- The paper applies asteroseismic ages with 9% precision and optical neutron-capture abundances to analyze s-process clocks, indicating that while first-peak enrichment is well-reproduced, second-peak enrichment remains systematically underpredicted for ages under ~8 Gyr.
- High-metallicity AGB yields of Ce are explored using amended models, and hence it is shown simple rescaling yield adjustments are insufficient to align results with observed data, indicating a more fundamental issue in the understanding of late-time s-process nucleosynthesis.
- The study distinguishes the systematic effects of dynamical migration in the context of chemical clock relations, proposing that dynamically matured stars skew age-space scatter rather than cause significant metallicity scatter, offering context to address age vs metallicity biases in the model.
This paper presents a comparison between Galactic chemical evolution (GCE) model predictions for two s-process chemical clocks, [Zr/Ti] and [Ce/Ti], and a high-precision observational dataset of 68 red giant stars in the Kepler field (2608.17480). The work extends a prior modelling effort based on Gaia-ESO open clusters by adopting asteroseismic ages derived from individual oscillation-mode frequencies, combined with high-resolution optical spectroscopy of neutron-capture elements. The central finding is that while first-peak s-process enrichment is well reproduced, second-peak production over the last ∼6 Gyr remains systematically underpredicted, and that simple rescaling of high-metallicity AGB yields cannot resolve this deficit.
Observational sample
The dataset consists of 68 Kepler red giants selected from the RGB catalogue cross-matched with APOGEE DR17, spanning −0.8≤[Fe/H]≤0.4 dex and sampling both the low- and high-α sequences. Ages were obtained through Bayesian inference using the AIMS code with individual mode frequencies, achieving a typical age precision of 9%. Complementary HARPS-N (R∼115,000) and FIES (R∼67,000) spectra provide abundances for neutron-capture species inaccessible in APOGEE infrared spectra, analysed homogeneously via equivalent widths with DOOp/DAOSPEC, MOOG, and MARCS atmospheres, with surface gravities fixed to seismic values. The chemical clocks [Zr/Ti] and [Ce/Ti] exhibit observed scatters of only s=0.01 dex and s=0.08 dex versus age respectively — exceptionally tight relations that make this dataset a stringent test for GCE models, extending to ages above 13 Gyr where open cluster samples are unavailable.
Nucleosynthetic prescriptions
Zr is approximately 82% s-process at solar metallicity and Ce approximately 85%, so both are dominated by the main s-process operating in LIMS during the AGB phase via the 13C(α,n)16O neutron source. The models adopt FRUITY yields for LIMS and rotating massive-star yields (set R) from Limongi & Chieffi with metallicity-dependent rotation distributions favouring faster rotators at lower metallicities.
A key physical ingredient is the well-established decline of second-peak AGB yields at high metallicity: increasing iron seed nuclei lower the neutron-to-seed ratio, suppressing the multiple captures needed to reach the A∼130 peak while leaving first-peak production largely unaffected. Four models are tested:
| Model |
Ce yield prescription |
| Model 1 |
Baseline FRUITY yields |
| Model 2 |
Ce yields at Z>0.01 replaced by those at −0.8≤[Fe/H]≤0.40 |
| Model 3 |
High-metallicity Ce yields boosted by factor 1.5 |
| Model 4 |
High-metallicity Ce yields boosted by factor 2.0 |
A notable methodological concession concerns Ti itself: because Ti is systematically underproduced by all CC-SN yield sets, the authors apply a phenomenological metallicity-independent scaling factor of 4 to CC-SN Ti yields. They verify that conclusions hold when Ca or Si are used as reference −0.8≤[Fe/H]≤0.41-elements instead, although those clocks show larger observed scatter.
Results
The baseline model reproduces the [Zr/Ti] clock and the high-−0.8≤[Fe/H]≤0.42 sequence satisfactorily in both age and metallicity space, indicating a well-constrained enrichment history for first-peak elements. In contrast, [Ce/Ti] turns downward at ages −0.8≤[Fe/H]≤0.43 Gyr, opposite to the observed rise — a persistent deficit in second-peak s-process production over the last several Gyr of thin-disc evolution.
The yield modifications provide only partial relief. Model 2 reduces the spurious young-age decrease but amplifies an unobserved local peak near 10–11 Gyr; Models 3 and 4 shift predictions toward higher [Ce/Ti] at intermediate to high [Fe/H], yet none reproduces the most Ce-enhanced young stars at [Fe/H] −0.8≤[Fe/H]≤0.44. This leads to the paper's strongest claim: simple rescaling of high-metallicity AGB yields is insufficient, and more fundamental revisions to high-metallicity s-process nucleosynthesis may be required.
The authors further argue against ad hoc yield enhancements on three independent grounds. First, inside-out disc formation means solar-neighbourhood high metallicities are also reached in the inner disc at older epochs, so boosting yields would degrade agreement with inner-disc open clusters at −0.8≤[Fe/H]≤0.45 kpc. Second, within the two-infall framework, high metallicities occur already at −0.8≤[Fe/H]≤0.4610–11 Gyr during the first infall phase, producing unobserved peaks in the age–abundance relations. Third, there is no nucleosynthetic mechanism that would selectively enhance the second peak without affecting the first, particularly since decreasing [heavy-s/light-s] ratios in barium stars support the expected suppression of second-peak production at high metallicity.
A robust diagnostic result emerges from comparing model performance across projections: agreement is systematically tighter in [X/H] vs. [Fe/H] than in [X/H] vs. Age. Migrated stars scatter predominantly along the age axis rather than the metallicity axis, because stars of similar birth radius share comparable abundance patterns regardless of current location, whereas stars of similar age span wide [X/H] ranges reflecting their diverse birth radii. This implies that the residual scatter in the age-space chemical clock relations is partly a dynamical artefact of radial migration, absent from the one-zone-per-radius GCE framework adopted here. Consistent with this, the dataset contains a few old (−0.8≤[Fe/H]≤0.4710–11 Gyr), metal-poor low-−0.8≤[Fe/H]≤0.48 stars suggesting thin-disc onset earlier than the canonical −0.8≤[Fe/H]≤0.498–9 Gyr estimate.
Limitations and open questions
Several caveats bear directly on the results. The Ti scaling factor of 4 is explicitly phenomenological; although appendix tests with Ca and Si confirm the Ce deficit conclusion, the reference-element choice does modulate details such as which stars are underproduced in metallicity space. The unobserved model peak at 10–11 Gyr persists across all four yield prescriptions, and appendix experiments with alternative massive-star rotation distributions show that only extreme, independently disfavoured fast-rotator distributions flatten it — and even then at the cost of losing agreement with the data overall. The authors therefore leave open whether the peak reflects incorrect relative nucleosynthetic timescales, a modified star formation history, or limitations of the two-infall scenario itself. Finally, the self-consistent inclusion of radial migration within the GCE framework is deferred to ongoing work, so its quantitative contribution to reconciling the [Ce/Ti] clock remains undetermined.
Conclusion
Using asteroseismic ages with 9% precision and optical neutron-capture abundances, this study demonstrates that first-peak s-process chemical clocks are well captured by current multi-zone GCE models, whereas second-peak clocks in the young, metal-rich thin disc are not — and that the deficit cannot be fixed by rescaling high-metallicity AGB Ce yields without generating contradictions elsewhere in the Galaxy. The origin of the missing late-time second-peak s-process material, whether rooted in AGB physics beyond current grids or coupled to stellar migration, remains the central unresolved question raised by these results.