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The growth of a lithium abundance dispersion in pre main sequence stars

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2504.18265 v1 pith:3G6CY5GK submitted 2025-04-25 astro-ph.SR astro-ph.GA

R. J. Jackson (1) , R. D. Jeffries (1) , E. Tognelli (2) ((1) Keele University UK , (2) University of New Haven USA) This is my paper · ORCID
classification astro-ph.SRastro-ph.GA
keywords lithiumdepletionpre-main-sequencestarsstarspotsstellarrotationopenclustersequivalentwidthdispersionlow-massGaia-ESOsurvey
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

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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 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.

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 (3)
  1. [§3.1, Fig. 3] 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.
  2. [§4.5, Eq. (3), Fig. 12] 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.
  3. [§3.3, Fig. 5] 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.
minor comments (4)
  1. [§5, paragraph on weaknesses] The text '25-125 yr' in the first weakness paragraph should read '25–125 Myr'.
  2. [§4.2] 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.
  3. [§3.4, Eq. (2)] 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.
  4. [Table 2] 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).

Circularity Check

1 steps flagged · score 5.0 of 10

The rotation-dependent starspot model is calibrated to the very Li–rotation correlation it is then said to reproduce; the empirical onset of the dispersion and the non-rotational Pleiades-based model are independent.

  1. fitted input called prediction [Sec. 4.5 (Eq. 3; Figs. 8 and 12)]
    "Taking all the targets in the ZAMS K-dwarf mass range from Fig. 6 in the age range 12 to 75 Myr, the epoch of PMS lithium burning, a linear least squares fit gives ⟨δEWLi⟩ = 26 − 95 log(period/d), (3) ... The temporal behaviour of the predicted Li dispersion is very similar to the saturated model but, by design, the extra rotation-dependence injects significantly more dispersion at all ages and nearly enough to match the data."

    The rotation-dependent spot model is constructed by inverting Eq. 3, which is a least-squares fit to the observed δEWLi–period correlation for the same 12–75 Myr K-dwarf sample. The resulting β(period) distribution is then fed through the evolutionary models and used to compute ΔEWm, so the agreement in Fig. 12 is not an independent prediction of the rotation-correlated dispersion: it is the input correlation converted into spot-coverage units. The paper's phrase 'by design' concedes that the extra dispersion is inserted to match the data, not derived from an external constraint. The non-rotational Pleiades-based model in Sec.

full rationale

The core observational result — that an intrinsic EWLi dispersion develops at 10–20 Myr, coincident with the onset of Li depletion, including in fully convective M dwarfs, and is correlated with rotation — is derived directly from Gaia-ESO spectra and does not depend on the spot model. It is an independent empirical claim, and the main caveat about internal age spreads (Sec. 3.1 and Sec. 5) is a statistical robustness concern, not a circularity. The forward starspot model of Sec. 4.3 uses an external Pleiades spot-coverage distribution (Cao & Pinsonneault 2022) and predicts the temporal and mass-dependent shape of the dispersion without being fitted to the age-dispersion curve; although it underpredicts the amplitude by a factor of two, that is a legitimate falsifiable input. The circular step is confined to Sec. 4.5: the rotation-dependent β(period) relation is fit to the same EWLi–rotation correlation that the model is then said to reproduce, so the resulting ΔEWm match is by construction. The paper is transparent about this with the phrase 'by design' and labels the model speculative. Self-citations to Jeffries et al. (2023a) supply ages and EAGLES isochrones, but these are cross-checked against independent lithium-depletion-boundary ages and the code/data are public, so they are not the load-bearing circular element. Overall, the empirical discovery stands independently; only the rotational component of the model is a calibrated consistency check rather than a prediction, warranting a partial-circularity score of 5.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper's new observational result rests on external catalogues, models, and assumed ages. The model explanation adds a fitted rotation-dependence of spot coverage and assumes higher PMS spot coverage than directly measured. No new physical entities are introduced.

free parameters (4)
  • Mean spot flux-blocking factor beta for PMS stars = 0.2 (ages <75 Myr), 0.1 (older clusters)
    Adopted in Sec. 2.3 to set Teff mass boundaries and for Li-depletion model comparisons; based on earlier isochrone fits, not measured in this sample.
  • Rotation-dependent beta amplification = not given as constant; a relation derived from the observed slope dEWLi/dlogP (Eqn. 3)
    Sec. 4.5: fitted to reproduce the observed EWLi-period correlation, then used to predict the dispersion.
  • Initial lithium abundance A(Li) = 3.30
    Sec. 4.1: assumed consistent with the largest EWLi in young clusters and F-star abundances in the same GES clusters.
  • Spot temperature contrast xspot = 0.8
    Fixed by SPOTS models; sensitivity to xspot=0 and grey surface checked in Sec. 4.4.
assumptions (5)
  • domain assumption PMS stellar evolution models (SPOTS and Pisa) correctly predict Li depletion as a function of mass, age, and spot coverage beta.
    Used in Sec. 4.1 and 4.3 to convert spot coverage into Li abundance and EWLi; the models omit non-convective mixing, which the paper acknowledges.
  • domain assumption The template-subtraction EWLi measurements and the LTE/NLTE curves of growth yield unbiased Li line strengths.
    Used in Secs. 2.1, 3, and 4.2; the paper notes approximations below 4000 K.
  • domain assumption Kinematic cluster membership from Jackson et al. (2022) is unbiased with respect to Li abundance.
    Sec. 2.1: membership selected on radial velocity, Teff, gravity, and Gaia proper motions, not on Li.
  • domain assumption The adopted fiducial cluster ages are correct and internal age spreads are small enough not to create the dispersions.
    Sec. 3.1: the paper discusses age spreads but assumes coeval clusters; ages are model-dependent.
  • domain assumption Rotation periods estimated from vsini assuming random spin orientations and SPOTS radii are statistically valid.
    Sec. 3.4, Eqn. 2: used for the Li-rotation correlation and Rossby numbers.

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Cite this review

Pith. "Pith review of The growth of a lithium abundance dispersion in pre main sequence stars." pith.science (2026). https://pith.science/paper/3G6CY5GK

@misc{pith2026250418265,
  author       = {Pith},
  title        = {Pith review of: The growth of a lithium abundance dispersion in pre main sequence stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3G6CY5GK}},
  note         = {Machine review of arXiv:2504.18265}
}
read the original abstract

Lithium is predicted, and observed, to be depleted in contracting, low-mass pre main sequence (PMS) stars. Yet these stars reach the zero age main sequence (ZAMS) with a spread in lithium abundance at a given effective temperature that is not predicted by standard stellar evolutionary models and which appears to be correlated with rotation. Using a homogeneous dataset provided by the Gaia-ESO spectroscopic survey, we have followed the evolving photospheric lithium content of cohorts of stars destined to be ZAMS late G-, K- and M-dwarfs, in clusters at ages of 2-300 Myr. We show that a dispersion in the LiI 6708A line strength develops in the lower mass stars after 10-20 Myr on the PMS, as soon as Li depletion begins, even in fully convective stars. A model based on a surface starspot coverage varying from star-to-star, leading to a differential Li-burning rate, can explain this temporal behaviour and its mass dependence. However, to fully explain the magnitude of the Li dispersion and its correlation with rotation, the spot coverage during Li-burning would need to be a factor of two larger on average than measured in ZAMS clusters like the Pleiades and continue increasing with rotation in PMS stars beyond the usual "saturation limit" observed for other magnetic activity indicators.

Figures

Figures reproduced from arXiv: 2504.18265 by the authors.

Figure 1
Figure 1. Upper plots show MG versus Teff for four relatively well populated clusters using data from [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. RMS variation in EWLi for individual clusters, as a function of fiducial age (column 2 in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Intrinsic dispersion of stars in the ZAMS K-dwarf mass range (according to the SPOTS models) as a function of age. Plot (a) shows ∆EWLi (see Eqn. 1) for individual clusters as a function of log age, with small offsets to identify each cluster. Plot (b) shows the same data without age offsets, with a histogram and text on the plot showing the weighted mean ∆EWLi (in mÅ) in four age bands (see §3.1). The dashed line i… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Empirical dispersion as a function of age and spectral type for targets in the early M and late G dwarf mass ranges (see [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Empirical dispersion, ∆EWLi versus log age for the mid M-dwarf mass range (see §3.3). Points show results for individual clusters with 5 or more targets in the mass range. The histogram and text on the plot shows the weighted mean dispersion in four age bands. The dash…
Figure 6
Figure 6. Figure 6: The offset of measured EWLi for targets in the ZAMS K-dwarf mass range (from the SPOTS models) with respect to the EAGLES EWLi isochrone, at the Teff and age of the target, versus rotation period estimated from v sin i (see §3.4). Red lines show a linear least-squares …
Figure 7
Figure 7. Figure 7: Evolutionary tracks of log10(Li/Li0) from the SPOTS models for different levels of spot coverage (labelled with the flux blocking fraction β) and at 4 different masses. Red crosses and diamonds on each curve mark when the core inertia has reached 5 per cent and (for th…
Figure 8
Figure 8. Figure 8: Cumulative probability distribution of flux blocking factor, β, used to calculate the model EWLi dispersion. The left hand curve (in black) shows the CDF for a normal distribution in log β with a mean of -0.822±0.121 dex (see §4.3). The curves to the right show the CDF…
Figure 9
Figure 9. Figure 9: Calculated levels of dispersion in Lithium equivalent width, ∆EWm as a function of age using tabulated data from the SPOTS (Cao & Pinsonneault 2022) and Pisa (Tognelli et al. 2021) evolutionary models. Results are averaged over 3 mass ranges representing M, K and G-dwa…
Figure 10
Figure 10. Figure 10: (a) The relationship between mean flux blocking factor ⟨β⟩ and rotation period required to produce the corresponding observed correlation between the offset in EWLi from an EAGLES-predicted isochrone versus ro￾tation period, for targets in the ZAMS K-dwarf mass range …
Figure 11
Figure 11. Figure 11: Plots a and b show predicted values of log Li/Li0 and EWm as a function of Teff using the SPOTS model. Black lines show results at increasing levels of β. Red triangles show random results drawn from a Normal distribution of log β = −0.822 ± 0.121. Vertical dashed lin…
Figure 12
Figure 12. Figure 12 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]

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    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.