as the corresponding left column) for better comparison. The colored lines and shaded areas show the running median and median absolute deviation (MAD) for different mono-metallicity populations, respectively. The subplots under each figure in the top row show the MAD as a function of mass for better visualization. The metal-poor, high-mass stars in the LMC and SMC hint that extra-mixing might not be effective for stars more massive than $\sim$1.8 $M_{\odot}$ at [Fe/H] $\sim -$0.7, where the running median of the lower metallicity line crosses that of the higher metallicity line in the LMC. The lines also cross for the MW at $\sim$0.1 dex, respectively, most likely due to the increase in scatter around the line.
• Figure 3: Thermohaline + rotation mixing models from Lagarde2012 compared with the data in the LMC and SMC at different masses. Each row shows stars in different metallicity bins and each column shows those in different mass bins. The models are shifted up by 0.4 dex in [C/N] to better match the observations. The models over-predict the log$g$ dependence of extra-mixing, as the data does not show a strong relation between log$g$ and [C/N], as also seen in the MW Shetrone2019. An upturn of [C/N] is seen in the LMC at low log$g$ that could be caused by systematics in the abundance measurements Sit2024.
• Figure 4: Models from Lagarde2012 comparing with the LMC (top) and SMC (bottom) data. The initial $Z$ and mass fractions are converted to abundance ratios using the solar composition from Asplund2005. The masses for the models are taken to be the initial mass. The models are plotted in black outlined points, colored by their initial metallicity. Stars with the same initial mass and metallicity are connected by lines for better visualization. The scatter for each metallicity at the same mass for the models is caused by the log$g$ selection, where thermohaline mixing continues to affect the [C/N] ratio in a log$g$ dependent way. We only selected RGB stars with log$g$ between 0.6 and 1.2 for the LMC and 0.8 and 1.2 for the SMC to match the observed range. The range of [C/N] for each model at a metallicity and mass can also be seen in \ref{['fig:5']}. We shift the model up by 0.4 dex to better match the data. For the observations, we select the same log$g$ range for consistency. The metallicity range is selected to be 0.1 dex around the model metallicity. The data is plotted in crosses, colored by their [Fe/H], and the lines show the running median for better visualization. The models fit well at [Fe/H] = $-0.5$ for the LMC but likely over-predict the effect of extra-mixing at $-0.8$ dex at lower masses ($\sim$1.2 $M_{\odot}$).