{"id":"4953483d-c85e-403c-b10c-f028c53da273","arxiv_id":"2504.18265","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The lithium abundance dispersion in low-mass PMS stars develops at 10-20 Myr, coincident with the onset of lithium depletion, even in fully convective stars.","lead":"Using a homogeneous sample of thousands of stars in 19 clusters, this paper finds that the spread in lithium among low-mass pre-main-sequence stars appears at 10-20 million years, just as lithium depletion starts. The result matters because it challenges standard models and points to starspots or other rotation-dependent effects as the cause.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed 10–20 Myr onset of the Li dispersion may be inflated by internal age spreads during the steepest Li-depletion phase; the coeval-cluster assumption is untested in that age bin.","rationale":"The reader's weakest assumption concerns the starspot model's required spot coverage and its rotation dependence beyond saturation. That is a legitimate concern about the explanatory model, but the paper itself states this limitation clearly, and the central observational claim of a Li dispersion is independent of the spot interpretation. My concern targets the observational measurement itself: the paper's coeval-cluster assumption in §3.1 is least secure precisely in the 13–25 Myr bin where the Li-depletion timescale is shortest. The paper asserts that age spreads ≤10 Myr will not inflate older clusters, but that argument is not quantified for the steepest phase, and the M-dwarf peak is even more sensitive because Li depletion is faster at lower mass. The age-spread scenario can simultaneously produce the apparent onset of dispersion and the Li–rotation correlation, making it a load-bearing threat to the claimed timing and to the 'fully convective' conclusion. The reader's CONDITIONAL verdict remains appropriate, perhaps with a stronger caveat: the 10–20 Myr onset should be regarded as tentative until age-spread effects are quantified. I partially agree with the reader because the spot-model assumptions are also a real weakness, but I judge the age-spread issue to be the single most load-bearing concern for the central claim.","tokens_in":22450,"tokens_out":12083,"duration_ms":127913,"concrete_test":"For each cluster in the 13–25 Myr bin and the mid-M dwarf sample, propagate published internal age-spread estimates (e.g., from Li-depletion boundaries, CMD broadening, or literature analyses) through the EAGLES EWLi(age, Teff) relation to predict the age-spread contribution to σoff. Subtract this in quadrature, as in Eq. 1, and recompute ∆EWLi for the 13–25 Myr bin and the mid-M dwarf peak. If the residual dispersion is not significantly above zero, the claimed onset at 10–20 Myr is not established; an additional check is to repeat Fig. 6 after removing the predicted age-spread-induced EWLi–period correlation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In §3.1 the paper explicitly assumes each cluster is coeval and asserts that age spreads ≤10 Myr 'will not greatly inflate the dispersion in older clusters because |d⟨EWLi⟩/dt| is not steep enough.' This reasoning is not applied to the 13–25 Myr bin, where Fig. 3c shows the steepest decline of ⟨EWLi⟩ with age. From Fig. 3c, the mean EWLi falls from roughly 500 mÅ at ~10 Myr to ~300 mÅ at ~25 Myr, a slope of ~13 mÅ/Myr (and steeper for M dwarfs). A 5 Myr internal age spread would then produce RMS variations of several tens of mÅ, comparable to the observed ∆EWLi≈60–70 mÅ in that bin. Since angular momentum loss also makes older stars in a cluster slower rotators, the same age spread would generate a spurious Li–rotation correlation in Fig. 6 without any rotation-dependent Li burning. The paper's caveat in §5 about combining stars in bins of Teff and age does not quantify this effect, and the M-dwarf peak in Fig. 5, where Li depletion is even faster, is similarly vulnerable.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper measures the intrinsic dispersion of the Li I 6708 Å equivalent width (EWLi) in low-mass pre-main-sequence (PMS) stars using a homogeneous Gaia-ESO spectroscopic sample of 19 clusters with fiducial ages between 2 and 300 Myr. After subtracting measurement and Teff-related uncertainties in quadrature, the authors report that a dispersion develops at 10–20 Myr in stars destined to be ZAMS K- and M-dwarfs, coincident with the onset of lithium depletion, and that the dispersion is correlated with rotation. They then test a starspot model: using the Pleiades spot-coverage distribution as an input reproduces the temporal behavior of the dispersion but under-predicts its magnitude by about a factor of two; a rotation-dependent spot coverage can nearly match the observed magnitude, but the required β–rotation relation is fitted to the observed EWLi–period correlation and requires spot coverage to increase with rotation beyond the saturation Rossby number, for which the paper states there is no direct evidence.","tokens_in":22693,"tokens_out":4672,"duration_ms":51605,"significance":"If the empirical result is robust, it is an important constraint on PMS lithium-depletion theory: standard evolutionary models predict no dispersion, and the appearance of the dispersion while mid-M dwarfs are still fully convective would disfavor radiative-core shear or core-envelope decoupling mechanisms for the lowest-mass stars. The paper's strengths are its homogeneous dataset, explicit treatment of measurement uncertainties, exclusion of accretors and photometric outliers, and the use of an external Pleiades spot-coverage distribution as an input in §4.3. However, the central onset claim depends on the untested assumption that internal age spreads do not inflate the 13–25 Myr dispersion, and the rotation-dependent spot model in §4.5 is fitted to the very correlation it is meant to explain. The paper is therefore valuable and publishable in principle, but the load-bearing empirical and model claims need additional quantitative support.","major_comments":[{"comment":"The claim that the dispersion first appears at 10–20 Myr is vulnerable to internal age spreads in the 13–25 Myr bin, because this is the steepest part of the ⟨EWLi⟩–age relation. From Fig. 3c the mean EWLi declines from roughly 500 mÅ at about 10 Myr to roughly 300 mÅ at about 25 Myr, a slope of about 13 mÅ/Myr, and the decline is steeper for the lower-mass stars in the sample. A 5 Myr internal age spread would therefore produce an RMS contribution of several tens of mÅ, comparable to the measured ΔEWLi ≈ 60–70 mÅ in that bin. The same age spread would also introduce a spurious Li–rotation correlation in Fig. 6, because angular-momentum evolution makes older cluster members slower rotators. The discussion in §3.1 explicitly limits the age-spread argument to clusters where |d⟨EWLi⟩/dt| is not steep, and the caveat in §5 is not quantitative. I request a synthetic-population test that injects a plausible age spread into the 13–25 Myr bin and recomputes ΔEWLi and the Fig. 6 slopes, or an equivalent demonstration that the dispersion and rotation correlation survive this confounder.","section":"§3.1, Fig. 3"},{"comment":"The rotation-dependent spot model is not an independent test of the spot hypothesis. Equation (3) is a linear least-squares fit to the observed δEWLi–log(period) relation, and the β(Prot) relation in Fig. 10a is inverted from that fit; the resulting increase in ΔEWm in Fig. 12 therefore follows by construction, as the text itself acknowledges with the phrase 'by design'. The factor-of-two shortfall of the Pleiades-based model (§4.3, Fig. 9) and the absence of direct evidence for a β–rotation relation in PMS stars are acknowledged, but the abstract and conclusions still state that the dispersion 'might be reproduced' by such a model. To make this a falsifiable explanation rather than a demonstration of possibility, the paper needs an external constraint on β(Prot) from, for example, spot-filling-factor measurements or Zeeman broadening in PMS stars, or an explicit statement that the required β–rotation relation is unverified and extrapolated beyond the saturation Rossby number. As written, the comparison in Fig. 12 does not validate the model because the input was constructed from the output.","section":"§4.5, Eq. (3), Fig. 12"},{"comment":"The 'fully convective' argument for mid-M dwarfs is the cleanest way to rule out radiative-core mechanisms, but it currently rests on the 13–25 Myr bin, where the lithium-depletion timescale is shortest and the number of clusters with at least five targets is small. The transient peak in ΔEWLi in Fig. 5 is exactly what an internal age spread would produce during the rapid transition from undepleted to fully depleted lithium, and the same concern applies to the early-M sample in Fig. 4a. I ask for a quantitative control: recompute ΔEWLi for the M-dwarf bins after excluding stars within a few Myr of the expected depletion boundary, or demonstrate that the peak survives a Monte Carlo implementation of plausible cluster age spreads. Without such a test, the statement that the dispersion develops 'even in fully convective stars' is not fully supported by the present data.","section":"§3.3, Fig. 5"}],"minor_comments":[{"comment":"The text '25-125 yr' in the first weakness paragraph should read '25–125 Myr'.","section":"§5, paragraph on weaknesses"},{"comment":"The NLTE corrections and curves of growth do not extend below 4000 K and require extrapolation for M dwarfs; this systematic uncertainty should be flagged in the captions of the M-dwarf model figures, not only in the text.","section":"§4.2"},{"comment":"The relation Prot = 39.8 (v sin i / km s−1)−1 (R/R⊙) days with ⟨sin i⟩ = π/4 should state explicitly that this is an expectation value for a single star and that the resulting period is a statistical estimate, since the paper uses it to bin stars and to assign Rossby numbers.","section":"§3.4, Eq. (2)"},{"comment":"Repeated cluster names such as 'NGC2451b' and 'NGC2451a' should be formatted consistently with the rest of the table, and the age column should note that these are fiducial geometric-mean ages from Jeffries et al. (2023a).","section":"Table 2"}],"recommendation":"major_revision","confidential_remarks":"The paper is honest and well written, and the observational dataset is valuable. The main problem is not the speculative spot model per se, which the authors already caveat heavily, but the age-spread confounder in the 13–25 Myr bin that underlies both the onset claim and the fully-convective interpretation. I do not recommend rejection because the central empirical claim can plausibly be rescued with additional synthetic-age-spread tests and a sharper separation of the fitted rotation-dependent model from an independent validation. I would also encourage the editor to ensure the abstract's final sentence retains the hedging that the conclusions already carry."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is the first homogeneous multi-cluster look at when the Li dispersion appears in PMS stars, and that is worth having. The Gaia-ESO data, the careful quadrature treatment of EW and Teff errors, the filtering of accretors—all of that is done properly. The claim that the dispersion grows after 10–20 Myr, in K and M dwarfs, including fully convective M dwarfs, is a real observational result that narrows the field. I'd want to cite the dispersion-age curves regardless of the model outcome.\n\nBut the stress-test note lands. In §3.1 they assert that age spreads ≤10 Myr won't inflate older clusters because the EWLi slope is not steep enough. That is fine for the 25–125 Myr bins, but it is exactly wrong for the 13–25 Myr bin, where the mean EWLi drops from ~500 to ~300 mÅ with a slope near 13 mÅ/Myr. A 5 Myr spread in a cluster on the steep part of the depletion curve produces RMS scatter of several tens of mÅ, comparable to the measured ∆EWLi of 60–70 mÅ in that bin. And because angular momentum loss makes older cluster members slower rotators, the same age spread produces a spurious Li–rotation correlation in Fig. 6. The paper's caveat in §5 that they bin in Teff and age does not quantify this. This is not a fatal flaw—the dispersion is visible in multiple clusters and in the normalized version—but the 10–20 Myr onset timing and the rotation-correlation significance are both overstated as they stand.\n\nThe spot model section is honest and well-structured. Using the Pleiades spot distribution gives the right temporal shape but under-predicts the dispersion by half, and the rotation-dependent beta is fitted to the observed Li–Period relation, so the match is by construction. The paper says plainly that there is no direct evidence for such a rotation dependence and it may conflict with saturation. Good that they say it, but it means the model is a demonstration of possibility, not a confirmed explanation.\n\nThe citation pattern is fine; they build on their own prior work but also cite alternatives. No sign of caricature.\n\nSo: this deserves a serious referee. The observational core is novel and mostly solid, but the referee should push hard on the age-spread issue, especially in the 13–25 Myr bin, and ask for a quantitative treatment (e.g., Monte Carlo using known or plausible intra-cluster age spreads). If that doesn't wash out the result, it's a strong paper. If it does, the epoch of onset becomes much less certain. Either way, it's a useful paper for anyone working on Li depletion or PMS rotation.","headline":"A genuinely new homogeneous multi-cluster measurement of when the Li dispersion appears in PMS stars, but the 10–20 Myr onset timing and the rotation correlation are both suspect until the age-spread issue in the 13–25 Myr bin is quantified.","tokens_in":23230,"tokens_out":3512,"would_cite":true,"duration_ms":36291,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"An intrinsic dispersion in lithium equivalent width develops in low-mass pre-main-sequence stars at 10–20 Myr, coincides with the onset of lithium depletion, and correlates with rotation even in fully convective stars.","keywords":["lithium depletion","pre-main-sequence stars","starspots","stellar rotation","open clusters","equivalent width dispersion","low-mass stars","Gaia-ESO survey"],"falsifier":"Measure spot filling factors in a sample of K-dwarfs in clusters aged 12–75 Myr, for example via two-temperature fits to TiO bands or light-curve modeling, and plot β against rotation period. If the mean β is not close to twice the Pleiades value, or if β is flat for rotation periods below the saturation Rossby number rather than rising toward 0.3-day rotators, the starspot model cannot explain the magnitude or the rotation dependence of the lithium dispersion.","tokens_in":22267,"feed_emoji":"⭐","tokens_out":6071,"duration_ms":61453,"temperature":0.7,"pith_summary":"The paper follows photospheric lithium in roughly 2,500 stars across 19 open clusters aged 2–300 Myr and shows that a spread in the strength of the Li I 6708 Å line appears in low-mass stars at 10–20 Myr, exactly when lithium burning begins and well before a radiative core can matter in the lowest-mass stars. Standard pre-main-sequence models predict lithium depletion that is a single function of mass and temperature, so this dispersion is unanticipated. The paper argues that star-to-star differences in dark starspot coverage can produce differential lithium-burning rates and reproduce the timing and mass dependence of the scatter, but only if PMS spot coverage is about twice the value seen in the Pleiades and continues to increase with spin beyond the rotation rate at which other magnetic activity indicators saturate. If correct, the lithium dispersion is a rotation-dependent surface effect, and the lithium abundance a young low-mass star carries onto the main sequence depends on its rotational history.","feed_headline":"Lithium scatter appears by 20 Myr in fully convective stars","feed_subtitle":"Homogeneous data from 19 clusters show the lithium spread begins at 10–20 Myr and tracks rotation.","key_machinery":"The central mechanism is a surface starspot model: a variable fractional flux-blocking factor β, the fraction of a star's surface covered by cool spots with spot temperature 0.8 times the photospheric temperature, changes both the interior structure and the observed line. Spots inflate the star and lower its central temperature, delaying and slowing lithium burning, while the curve of growth is temperature-sensitive, so the same true abundance yields different Li I 6708 Å equivalent widths depending on spot coverage. The paper folds SPOTS and Pisa evolutionary tracks for lithium abundance through NLTE-corrected curves of growth to predict equivalent-width dispersions, and compares them with the observed dispersion measured about an empirical EAGLES isochrone built for each cluster.","core_discovery":"The central discovery is that an intrinsic dispersion in the Li I 6708 Å equivalent width does not exist at 2–10 Myr, but grows rapidly between 10 and 20 Myr in stars destined to be ZAMS K- and M-dwarfs, coincident with the onset of lithium depletion. For future M-dwarfs the dispersion is fully established while the stars are still essentially fully convective, which rules out explanations that require a radiative core, such as rotational shear at a core/envelope boundary or convective overshoot. The same data show that the dispersion is correlated with rotation, and that this correlation appears as early as 13–25 Myr. The paper then shows that a variable starspot model reproduces the temporal shape and mass dependence of the scatter, but that the Pleiades-based spot distribution under-predicts its magnitude by a factor of two and predicts no rotation correlation. A rotation-dependent spot distribution with an average flux blocking factor near β ≈ 0.2 during the lithium-burning phase and β rising by a factor of a few from 10-day to 0.3-day rotators can match both, but it requires spot coverage to grow with rotation beyond the saturation limit seen in X-ray and chromospheric activity indicators.","pith_inferences":["If the starspot interpretation is right, the same scatter should appear in other temperature-sensitive photospheric diagnostics, and the K I 7699 Å line, formed under similar conditions but not altered by lithium burning, could separate true abundance spreads from activity-induced line-strength changes.","The required growth of spot coverage beyond saturation predicts that Zeeman-broadening magnetic field measurements of fast PMS rotators should keep rising toward the fastest rotation, a trend already hinted at in Pleiades M-dwarfs; this is testable with existing spectropolarimetric data.","The timing result implies that any cluster older than about 20 Myr is unsuitable as a probe of the initial lithium abundance distribution of low-mass stars, which affects chemical-evolution and young-star identification studies that rely on lithium.","A direct test would be to measure spot filling factors for the same stars whose lithium equivalent-width offsets are known, converting the lithium-rotation relation into a lithium-spot relation."],"forward_implications":["The lithium dispersion in ZAMS K-dwarfs is not inherited from birth but grows during the PMS phase, so standard PMS models are missing a rotation-dependent ingredient.","Because the dispersion appears in fully convective M-dwarfs, mechanisms requiring a radiative core cannot be the general cause of the scatter.","The lithium-rotation correlation sets in by 13–25 Myr, so rotation history must be known when using lithium as an age indicator for young low-mass stars.","If starspots drive the scatter, spot coverage in 12–75 Myr PMS stars must average about twice the Pleiades value and increase by a factor of a few with spin; direct spot measurements in this age range can confirm or refute the model.","The mean lithium abundance a star brings to the ZAMS depends on spot coverage and rotation, so main-sequence lithium depletion starts from a rotation-dependent initial condition."],"supporting_citations":[{"why":"Supplies the homogeneous EWLi measurements, cluster temperatures, and empirical EAGLES isochrones from which the dispersion is measured.","marker":"Jeffries et al. 2023a"},{"why":"Provides the kinematic cluster membership probabilities that keep the sample unbiased with respect to lithium, colour, and magnitude.","marker":"Jackson et al. 2022"},{"why":"Provides the Pleiades spot-filling-factor distribution used as the template for the non-rotating starspot model.","marker":"Cao & Pinsonneault 2022"},{"why":"Supplies the SPOTS evolutionary tracks with varying spot coverage that predict lithium depletion as a function of age, mass, and β.","marker":"Somers et al. 2020"},{"why":"Supplies the Pisa models with spot coverage used as an independent check on the lithium-depletion predictions.","marker":"Tognelli et al. 2021"},{"why":"Supplies the curves of growth used to convert model lithium abundances into predicted Li I 6708 Å equivalent widths.","marker":"Franciosini et al. 2022b"},{"why":"Supplies the measured rotation periods adopted for Pleiades stars in the lithium-rotation analysis.","marker":"Bouvier et al. 2018"},{"why":"Provides the classic Pleiades equivalent-width measurements that establish the ZAMS lithium dispersion baseline.","marker":"Soderblom et al. 1993"}],"fun_headline_variants":["Lithium scatter emerges by 20 Myr even in fully convective stars","Lithium spread appears at 10–20 Myr, defying standard models","Starspots could drive the lithium spread in young low-mass stars","Lithium dispersion grows by 20 Myr, tied to rotation, spot model explains","Fully convective stars show lithium scatter after 10–20 Myr"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The starspot explanation stands or falls on the claim that PMS stars aged 12–75 Myr have spot coverage about twice the Pleiades value and that this coverage continues to increase with faster rotation even past the saturation point seen in X-ray and chromospheric activity indicators; the paper states there is no direct evidence for such a rotation-spot relation.","fun_headline_variants_meta":{"raw":{"variants":["Lithium scatter emerges by 20 Myr even in fully convective stars","Lithium spread appears at 10–20 Myr, defying standard models","Starspots could drive the lithium spread in young low-mass stars","Lithium dispersion grows by 20 Myr, tied to rotation, spot model explains","Fully convective stars show lithium scatter after 10–20 Myr"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000527,"raw_usage":{"total_tokens":2588,"prompt_tokens":1038,"completion_tokens":1550,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":654,"completion_tokens_details":{"reasoning_tokens":1451}},"tokens_in":654,"tokens_out":1550,"duration_ms":11265,"temperature":1.0,"reasoning_tokens":1451,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:19:57.301792+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure spot filling factors in a sample of K-dwarfs in clusters aged 12–75 Myr, for example via two-temperature fits to TiO bands or light-curve modeling, and plot β against rotation period. If the mean β is not close to twice the Pleiades value, or if β is flat for rotation periods below the saturation Rossby number rather than rising toward 0.3-day rotators, the starspot model cannot explain the magnitude or the rotation dependence of the lithium dispersion.","supporting_citations":[{"cited_title":"G., Lamia L., Pizzone R","cited_arxiv_id":null,"evidence_quote":"Supplies the Pisa models with spot coverage used as an independent check on the lithium-depletion predictions."}],"review_version":1}