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The non-LTE abundances of magnesium and yttrium and asteroseismic ages for the chemical clock calibration

T0 review · 3 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The empirical [Y/Mg]–age relation is not a universal chemical clock: its calibration depends on Galactic location and stellar metallicity.

desk verdict Solid sample paper extending Paper I; the non-universality result is not new, but the NLTE-calibrated dataset is a real resource—main weakness is missing statistical significance testing on the slopes. read the letter →

arxiv 2607.15017 v1 pith:KQOUQC2N submitted 2026-07-16 astro-ph.SR astro-ph.GA

Š. Mikolaitis , G. Tautvaišienė , E. Pakštienė , A. Drazdauskas , V. Bagdonas , C. Viscasillas Vázquez , M. Ambrosch , Y. Chorniy
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R. Minkevičiūtė E. Stonkutė B. Bale B. Ćurjurić A. Sharma K. Diktanaitė
This is my paper
classification astro-ph.SRastro-ph.GA
keywords chemicalclock[Y/Mg]rationon-LTEabundancesasteroseismicagesGalacticdiscyttriummagnesiumevolution
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper establishes that the [Y/Mg] abundance ratio, a popular 'chemical clock' for stellar ages, behaves differently in different parts of the Milky Way. Using a sample of 736 field stars with non-LTE (NLTE) abundances of magnesium and yttrium, and ages from asteroseismology for 525 of them and isochrone fitting for the rest, the authors fit linear relations between log(age) and [Y/Mg] for the inner, solar, and outer thin disc and for the thick disc. The slopes differ markedly (from –7.1 in the outer disc to –17.9 in the thick disc) and the correlation is strongest in the outer disc (Pearson correlation coefficient –0.60). The relation also depends on metallicity: more metal-rich stars have higher [Y/Mg] at a given age, but at supersolar metallicity the relation flattens. The authors conclude that [Y/Mg] cannot be used as a one-size-fits-all age indicator; calibrations must account for Galactic environment and metallicity.

What carries the argument

The central object is the [Y/Mg] abundance ratio used as a chemical clock. Magnesium is produced promptly by core-collapse supernovae, while yttrium builds up slowly through the s-process in asymptotic giant branch stars, so [Y/Mg] is sensitive to the time since the onset of star formation. The paper's argument is carried by linear regressions of log(age) on [Y/Mg] computed separately for four Galactic subsamples (inner, solar, outer thin disc, and thick disc) and for metallicity bins, with ages from asteroseismic scaling relations via PARAM and isochronal ages from SPInS.

What would settle it

A sample of stars in the inner, solar, and outer disc that all have asteroseismic ages (no isochronal ages) and identical age-determination methods, with well-measured NLTE [Y/Mg] and metallicity, would test the claim: if the linear fits of log age versus [Y/Mg] for the three radius bins turn out to have statistically indistinguishable slopes, the spatial dependence is falsified. Alternatively, if a single universal slope fits the combined data once metallicity is accounted for, the paper's core claim fails.

Watch

Extended reading notes

Core claim

Across 736 Galactic field stars with NLTE-corrected Mg and Y abundances and ages anchored by asteroseismology, the [Y/Mg]–age relation is not universal. Fitting log Age = m·[Y/Mg] + c to four subsamples yields different slopes: m = –16.1 for the inner disc (R_mean < 7.5 kpc), –12.5 for the solar region, –7.1 for the outer disc (R_mean > 8.5 kpc), and –17.9 for the thick disc, with correlation coefficients of –0.22, –0.35, –0.60, and –0.20 respectively. The steep outer-disc relation indicates stronger s-process temporal evolution where star formation is less efficient, while the flat inner-disc and thick-disc relations indicate rapid enrichment. Dividing the thin disc by metallicity, [Y/Mg] i

Load-bearing premise

The two age-determination methods (asteroseismic PARAM and isochronal SPInS) are assumed to be on a consistent age scale, and the isochronal ages, which carry roughly 30% relative uncertainty, are used for a large fraction of stars; if the two scales differ systematically by more than about 0.5 Gyr, the fitted slope differences between Galactic regions could be artifacts rather than real spatial variations.

Editorial extensions

If this is right

  • Stellar ages inferred from [Y/Mg] must be calibrated for the star's Galactic region; applying a single relation leads to systematic age errors, especially in the outer disc where the relation is steepest.
  • The steep outer-disc relation implies that [Y/Mg] is most sensitive to age in low star-formation-efficiency environments, potentially making it a precise tool for outer-disc stars.
  • The weak thick-disc correlation supports a rapid formation scenario dominated by Type II supernovae, with little contribution from asymptotic giant branch s-process enrichment.
  • The metallicity dependence means that metallicity must be included as a second parameter in any chemical-clock calibration, with a flatter relation expected above [Fe/H] > 0.1.
  • These results motivate chemical-evolution models to reproduce the radial gradient in the [Y/Mg]–age relation as a constraint on star formation histories.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The demonstrated spatial variation suggests that other s-process abundance ratios used as chemical clocks (e.g., [Ba/Mg] or [Ce/Mg]) are also likely to vary with Galactocentric radius, so future calibrations should quote region-specific coefficients.
  • If the supersolar flattening is confirmed with larger samples, [Y/Mg] ages for metal-rich stars will need a separate, possibly non-linear calibration; the current sample contains only 31, 5, and 7 supersolar stars in the solar, inner, and outer regions respectively.
  • The use of isochronal ages for a substantial fraction of stars could introduce systematic bias; a direct test would be to compare single-age open clusters across the disc, using only asteroseismic ages, to see if the fitted slope differences in each radius bin persist.
  • The observed radial slope gradient may provide a new diagnostic to distinguish among different AGB yield prescriptions (e.g., with or without magnetic mixing) in multi-zone chemical evolution models.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper presents new high-resolution VUES spectroscopy for 528 F/G/K stars, derives NLTE-corrected Mg and Y abundances, and combines these with the 208 stars from Paper I to assemble a 736-star sample with ages from PARAM asteroseismology (307 stars) or SPInS isochrone fitting (221 stars). The central result is that the empirical [Y/Mg]–age relation varies systematically across the Galactic disc: fits for inner, solar, outer, and thick-disc populations are given in Eqs. 1–4, with the outer disc showing the strongest correlation (PCC = −0.60) and the thick disc a weak correlation (PCC = −0.20). The paper further reports a metallicity dependence in which [Y/Mg] increases with [Fe/H] across most of the age range, but the trend may flatten at supersolar metallicities (Table 1, Fig. 11). The authors conclude that [Y/Mg] is not a universal chemical clock and must be calibrated by environment and metallicity.

Significance. If the claimed spatial and metallicity variations are statistically robust, the paper strengthens the emerging consensus that the [Y/Mg] chemical clock is not universal, adding a homogeneous NLTE abundance analysis and asteroseismic ages to a larger sample than Paper I. The manuscript's strengths include the explicit use of NLTE corrections for Mg and Y, the combination of asteroseismic and isochronal ages with a cross-check, and the provision of machine-readable tables with full parameter sets. However, the quantitative support for the central claim is currently incomplete: the slope differences in Eqs. 1–4 and Table 1 are reported without uncertainties or significance tests, and the age-scale combination is only checked qualitatively. The paper is therefore a useful empirical contribution in need of revision to demonstrate that the reported gradients are statistically meaningful rather than artifacts of the fitting method, sample selection, or age-scale heterogeneity.

major comments (3)
  1. [§3.1, Eqs. 1–4; Table 1] The central claim that the [Y/Mg]–age relation varies systematically across the disc rests on the slopes in Eqs. 1–4. These are quoted as point values with no confidence intervals, and no test is performed of whether the regional slope differences are significant. With PCCs of −0.22, −0.35, −0.60, and −0.20 for sample sizes of 154, 318, 151, and 29, the 95% confidence intervals on the slopes are likely wide; for example, the inner- and solar-region slopes may not be distinguishable. The 95% confidence bands in Fig. 9 are shown but not quantified, and no overlap test is reported. The same issue applies to Table 1, where the supersolar flattening claim rests on subsamples of 31, 5, and 7 stars. Please provide slope uncertainties (e.g., bootstrap or covariance-based), p-values or equivalence tests for slope differences, and a clear statement of the regression method, including whether age u
  2. [§2.4.2, §3.1, Figs. 8 and 9] The main age scale is a combination of 307 PARAM asteroseismic ages and 221 SPInS isochronal ages. The paper states that Fig. 8 shows good agreement and that removing SPInS stars does not significantly change the fits, but both checks are only visual and qualitative. Since SPInS ages carry a mean relative uncertainty of ~30% and the fraction of SPInS stars may differ between radial bins, an unrecognized systematic offset between the two age scales could bias the regional slopes and the inferred radial gradient. I request a quantitative assessment: for example, include an age-method indicator in the regression and test its coefficient, or repeat the regional fits using only the 525 asteroseismic-age stars and formally compare the slopes and intercepts with the full-sample values. This is load-bearing because the claimed radial slope differences could in principle be produced by different
  3. [§3.2, Fig. 11, Table 1, Abstract] The conclusion that the [Y/Mg]–age relation becomes flatter at supersolar metallicity is based on extremely small subsamples: 31 stars in the solar region and only 5 and 7 stars in the inner and outer regions, respectively. The text acknowledges the small samples but still states that 'the flattened relation is visible,' and the abstract generalizes this tendency. With 5 or 7 points, the slope estimate is dominated by a few stars and no meaningful regression can be performed. Please either report the uncertainties on the supersolar fits and explicitly state that the inner/outer claims are not statistically testable with the present sample, or soften the abstract and conclusions to match the limited evidence. The wording 'may not hold' in the abstract is appropriately cautious, but the same caution is not consistently applied in the discussion.
minor comments (4)
  1. [§3.1, Eqs. 1–4] The text describes the outer-disc relation as 'steeper' and the inner-disc relation as 'flatter,' but the fitted coefficients m in Eqs. 1–4 have |m| = 16.1 (inner) versus |m| = 7.1 (outer). Since the equations are written as log Age = m [Y/Mg] + c, the slope of [Y/Mg] versus log Age is 1/m, so the outer disc has a larger |1/m|. Please clarify the slope convention used in the text, especially when comparing 'steepness' across regions.
  2. [§2.1] The list of known binaries appears to contain an inconsistency: the text says 'three previously known binaries' but then lists four identifiers. Please check the count and the catalogue IDs.
  3. [§2.3] The notation TD/D is used without explicit definition; define the thick-to-thin disc probability ratio in the text or a table footnote for clarity.
  4. [Fig. 7] The bottom-right histogram would benefit from labels distinguishing the PARAM ages from the SPInS ages in the printed figure, as the caption relies on colors that may not be distinguishable in all versions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eqs. 1-4 are direct empirical fits to measured abundances and ages, with no fitted parameter renamed as a prediction and no input defined in terms of the claimed output.

full rationale

The paper's central claims are empirical characterisations of the [Y/Mg]-age relation across Galactic regions and metallicity bins, obtained by linear least-squares fits to measured abundance ratios and independently derived ages. The relations in Eqs. 1-4 are not derived from, nor equivalent to, any input parameter that was itself fitted to those relations. Asteroseismic ages are computed from TESS pulsation quantities (nu_max, Delta_nu) and spectroscopic Teff/[Fe/H] via PARAM, with no dependence on [Y/Mg] or Mg/Y abundances. Isochronal SPInS ages use Teff, log g, [Fe/H], M_V, and B-V as constraints; again [Y/Mg] is not an input. The comparison in Fig. 8 and the check that removing SPInS stars does not change the fits are calibration/robustness checks, not circular reductions. NLTE abundance corrections are imported from external, non-overlapping groups (Bergemann et al. 2017; Storm & Bergemann 2023; Storm et al. 2024), so the abundance scale is not defined by the present paper's target result. Self-citations to Paper I supply sample continuity, region definitions, and a prior interpretive framework, but the spatial-variation claim is also supported by independent references (e.g., Casali et al. 2020; Viscasillas Vazquez et al. 2022; Ratcliffe et al. 2024) and by the new 528-star sample analysed here, so the self-citation is not load-bearing in a circular sense. The paper itself flags the small supersolar subsamples in the inner and outer regions (Sect. 3.2: 'we had just five and seven stars, respectively') and reports ~30% relative SPInS age uncertainties (Sect. 2.4.2); these are statistical-robustness limitations, as is the absence of reported slope uncertainties, but none of these limitations makes any step equivalent to its inputs. No circular step meeting the required standard can be exhibited, so the appropriate score is 0.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on empirically fitted linear relations and on external model grids and age-determination methods. No new physical entities are postulated; the newly identified spectroscopic binaries are observational classifications. The main unvalidated burden is the consistency of the two age scales and the hand-chosen binning thresholds.

free parameters (7)
  • Inner thin-disc [Y/Mg]-age slope and intercept = m=-16.129, c=8.113
    Linear fit to 154 inner-region stars (Eq. 1); defines the claimed flattening in the inner disc.
  • Solar-region [Y/Mg]-age slope and intercept = m=-12.5, c=8.938
    Eq. 2, 318 stars; the baseline for comparing radial differences.
  • Outer-disc [Y/Mg]-age slope and intercept = m=-7.092, c=9.206
    Eq. 3, 151 stars; steepest in the [Y/Mg]-versus-age representation and strongest PCC.
  • Thick-disc [Y/Mg]-age slope and intercept = m=-17.857, c=4.696
    Eq. 4, 29 stars; supports the 'flat thick disc' interpretation despite a similar numerical m to the inner disc.
  • Metallicity-bin relation parameters (Table 1) = 7 slope/intercept pairs
    Fits for [Fe/H]>0.1, -0.2<[Fe/H]<0.1, and <=-0.2 in inner/solar/outer regions; these support the metallicity-dependence conclusion.
  • Radial and metallicity bin boundaries = Rmean=7.5, 8.5 kpc; [Fe/H]=-0.2, 0.1 dex; age cut 0.17 Gyr
    Chosen bin edges inherited from Paper I and references; slope comparisons can depend on these hand-selected thresholds.
  • Disc membership thresholds = v>85 km/s (thick), v<100 km/s (thin), TD/D>0.5 or <4, [Mg/Fe] enhancement
    Hand-chosen kinematic and chemical criteria divide the sample into thin disc, thick disc, halo, and unclassified populations; misclassification can contaminate the thick-disc relation (Eq. 4).
assumptions (5)
  • domain assumption 1D LTE MARCS model atmospheres are adequate for deriving Teff/logg/[Fe/H] and for the spectral synthesis of Mg and Y lines.
    Used throughout Section 2.2; if 3D structure or NLTE effects beyond the applied abundance corrections matter, the derived abundances could be biased.
  • domain assumption The NLTE corrections of Bergemann et al. (2017) for Mg I and Storm & Bergemann (2023)/Storm et al. (2024) for Y II are accurate in the stellar parameter range studied.
    Section 2.2; the paper's central selling point is the NLTE treatment, so the validity of the external NLTE grids is load-bearing.
  • domain assumption PARAM asteroseismic ages and SPInS isochronal ages are on a consistent and unbiased age scale.
    Section 2.4 and Fig. 8; combining 307 asteroseismic and 221 isochronal ages assumes no systematic offset, and SPInS ages have ~30% relative uncertainties.
  • domain assumption galpy's MWPotential2014, the adopted solar motion/position, and the Gaussian velocity ellipsoid priors (Bensby et al. 2014; Vieira et al. 2022) reliably classify thin- and thick-disc membership.
    Section 2.3; the thick-disc relation in Eq. 4 rests on only 29 stars classified by this threefold kinematic/chemical criterion.
  • domain assumption The bright V<8 TESS-monitored sample represents the underlying disc populations without strong selection biases in the [Y/Mg]-age plane.
    Section 2.1; target selection is brightness-limited and photometrically selected, not volume-complete, which could skew the apparent age-metallicity-radius distributions.

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Cite this review

Pith. "Pith review of The non-LTE abundances of magnesium and yttrium and asteroseismic ages for the chemical clock calibration." pith.science (2026). https://pith.science/paper/KQOUQC2N

@misc{pith2026260715017,
  author       = {Pith},
  title        = {Pith review of: The non-LTE abundances of magnesium and yttrium and asteroseismic ages for the chemical clock calibration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KQOUQC2N}},
  note         = {Machine review of arXiv:2607.15017}
}
read the original abstract

Building on our previous study, which demonstrated the importance of accounting for departures from local thermodynamic equilibrium (LTE) in elemental-abundance determinations and of using asteroseismic ages, we investigate spatial variations in the empirical [Y/Mg]-age relation across the Galactic disc using a substantially larger stellar sample. We analysed high-resolution stellar spectra and determined Mg and Y abundances through spectral synthesis of multiple spectral features, rigorously accounting for non-LTE (NLTE) effects. We derived asteroseismic ages for stars exhibiting solar-type oscillations and used cross-checked isochrone-based methods for the remaining stars. We determined atmospheric parameters and Mg and Y abundances for 528 Galactic field stars, together with asteroseismic ages for 307 stars and isochronal ages for 221 stars. We also identified two new triple-lined and nine double-lined spectroscopic systems. Combining the present sample with that of our previous study yielded a total of 736 stars, which we used to examine the [Y/Mg]-age relation across the Galactic disc. The relation shows systematic spatial variations that likely reflect differences in star-formation and chemical-enrichment histories. In general, [Y/Mg] tends to increase with metallicity over the investigated age range. At supersolar metallicity, however, this trend may weaken, and the [Y/Mg]-age relations become flatter than those of solar-metallicity stars, which show lower [Y/Mg] values at young ages and higher values at old ages.

Figures

Figures reproduced from arXiv: 2607.15017 by the authors.

Figure 1
Figure 1. Example CCFs showing triple-line features in the spectra [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Distributions of the stellar orbital parameters of the full [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Toomre diagram of the investigated stars, attributed to the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: [Mg/Fe] versus [Fe/H] plot indicating stars of the thin and thick discs, the halo star, and the unclassified stars. Symbols are as in [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: Distribution of νmax and ∆ν determined. We computed pulsation spectra for all stars, but robust deter￾minations of νmax and ∆ν were possible for just 307 stars. Only stars showing clear solar-like pulsations with easily recognisable ridges of ℓ = 0, 1, and 2 modes in é…
Figure 7
Figure 7. Figure 7: Distributions of stellar parameters in the sample stars. [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 8
Figure 8. Figure 8: Comparison of ages determined with the PARAM and [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: [Y/Mg] as a function of stellar age for thin- and thick-disc stars. Stars with Rmean < 7.5 kpc are attributed to the inner Galactic disc, the solar region is at 7.5 ≤ Rmean ≤ 8.5 kpc, and the outer disc is at Rmean > 8.5 kpc. Linear fits for different Galactic regions …
Figure 10
Figure 10. Figure 10: [Y/Mg] as a function of stellar age for the thin-disc stars divided into the inner, solar, and outer Galactic regions and divided according to metallicity. The continuous lines are for stars with [Fe/H]> −0.2, and the dashed lines are for [Fe/H] ≤ −0.2. Linear fits wi…
Figure 11
Figure 11. Figure 11: [Y/Mg] as a function of stellar age for the thin-disc stars in the solar region divided according to metallicity. The dotted line is for stars with [Fe/H]> 0.1, the continuous line is for stars with −0.2 < [Fe/H] < 0.1, and the dashed line is for stars with [Fe/H] ≤ −…

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