{"id":"e6c83d5a-8f3a-4261-b0e0-e14cf75d0961","arxiv_id":"2506.15546","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The authors calibrate [Ce/Mg] and [Zr/Ti] chemical clocks on 68 Kepler giants and transfer them to APOGEE and Gaia-ESO to map stellar ages across the Galactic disc.","lead":"Astronomers used 68 bright red giant stars with extremely precise asteroseismic ages and new high-resolution spectra to calibrate 'chemical clocks': abundance ratios that change predictably with stellar age. Applying these clocks to 270,000 survey stars recovered known structures of the Milky Way, including the thick disc and the flaring outer disc.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Birth-radius dependence of the [Ce/Mg]-age slope in Table 4 is ignored when transferring the relation to APOGEE, so the recovered disc structures may be biased.","rationale":"I read the paper as claiming two things: first, that high-precision [Ce/Mg] and [Zr/Ti] correlate tightly with asteroseismic age in 68 Kepler giants, and second, that the calibrated linear relations transfer to APOGEE and Gaia-ESO and reproduce known Galactic age structures. The evidence for the first claim is strong: high-resolution abundances, individual-mode asteroseismic ages, in-sample recovery tests, and a clear degradation test showing that APOGEE abundances produce larger scatter. The evidence for the second claim is weaker and is the load-bearing part of the headline. The most concrete threat is not simply extrapolation in [Fe/H] but the paper's own Table 4: the [Ce/Mg] slope changes by roughly 3 sigma between birth-radius bins. Because the application bins by guiding radius or not at all, and because guiding radius is a poor proxy for birth radius for migrated stars, field ages can be biased in a way that correlates with Galactic radius and height. That correlation is exactly what would produce the claimed disc flaring and age-metallicity trends. A direct out-of-sample test against Kepler giants with independent ages would settle whether the birth-radius dependence actually biases the transferred ages. I do not see a reason to reject the calibration itself; the paper is honest about limitations and the in-sample precision is impressive. But the transferability claim needs the additional robustness check, so conditional acceptance remains appropriate. My concern is a sharpening of the reader's weakest-assumption point: the linear model of Eq. (2) is assumed to be universal across the disc, and the table of fitted parameters already shows a radial dependence that the application does not correct for.","tokens_in":39186,"tokens_out":13804,"duration_ms":137629,"concrete_test":"Apply the paper's no-binning and Rg-binned [Ce/Mg] relations to APOKASC-3 Kepler giants that were not among the 68 calibrators and that have APOGEE abundances and asteroseismic ages. Estimate each star's birth radius from its asteroseismic age and metallicity using the Lu et al. (2024) method. Regress the residual (chemical age minus asteroseismic age) against Rb. If the residual slope exceeds about 2 Gyr across the Rb range covered by APOGEE, or if an iterative Rb-binned recalibration changes the disc-flaring map, then the single-relation transfer is biased and the central application is not supported.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The transfer step in Section 4 applies a single [Ce/Mg]-age relation, binned in guiding radius Rg or unbinned, to about 270,000 APOGEE stars. However, Table 4 shows that the fitted slope m1 of the [Ce/Mg] relation depends on birth radius Rb: -0.018 +/- 0.006 dex/Gyr for Rb < 6 kpc versus -0.049 +/- 0.008 dex/Gyr for Rb > 7 kpc, a difference of about 3 sigma. The paper itself notes (Section 4) that the Rb-binned relations cannot be applied to field stars because Rb requires an age, but then uses the adopted relation to compute Rb for old metal-rich stars in Section 4.3. The Rg-binned alternative is not a substitute: the calibrators' Rg distribution is narrow, peaked near 8 kpc (Fig. 5), while APOGEE spans much smaller and larger radii. If this birth-radius dependence is real, as previously reported for Ce by Casali et al. (2023) and Ratcliffe et al. (2023), then stars born in the inner and outer disc receive systematically biased chemical ages. The age-metallicity relation, old metal-rich population, and disc flaring recovered in Section 4 could then be artifacts of applying an averaged slope rather than genuine Galactic structure. The central claim that the 68-star calibration transfers to field surveys therefore rests on an untested assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper calibrates empirical chemical clock relations [Ce/Mg] and [Zr/Ti] against stellar age and metallicity using 68 Kepler red giants with high-resolution HARPS-N/FIES spectroscopy and asteroseismic ages from individual mode frequencies (AIMS) at roughly 8% typical precision. The relations are fitted with a linear model in age and [Fe/H] (Eq. 2), in bins of guiding radius Rg and birth radius Rb, with parameters in Table 4. The authors then apply the Rg-binned and unbinned relations to roughly 270,000 APOGEE DR17 stars and about 1,500 Gaia-ESO stars, obtaining chemical ages that reproduce the age separation of the low- and high-alpha sequences, an age-metallicity relation, disc flaring, and the presence of old metal-rich and old metal-poor low-alpha populations.","tokens_in":39472,"tokens_out":6849,"duration_ms":66764,"significance":"If the transfer of the 68-star calibration to field surveys is valid, the paper provides a large sample of chemical ages for field stars and demonstrates the importance of high-precision calibration data. A particularly valuable result is the quantitative demonstration that APOGEE-quality abundances degrade the intrinsic scatter of the relation (about 0.15 dex versus 0.08 dex), a cautionary result for survey-level chemical clocks. However, the central claim that the calibration transfers to APOGEE and Gaia-ESO rests on an untested assumption about the universality of the [Ce/Mg]-age relation across birth radii, and the recovery test used to quote accuracy and precision is performed on the calibrators themselves. These issues limit the significance of the field-star results until they are addressed.","major_comments":[{"comment":"The [Ce/Mg]-age slope shows a 3-sigma dependence on birth radius: m1 = -0.018 +/- 0.006 dex/Gyr for Rb < 6 kpc versus -0.049 +/- 0.008 dex/Gyr for Rb > 7 kpc. In the transfer to APOGEE in Section 4, the authors apply the Rg-binned or no-binning relations, whose slopes are intermediate, without quantifying the systematic age bias that this introduces for field stars with a broad Rb distribution. The statement in Section 4 that the Rb-binned relations cannot be used because Rb requires an age is correct, but it does not establish that the adopted relation is unbiased. I ask the authors to quantify this bias, for example by computing chemical ages for their 68 calibrators with the extreme Rb-binned relations and comparing to the asteroseismic ages, or by estimating the expected bias using the APOGEE Rg and [Fe/H] distributions together with the Lu et al. (2024) birth-radius prescription. Without such a test, the recovered disc flaring, age-metallicity relation, and old metal-rich star populations could be artifacts of applying an averaged relation.","section":"Section 3.1 and Table 4; Section 4"},{"comment":"The recovery test in Section 3.2 is performed on the same 68 stars used to build the relations, as the authors state: it compares chemical ages against 'input asteroseismic ages used to build the relations.' This measures self-consistency rather than predictive accuracy on independent data, yet the abstract and Section 5 present the resulting accuracy and precision (7% accuracy, 60-70% precision) as properties of the method. I request either an independent validation, for example using asteroseismic ages from APOKASC-3 stars not in the calibration sample or open clusters with known ages, or a clear statement in the abstract and conclusions that the quoted accuracy is in-sample and that the field-star results rely on the qualitative reproduction of known age trends rather than on independently validated absolute ages.","section":"Section 3.2 and Section 5"},{"comment":"The birth radii Rb of the old super metal-rich stars are computed using the chemical ages derived from the same [Ce/Mg] relation whose birth-radius dependence is ignored in the transfer. Since the Rb estimate depends on the age through the Lu et al. (2024) prescription, and the age estimate depends on the assumed [Ce/Mg]-age slope, the conclusion that these stars 'show their origin from the inner disc' may be circular. I ask the authors to cross-check this conclusion using an independent age source for a subset (for example asteroseismic ages from the literature) or to demonstrate that the inferred Rb distribution is robust when the slope is varied across the 1-sigma range of the no-binning or Rg-binned values in Table 4.","section":"Section 4.3 and Figure 16"}],"minor_comments":[{"comment":"The paper states that chemical ages for stars outside the calibration metallicity range [-0.8, 0.2] dex are extrapolated, but it does not report how many APOGEE stars fall outside this range or how the extrapolated ages behave. A brief quantification would help the reader assess the impact of the extrapolation on the field-star results.","section":"Section 4, first paragraph"},{"comment":"The revised solar silicon abundance is based on the analysis of a single HARPS solar spectrum; the authors report excellent agreement but do not describe the S/N or line list used. A short note on the robustness of this revision would strengthen the justification for the 0.07 dex adjustment.","section":"Section 2.2"},{"comment":"The comparison between AIMS and PARAM ages shows a mean normalized difference of -0.72 and the paper notes that APOKASC-3 ages are younger by up to 1.7 Gyr at the oldest ages. The authors attribute this to possible mass overestimation in APOKASC-3, but a brief discussion of the impact of systematic age-scale offsets on the absolute calibration of the chemical clocks would be useful.","section":"Section 2.3"},{"comment":"There are several typos and grammatical errors: 'deference' should be 'difference' (Section 4), 'worst' should be 'worse' (Section 5), 'Montalbàn' is inconsistent with 'Montalbán', 'corrisponging' should be 'corresponding' (page 10), and 'the difference less than 1σ among the parameters' (Section 5) is ungrammatical. A careful proofread is needed.","section":"Throughout"},{"comment":"The paper states that data will be shared upon reasonable request, but for reproducibility of the MCMC fits and the derived age catalog of about 270,000 APOGEE stars, a public release of the fit parameters and the chemical-age catalog, for example as a machine-readable table, would be highly valuable.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"The manuscript presents a valuable dataset (68 high-quality Kepler calibrators with detailed abundances and individual-frequency asteroseismic ages) and an important negative result about the precision floor of survey abundances. The central transfer claim, however, is weakened by the paper's own Table 4 showing a birth-radius dependence of the [Ce/Mg]-age slope that is ignored when applying the relation to APOGEE, and the recovery test is in-sample. These are fixable with additional analysis or a more carefully qualified presentation, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should read this one. The paper delivers a genuinely useful calibrating sample: 68 Kepler giants with high-resolution optical abundances (HARPS-N/FIES) and asteroseismic ages from individual mode frequencies, which is a step up in precision from most calibration work. The headline result—[Zr/Ti] with ~0.01 dex intrinsic scatter, and [Ce/Mg] at ~0.08 dex—is a solid empirical finding that will be cited. The comparison between their abundances and APOGEE DR17, including the Ce offset and its metallicity dependence, is careful and useful. It honestly distinguishes precision from accuracy and shows that the quality of abundances matters more than the quality of ages for calibrating these relations.\n\nThe main soft spot is the birth-radius dependence of the [Ce/Mg] slope, which the stress-test note correctly identifies. Table 4 shows m1 = -0.018 ± 0.006 for Rb < 6 kpc and -0.049 ± 0.008 for Rb > 7 kpc, a ~3 sigma difference. The authors see it, mention it, but then apply the no-binning relation to ~270,000 APOGEE stars. They say qualitative results don't change with Rg binning, but Rg is not the same as Rb, and the Rb trend is specifically what could bias ages for stars born in the inner and outer disc. The claim that they recover known features like disc flaring and old metal-rich stars is reassuring, but those features are also broadly expected from the [Fe/H] term in the fit, so the validation is weaker than it looks. The old metal-rich stars in Section 4.3 are the most problematic: they compute Rb using the very chemical ages under question, and then use that Rb to argue these stars formed in the inner disc. That's circular, and it deserves explicit acknowledgement.\n\nThe recovery test is also on the calibrators themselves, as the paper states. That is not a crime, because the application to APOGEE is the real test, but it limits what the internal test can tell you.\n\nIs the birth-radius issue fatal? Probably not. The central result—that [Ce/Mg] and [Zr/Ti] correlate tightly with age when abundances and ages are precise—holds up. But the transfer to field surveys, especially for [Ce/Mg], carries an unquantified systematic that should be propagated or at least caveated clearly. I'd send this to a serious referee: the sample is valuable, the analysis is careful, and the remaining issue is addressable with a sensitivity test or a clear statement of the implied systematic uncertainty on the derived age trends.","headline":"A careful calibration of [Ce/Mg] and [Zr/Ti] as chemical clocks, worth refereeing, but the birth-radius dependence of the [Ce/Mg] slope is a real soft spot that needs confronting.","tokens_in":40077,"tokens_out":3171,"would_cite":true,"duration_ms":35833,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Two abundance ratios, [Ce/Mg] and [Zr/Ti], calibrated on 68 Kepler giants with precise asteroseismic ages, can be transferred to large spectroscopic surveys to date hundreds of thousands of Milky Way stars and recover the age structure of…","keywords":["chemical clocks","stellar ages","asteroseismology","red giants","s-process elements","alpha elements","Galactic archaeology","APOGEE"],"falsifier":"Take a sample of giants with independent asteroseismic ages from individual mode frequencies that were not used in the calibration---for example, additional Kepler giants from the same catalogue---and compare their measured $[\\mathrm{Ce}/\\mathrm{Mg}]$ and $[\\mathrm{Zr}/\\mathrm{Ti}]$ with the ages predicted by equation (2); a systematic residual that depends on $\\alpha$-enhancement, Galactocentric radius, or metallicity beyond $[\\mathrm{Fe/H}]$, or a typical bias larger than about 3 Gyr in the oldest regime, would falsify the transfer of the relations to the broader disc.","tokens_in":2333,"feed_emoji":"🌌","tokens_out":7618,"duration_ms":118270,"temperature":0.7,"pith_summary":"This paper aims to turn the chemical composition of red giant stars into ages for hundreds of thousands of Milky Way stars, where asteroseismic ages are unavailable. It builds a calibration set of 68 bright giants in the Kepler field with high-precision optical abundances and asteroseismic ages better than ten percent, then selects the abundance ratios [Ce/Mg] and [Zr/Ti] as the tightest chemical clocks. Fitting these ratios against age and metallicity, the paper derives empirical relations that reproduce the input ages to about seven percent accuracy, and applies them to roughly 270,000 APOGEE stars and 1,500 Gaia-ESO stars. The resulting chemical ages separate the low- and high-alpha sequences by age, recover the age-metallicity relation, show the Milky Way disc flaring, and identify a population of old, metal-rich stars. A sympathetic reader would care because this offers a practical route to statistical ages for millions of giants, provided the calibrated relations hold across the disc.","feed_headline":"Two abundance ratios date 270,000 Milky Way giants","feed_subtitle":"Calibrated on 68 Kepler stars, the chemical clocks recover disc flaring, old metal-rich stars, and the age split of the alpha sequences.","key_machinery":"The central objects are the chemical-clock ratios $\\mathrm{[Ce/Mg]}$ and $\\mathrm{[Zr/Ti]}$, logarithmic abundance ratios of a slow-neutron-capture (s-process) element to an $\\alpha$-element. The mechanism they exploit is nucleosynthetic delay: s-process elements such as Ce and Zr are released mainly by asymptotic-giant-branch stars on timescales of roughly 0.5 to 7 Gyr, while $\\alpha$-elements such as Mg and Ti are released promptly by Type II supernovae, so the ratio declines steadily with stellar age. The load-bearing calibration is the linear model of equation (2), $[\\mathrm{s}/\\alpha] = m_1\\,\\mathrm{Age} + m_2\\,[\\mathrm{Fe/H}] + c$, fitted with a Markov-chain Monte Carlo procedure that also yields an intrinsic scatter term; the fits are repeated in bins of guiding radius and birth radius to test whether the age slope changes across the disc. What carries the argument is the precision of the 68-star calibrator sample: high-resolution spectra with $R \\sim 67\\,000$--$115\\,000$ and asteroseismic ages from individual mode frequencies, which together reduce the scatter of the [Ce/Mg] relation from about 0.15 dex (using catalog abundances) to about 0.08 dex.","core_discovery":"The paper's central claim is that, with high-precision abundances and ages from individual oscillation frequencies, $\\mathrm{[Ce/Mg]}$ and $\\mathrm{[Zr/Ti]}$ are sufficiently tight functions of age and metallicity---intrinsic scatters of 0.08 and 0.01 dex, respectively---to serve as empirical chemical clocks across the full chronochemical history of the disc. The relations, written as $[\\mathrm{s}/\\alpha] = m_1\\,\\mathrm{Age} + m_2\\,[\\mathrm{Fe/H}] + c$, reproduce the asteroseismic calibration ages with roughly 7% accuracy and an absolute age deviation of about 2.95 Gyr. Applied to APOGEE and Gaia-ESO, they separate low- and high-$\\alpha$ sequences in age, recover the age-metallicity relation, reveal disc flaring in the Galactocentric-radius versus vertical-height plane, and identify a population of old, metal-rich stars whose inferred birth radii point to the inner disc. The paper also demonstrates that calibrating with lower-precision APOGEE abundances raises the intrinsic scatter to about 0.15 dex, degrading chemical ages more than using lower-precision seismic ages does.","pith_inferences":["If the [Ce/Mg] and [Zr/Ti] relations transfer without recalibration to surveys with different spectral coverage and line lists, the same approach could in principle extend to other large spectroscopic datasets that include neutron-capture lines, giving a uniform age scale across multiple surveys.","The paper's finding that the [Ce/Mg]-age slope steepens toward larger birth radii, if confirmed at larger sample sizes, would imply that chemical-age-based studies of radial migration need to account for birth-radius-dependent calibrations before interpreting apparent metallicity gradients.","The identification of old, metal-rich stars as migrated inner-disc objects is testable: a subset of APOGEE stars with asteroseismic ages from individual modes, outside the 68-star calibration set, should show the same age-metallicity pattern, providing an independent check of the transfer assumption.","A direct prediction of the calibration is that stars sharing the same [Fe/H] and [Ce/Mg] should have the same age regardless of kinematic population; this could be tested with open clusters spanning a range of Galactocentric radii and metallicities."],"forward_implications":["If the calibrated relations hold, chemical ages can be assigned to roughly 270,000 APOGEE giants and about 1,500 Gaia-ESO stars, extending age information to populations too faint for asteroseismology.","The chemical ages separate the low- and high-$\\alpha$ sequences cleanly: high-$\\alpha$ stars cluster near 11 Gyr with a narrow spread, while low-$\\alpha$ stars span from about 2 Gyr to ages as old as the high-$\\alpha$ sequence.","Recovering the age-metallicity relation suggests that old stars show a broad range of metallicities, with stars at both $[\\mathrm{Fe/H}] < -0.6$ and $>0.2$ dex consistently old, pointing to radial migration as a key mixing process.","The $\\mathrm{R_{GC}}$--$z$ plane, coloured by chemical age, shows disc flaring---young stars stay close to the plane while the vertical spread widens at larger radii---supporting an inside-out formation scenario for the Galaxy.","The paper finds a population of old, metal-rich ([Fe/H] > 0) stars, mostly with thin-disc kinematics and super-solar metallicities; their inferred birth radii are concentrated in the inner disc, suggesting they migrated outward.","Higher-precision abundances improve the chemical-clock calibration more than higher-precision ages do, so future gains in survey age precision will come primarily from improving abundance measurements."],"supporting_citations":[{"why":"Supplies the Kepler red-giant catalogue with high-quality power spectra from which the 68 calibrators were selected, and provides the reference age-precision baseline that the paper improves upon.","marker":"Miglio et al. 2021"},{"why":"Demonstrates the use of individual oscillation frequencies to reach roughly 11% age precision in field giants, the method the present work extends to better than 10%.","marker":"Montalbán et al. 2021"},{"why":"Previous [Ce/Mg] calibration attempt using APOGEE abundances and global seismic parameters, which the current high-precision data improve on by reducing the intrinsic scatter from about 0.15 dex to 0.08 dex.","marker":"Casali et al. 2023"},{"why":"Interprets radial gradients in [Ce/Mg] as evidence of rapid enrichment with Galactocentric radius and provides the birth-radius framework adopted for the mono-age population analysis.","marker":"Ratcliffe et al. 2023"},{"why":"Provides the APOGEE DR17 spectra, atmospheric parameters, and abundances used both for the APOGEE comparison and as the large field-star sample to which the relations are applied.","marker":"Abdurro'uf et al. 2022"},{"why":"Supplies the Gaia-ESO survey data used as a second, independent field-star test sample for the chemical-age relations.","marker":"Randich et al. 2022"},{"why":"Gives the empirical method for estimating birth radii from stellar age and metallicity, used here to compute $R_b$ and to interpret the spatial distribution of super metal-rich stars.","marker":"Lu et al. 2024"},{"why":"Provides the Milky Way gravitational potential model used through GalPy to compute stellar orbits, guiding radii, and the kinematic quantities used in the Toomre diagram analysis.","marker":"Bovy 2015"}],"fun_headline_variants":["Ce/Mg and Zr/Ti chemical clocks now date 270,000 giants","Kepler-calibrated abundance ratios set precise stellar ages","Tight Ce/Mg and Zr/Ti ratios reveal disc's age structure","New chemical clocks from Kepler giants map Galactic ages","Precision abundances make [Ce/Mg] and [Zr/Ti] age chronometers"],"cache_read_input_tokens":42112,"weakest_assumption_plain":"The linear relation between $[\\mathrm{Ce}/\\mathrm{Mg}]$ or $[\\mathrm{Zr}/\\mathrm{Ti}]$ and age plus metallicity, calibrated on 68 bright giants in the solar neighbourhood, is assumed to hold unchanged for all field stars across the Milky Way disc, including stars outside the calibrated metallicity range $[-0.8, 0.2]$ dex; if the real relation has non-linearities, population-dependent offsets, or radial dependence not captured by the $[\\mathrm{Fe/H}]$ term, the derived chemical ages will be systematically biased.","fun_headline_variants_meta":{"raw":{"variants":["Ce/Mg and Zr/Ti chemical clocks now date 270,000 giants","Kepler-calibrated abundance ratios set precise stellar ages","Tight Ce/Mg and Zr/Ti ratios reveal disc's age structure","New chemical clocks from Kepler giants map Galactic ages","Precision abundances make [Ce/Mg] and [Zr/Ti] age chronometers"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000348,"raw_usage":{"total_tokens":1948,"prompt_tokens":1035,"completion_tokens":913,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":651,"completion_tokens_details":{"reasoning_tokens":818}},"tokens_in":651,"tokens_out":913,"duration_ms":7666,"temperature":1.0,"reasoning_tokens":818,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:33:00.857515+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a sample of giants with independent asteroseismic ages from individual mode frequencies that were not used in the calibration---for example, additional Kepler giants from the same catalogue---and compare their measured $[\\mathrm{Ce}/\\mathrm{Mg}]$ and $[\\mathrm{Zr}/\\mathrm{Ti}]$ with the ages predicted by equation (2); a systematic residual that depends on $\\alpha$-enhancement, Galactocentric radius, or metallicity beyond $[\\mathrm{Fe/H}]$, or a typical bias larger than about 3 Gyr in the oldest regime, would falsify the transfer of the relations to the broader disc.","supporting_citations":[],"review_version":2}