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Meridional Circulation II: A Unified Mechanism for Lithium Depletion in Solar Analogs and the Lithium Dip in Mid-F Cluster Stars

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper claims that a single rotation-driven process, meridional circulation, can account for the lithium depletion seen in solar analogs and for the cool side of the lithium dip in open-cluster F stars.

desk verdict A transparent, reproducible extension of the authors' own giant-star mixing model to main-sequence Li depletion, but the central diffusion coefficient is borrowed rather than derived for the MS, so the 'unified mechanism' is still a hypothesis. read the letter →

arxiv 2508.19715 v1 pith:XQ2SC2G4 submitted 2025-08-27 astro-ph.SR astro-ph.GA

Xuefeng Li , Jianrong Shi , Yan Li , Hongliang Yan , Jinghua Zhang This is my paper · ORCID
classification astro-ph.SRastro-ph.GA
keywords lithiumdepletionmeridionalcirculationsolaranalogsdipopenclustersstellarrotationmain-sequencestarsproblem
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 tries to show that one physical process—meridional circulation, the large-scale flow inside a rotating star—can explain two long-standing lithium puzzles on the main sequence: why Sun-like stars lose lithium as they age, and why mid-F stars in open clusters show a sharp lithium dip. The authors take a diffusion coefficient for meridional circulation previously derived for red giants and apply it to main-sequence stars, where it drags lithium from the base of the surface convection zone into hotter layers where it is destroyed. With rotation speed as the main dial, their models reproduce the observed lithium–age correlation in solar analogs and the cool side of the lithium dip in most open clusters, plus the hot side in clusters like the Hyades. The same models still predict about 1.5 dex of solar lithium against the observed roughly 1.1 dex, and they miss the hot dip side in Praesepe and NGC 3680, so the paper argues for meridional circulation as the dominant—not the only—mixing agent.

What carries the argument

The carrying object is the meridional-circulation diffusion coefficient D_MC = 2π r2^2/(r1−r2) · R/τ_MC, with τ_MC = G^2 M^3/(3 L Ω0^2 R^4). D_MC is the only non-standard mixing term added to the stellar models; it sets how fast lithium is carried from the base of the surface convection zone (r1) down to the inner boundary of the uniformly rotating radiative zone (r2), where temperatures are high enough to burn it. Because τ_MC scales inversely with Ω0^2, D_MC grows as the square of the star's rotation speed, making rotation the control parameter for depletion. The companion inputs are the initial rotation velocity and the rotation–age relation used to spread model tracks across the observed

What would settle it

Take one open cluster with a lithium dip and measure true rotation periods (not just V sin i) for its F stars. The model predicts that on the cool side of the dip, A(Li) falls as rotation speed rises, with D_MC proportional to Ω0^2; a cluster where fast rotators keep high lithium on the cool side, or where the dip deepens without any rotation-velocity variation, would rule out the single-mechanism claim.

Watch

Extended reading notes

Core claim

The paper's central claim is that a single, rotation-driven transport process—meridional circulation, the large-scale flow that redistributes angular momentum in a spinning star—can account for most observed main-sequence lithium depletion once it is converted into a radial diffusion coefficient. Writing D_MC = 2π r2^2/(r1−r2) · R/τ_MC with τ_MC = G^2 M^3/(3 L Ω0^2 R^4), where r1 is the base of the surface convection zone and r2 is the inner boundary of the uniform-rotation region, the authors add this mixing to otherwise standard stellar models. The resulting tracks reproduce the observed lithium–age decline of solar analogs and the cool side of the lithium dip in open clusters; in clusters

Load-bearing premise

The load-bearing premise is that the diffusion coefficient worked out for red-giant-branch stars—where meridional circulation carries burning products outward—also tells how fast lithium is carried inward from the surface convection zone to the hot interior in main-sequence stars; every match with observation in this paper depends on that transfer working across two different structural regimes.

Editorial extensions

If this is right

  • If the mechanism holds, rotation alone—without convective overshoot, internal waves, or planet ingestion—can explain the observed decline of lithium with age in solar analogs.
  • In open clusters, the model predicts that lithium across the cool side of the dip should track the local rotation-velocity distribution: faster rotators show deeper depletion, so the dip's shape encodes the cluster's V sin i pattern.
  • The solar prediction (A(Li) ≈ 1.5 dex versus observed ≈ 1.1 dex) implies that some additional depletion process acts in the Sun beyond meridional circulation, or that the Sun's rotation history differs from the assumed 2–10 km/s tracks.
  • The age evolution of the lithium dip—shallow in young clusters, deeper and cooler in middle-aged ones, stable in old ones—follows naturally from spin-down: strong mixing early, cumulative depletion later, and negligible mixing once rotation stalls.

Reading between the lines

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

  • A sharp test of the paper's quadratic rotation dependence: in a single coeval cluster, cool-side stars at fixed effective temperature should show A(Li) decreasing as V sin i increases; existing cluster samples could be re-binned in V sin i to look for this without new observations.
  • The same D_MC formula applied to pre-main-sequence stars implies that initial spin and disk-locking history set the lithium floor a star enters the main sequence with; measuring lithium in young clusters with directly measured rotation periods would separate pre-main-sequence from main-sequence depletion.
  • If projection (V sin i versus true V) is the main cause of the hot-side failures, then true rotation periods from high-cadence photometry should show a tighter correlation with lithium than V sin i does for F stars in the dip; this is a directly testable extension of the paper's velocity-distribution argument.
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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

4 major / 5 minor

Summary. The paper proposes that a single non-standard mixing mechanism—radial diffusion driven by meridional circulation, with coefficient D_MC = 2π r_2^2/(r_1−r_2) R/τ_MC, τ_MC = G^2M^3/(3LΩ_0^2R^4) (Eq. 4)—can account for both the age-dependent lithium depletion of solar analogs and the cool side of the lithium dip in mid-F cluster stars. The authors implement this as the only extra mixing process in MESA models, calibrate α_MLT, and compare predicted A(Li) with published samples for solar analogs, the Hyades, Praesepe, and a few other clusters. They report that the solar-analog A(Li)-age and A(Li)-Teff relations are reproduced, that the predicted solar Li abundance (≈1.5 dex) exceeds the observed value (≈1.1 dex), and that the cool side of the Li dip is reproduced in the Hyades and Praesepe while the hot side is reproduced only in some clusters (e.g., Hyades) and not in others (Praesepe, NGC 3680).

Significance. If correct, the proposed mechanism would be important: it unifies two long-standing lithium anomalies with one rotationally driven process and is testable through the quadratic dependence on Ω_0. The paper makes its model code available on Zenodo and uses observational data from the literature. However, the strength of evidence is currently limited by (i) the unsupported transfer of a giant-branch diffusion law to main-sequence stars, (ii) an apparent inconsistency between Eqs. (3) and (4) for low-mass MS stars, and (iii) the absence of quantitative goodness-of-fit measures. The paper honestly reports its failures, which is a strength, but those failures need to be integrated into the central claim.

major comments (4)
  1. [§2.1, Eqs. (3)–(4)] As written, the inner-boundary definition is internally inconsistent with the diffusion coefficient. For a 1 M⊙ main-sequence star with no convective core and a rigidly rotating radiative zone, the third branch of Eq. (3) gives r2 = 0, which makes DMC = 0 in Eq. (4). Yet the solar-analog models in §3 show substantial post-ZAMS lithium depletion. Please provide the numerical values of r1 and r2 used in the MESA implementation and clarify whether r2 is actually zero in these models; if it is nonzero, explain how it is determined. This is load-bearing because every subsequent comparison uses DMC.
  2. [§2.1, Eq. (4)] DMC is taken from Paper I, where it was derived for red-clump giants with the mixing region bounded by the hydrogen-burning shell. For MS stars the paper replaces VMC by R/τMC and carries over the geometric factor 2π r2^2/(r1−r2) on the basis of uniform rotation. Uniform rotation does not by itself determine either the circulation velocity or the radial extent of the mixing region. Since DMC is the only non-standard mixing process in the model, an order-of-magnitude error in VMC propagates linearly into the predicted A(Li). Please provide an independent derivation or a numerical check (e.g., a 1D/2D meridional-flow solution for a 1 M⊙ ZAMS model) showing that Eq. (4) is a reasonable approximation on the MS.
  3. [§4.2 and Fig. 3] The cluster comparison is partly circular: the observed V sin i distribution is fed into the models, and because DMC ∝ Ω_0^2, any cluster whose V sin i(Teff) is convex will produce a Li dip. The successful reproduction of the Hyades cool side therefore mainly confirms the assumed quadratic scaling, not the absolute value of DMC. A more stringent test would predict the Li dip from a rotational-evolution model (spin-down starting from a distribution of initial V_ZAMS) without using the observed V sin i of each star as input.
  4. [§3.2–3.3, Figs. 1–2] The claimed agreement with solar-analog observations is visual. No error bars, scatter measures, or goodness-of-fit statistics are given. In Fig. 2, model trajectories are selected by hand from the ranges 0.85–1.05 M⊙, Z = 0.014–0.028, and 1–10 km/s, so the coverage of the observed locus is not a strong test. The paper should provide a quantitative comparison, including uncertainties on ages, masses, metallicities, and A(Li), and a sensitivity study of α_MLT and A(Li)_ini.
minor comments (5)
  1. [Fig. 2] The word 'trajectas' should be 'trajectories'. The legend 'Input of the models is reduced to (mass, metallicity, velocity)' is confusing because the figure labels use parentheses without units.
  2. [Abstract and §3.2] The abstract states 'reproduce the observed A(Li)-Age correlation' but §3.2 shows the solar value is overpredicted by about 0.4 dex. Please distinguish 'reproduce the trend' from 'match the absolute value' throughout.
  3. [Table 1] It would be useful to list the resulting log g and convective-boundary radii r1 and r2 for the calibrated solar model; this would directly address the concern about r2 in Eq. (3).
  4. [References] Several references are incompletely formatted (e.g., 'Matteucci et al. 2021a' appears as two separate entries; the Bossini et al. 2019 reference is used for the Pleiades parameters, though that paper is a cluster survey). A final reference cleanup is needed.
  5. [§4.1] The use of V sin i as V_ZAMS ignores the projection effect; the authors acknowledge this in §5.3, but the magnitude of the induced scatter should be estimated to show it does not affect the conclusions.

Circularity Check

2 steps flagged · score 6.0 of 10

Cluster Li-dip 'reproductions' largely transcribe the observed V sin i distribution through DMC ∝ Ω0^2, and the underlying diffusion coefficient is imported from the authors' own Paper I rather than derived for the main sequence.

  1. fitted input called prediction [Section 4.2 (Hyades/Praesepe results, around Eq. 4)]
    "As Equation (4) shows, DMC ∝ Ω2_0 and V = Ω_0R, implying that higher rotation velocities lead to more significant Li depletion. The velocity distribution of the samples in the Hyades presents a convex shape. Because of this feature, our models accurately recreate the Li dip in the parameter space of the Hyades members."

    The model ingests the observed V sin i as the input equatorial velocity (Section 4.1: 'we have collected more precise velocity samples, V sin i ... and use them as a reference for the input equatorial velocity'). Because DMC is proportional to Ω0^2 by Eq. (4), the predicted A(Li) is a monotone function of the input velocity at fixed age, mass, and metallicity. Feeding the observed convex V(Teff) curve into this map therefore produces a Li dip at the same location, i.e. the 'prediction' is the input velocity distribution re-expressed as Li depletion. The paper concedes this in Section 5.3: 'for our model to accurately simulate the Li dip behavior of a cluster, a convex distribution of rotation velocity in the corresponding temperature range is necessary.' The match on the cool side is thus

  2. self citation load bearing [Section 2.1 (Eqs. 1-4)]
    "According to Paper I, the specific expression of diffusion coefficient is obtained DMC = 2 π r2^2/(r1 − r2) R/τMC with τMC = G^2 M^3/(3 L Ω2_0 R^4). ... Based on asteroseismological evidence, the radiative zone of a rotating low-mass MS star can usually be regarded as maintaining nearly uniform rotation ... This implies that the work of Paper I can be extended to low-mass MS stars."

    The central transport coefficient used in every solar-analog and cluster calculation is taken verbatim from the authors' own Paper I, where it was derived for red-clump giants with r1 and r2 tied to the hydrogen-burning-shell geometry. The present paper does not re-derive the meridional circulation velocity for main-sequence dwarfs; the uniform-rotation statement supports only the absence of strong differential rotation, not the value VMC = R/τMC or the effective mixing-length factor r2^2/(r1−r2) in an MS star. Thus all predicted Li depletion rates inherit an untested, self-cited transfer of a giant-branch formula to the MS regime. The paper offers no independent MS circulation calculation or direct check that Eq. (4) reproduces a bona fide MS meridional flow, making the mechanism's quanti

full rationale

The paper's solar-analog A(Li)-age comparison is genuinely independent: it uses external samples (Carlos et al. 2019; Rathsam et al. 2023; Reggiani et al. 2024) and models with two fixed initial velocities, and it honestly reports that the predicted solar Li (≈1.5 dex) is higher than observed. The αMLT calibration is also a standard, non-circular external fit. The circularity is concentrated in two places. First, the cluster Li-dip 'reproductions' are largely the observed V sin i distribution transformed by the model: because DMC ∝ Ω0^2 and the observed velocities are used as input, a convex V(Teff) profile produces a Li dip by construction; the paper's own summary admits this requirement. Second, the diffusion coefficient itself is imported from the authors' Paper I, a giant-branch derivation, and its extension to MS dwarfs is asserted rather than derived from a main-sequence circulation calculation. These two issues make the central mechanism only partially self-contained: the qualitative correlation between rotation and Li depletion is plausible and broadly consistent with earlier work, but the quantitative agreements inherit both the assumed transport law and the input velocity distribution. Hence the central claim does not fully reduce to its inputs, but a substantial portion of the Li-dip 'prediction' is circular, and the load-bearing coefficient rests on a self-citation without an independent MS check.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on one prior self-derived diffusion law, a set of adjusted initial conditions (velocities, masses, metallicities, and alpha_MLT), and standard assumptions about uniform rotation and uniform cluster properties. No new particles or physical entities are invented; the main debt is the transfer of Paper I's giant-branch mixing coefficient to main-sequence stars.

free parameters (6)
  • Mixing length parameter alpha_MLT = 1.78
    Calibrated so a 1 Msun, Z=0.02 model with meridional circulation matches solar Teff, R, L at 4.57 Gyr (Table 1); applied globally to all models.
  • Initial rotation velocities for solar analogs = 2 and 10 km/s, plus grid 1.6-10 km/s
    ZAMS velocities chosen to bracket the observed A(Li)-age samples; real spin-down evolution is not modeled, only two constant-velocity tracks with a hand-drawn expected line between them (Section 3.1, Figure 1).
  • Solar analog mass and metallicity combinations = M in [0.85,1.05] Msun, Z in [0.014,0.028]; best fit around 0.9 Msun, Z=0.017
    Model grid is restricted to the observed sample domain, and the authors state that the optimal Li-Teff fit requires generally low masses and metallicities (Section 5.2), i.e. parameters are tuned to match the data.
  • Initial lithium abundance A(Li)_ini = 3.30 dex (or [Fe/H]+3.40 dex for clusters)
    Adopted from meteoritic/MESA default compositions rather than fitted to the target Li observations, but it is a chosen input that sets the normalization of all predicted abundances.
  • Cluster initial rotation velocities = observed V sini values, e.g. Hyades 3-68 km/s, Praesepe 10-90 km/s
    For clusters, V_ZAMS is set equal to current V sini, ignoring inclination and spin-down; the model then uses this input distribution to produce the Li dip, so the dip shape is partly inherited from the velocity data (Section 4.1, 5.3).
  • Cluster isochrone ages and metallicities = Hyades 0.72 Gyr, Z=0.0265; Praesepe 0.75 Gyr, Z=0.028
    Taken from literature, not fitted, but they are fixed inputs that determine which Teff range of model output is compared with each cluster.
assumptions (5)
  • domain assumption Radiative zones of low-mass main-sequence stars rotate nearly uniformly, so the Paper I meridional circulation formula can be applied to main-sequence stars.
    Invoked in the Introduction and Section 2.1 using asteroseismic references, but not demonstrated for the specific models here.
  • domain assumption Equation (4), DMC = 2 pi r2^2/(r1-r2) R/tau_MC with tau_MC = G^2 M^3/(3 L Omega_0^2 R^4), is a valid diffusion coefficient for lithium mixing in the MS radiative zone.
    Carried over from the authors' Paper I without derivation or independent calibration in this paper; it is the single physical mechanism tested.
  • domain assumption Meridional circulation is the only non-standard process needed to describe the main-sequence Li depletion patterns under study.
    The models exclude convective overshoot, waves, atomic diffusion, magnetic fields, mass loss, and planet effects; the discussion acknowledges solar Li needs additional processes (Section 5.2).
  • domain assumption Observed V sini values are usable proxies for the true equatorial rotation velocity V in cluster stars.
    The paper sets input V equal to V sini and notes in Section 5.3 that the real V is not observationally defined; inclination effects are known to blur the velocity distribution.
  • domain assumption All cluster members share a single age, metallicity, and initial lithium abundance.
    Uniform isochrone assumption stated in Section 4.1 and acknowledged as a limitation in Section 5.3.

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Cite this review

Pith. "Pith review of Meridional Circulation II: A Unified Mechanism for Lithium Depletion in Solar Analogs and the Lithium Dip in Mid-F Cluster Stars." pith.science (2026). https://pith.science/paper/XQ2SC2G4

@misc{pith2026250819715,
  author       = {Pith},
  title        = {Pith review of: Meridional Circulation II: A Unified Mechanism for Lithium Depletion in Solar Analogs and the Lithium Dip in Mid-F Cluster Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XQ2SC2G4}},
  note         = {Machine review of arXiv:2508.19715}
}
abstract

The behavior of lithium (Li) in Population I main sequence stars challenges standard stellar theory. Two phenomena stand out: the solar Li problem which extends to Li depletion in solar analogs and the Li dip observed in mid-F stars within open clusters. Building on the meridional circulation-driven radial mixing framework previously developed to explain Li-enriched red clump stars, we explore its relevance to Li depletion on the main sequence. First, our models reproduce the observed $A(\text{Li})$-Age correlation in solar analogs. Through detailed isochrone analysis, we find good agreement between the simulated and observed $A(\text{Li})$-$T_{\text{eff}}$ relationships within the solar analog parameter space. However, the predicted solar Li abundance ($\sim 1.5\,\text{dex}$) is still higher than current solar measurements. Second, our models partially explain the Li dip phenomenon in mid-F cluster stars. The models accurately reproduce Li distributions on the cool side of the Li dip in most clusters and capture the Li behaviors on the hot side observed in systems like the Hyades. However, we identify limitations in the models' ability to fully reproduce the dip morphology, particularly due to the rotation velocity distribution of sample stars in this temperature zone.

Figures

Figures reproduced from arXiv: 2508.19715 by the authors.

Figure 1
Figure 1. A(Li) vs. Age during the MS phase. The colorbar represents Teff. The scatter points in this figure are the samples of solar analogs: triangle (Rathsam et al. 2023), circle (Reggiani et al. 2024), and diamond (Carlos et al. 2019). The Sun is marked with a yellow star (A(Li) ∼ 1.10 dex (Grevesse & Sauval 1998), Age ∼ 4.57 Gyr, and Teff ∼ 5777 K). The lines are the A(Li) − Age relationship predicted by the models (1.0 … view at source ↗
Figure 2
Figure 2. A(Li) vs. Teff. The colorbar represents stellar age. The meaning of the geometric symbols is consistent with [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. A(Li) vs. Teff. The samples of the Hyades and Praesepe are, respectively, from the Tables 6 and 7 of Cummings et al. (2017). We mark the model results with ‘× (and +)’ and fit them with dashed lines. The input Li abundance on the upper and lower panels is respectively 3.3 and [Fe/H] + 3.4 dex. metallicity plays a significant role in Li evolution; higher metallicities increase opacity, necessitating larger temperatur… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Similar to [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

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Works this paper leans on

98 extracted references · 37 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

  3. [3]

    v u< nϮ䀎9 9zs`# ^V u.Ցq[I W

    thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

    arXiv 2021

  4. [4]

    & Grevesse, N.\ 1989, , 53, 197

    Anders, E. & Grevesse, N.\ 1989, , 53, 197. doi:10.1016/0016-7037(89)90286-X

    doi:10.1016/0016-7037(89)90286-x 1989

  5. [5]

    doi:10.1103/PhysRevLett.113.042501

    Anders, M., Trezzi, D., Menegazzo, R., et al.\ 2014, , 113, 042501. doi:10.1103/PhysRevLett.113.042501

    doi:10.1103/physrevlett.113.042501 2014

  6. [6]

    & Spruit, H

    Andr \'a ssy, R. & Spruit, H. C.\ 2015, , 579, A122. doi:10.1051/0004-6361/201526029

    work page doi:10.1051/0004-6361/201526029 2015

  7. [7]

    J., Deliyannis, C

    Anthony-Twarog, B. J., Deliyannis, C. P., Twarog, B. A., et al.\ 2009, , 138, 1171. doi:10.1088/0004-6256/138/4/1171

    doi:10.1088/0004-6256/138/4/1171 2009

  8. [8]

    J., Deliyannis, C

    Anthony-Twarog, B. J., Deliyannis, C. P., & Twarog, B. A.\ 2021, , 161, 159. doi:10.3847/1538-3881/abe0b7

    work page doi:10.3847/1538-3881/abe0b7 2021

Show all 98 references
  1. [9]

    J., et al.\ 2009, , 47, 481

    Asplund, M., Grevesse, N., Sauval, A. J., et al.\ 2009, , 47, 481. doi:10.1146/annurev.astro.46.060407.145222

    2009

  2. [10]

    J., & Schatzman, E.\ 1985, , 149, 309

    Baglin, A., Morel, P. J., & Schatzman, E.\ 1985, , 149, 309

    1985

  3. [11]

    doi:10.1086/175779

    Balachandran, S.\ 1995, , 446, 203. doi:10.1086/175779

    1995 doi

  4. [12]

    & Chabrier, G.\ 2010, , Effect of episodic accretion on the structure and the lithium depletion of low-mass stars and planet-hosting stars, 521, A44

    Baraffe, I. & Chabrier, G.\ 2010, , Effect of episodic accretion on the structure and the lithium depletion of low-mass stars and planet-hosting stars, 521, A44. doi:10.1051/0004-6361/201014979

    2010 doi

  5. [13]

    doi:10.3847/2041-8213/aa82ff

    Baraffe, I., Pratt, J., Goffrey, T., et al.\ 2017, , 845, L6. doi:10.3847/2041-8213/aa82ff

    2017 doi

  6. [14]

    A.\ 2007, , 669, 1167

    Barnes, S. A.\ 2007, , 669, 1167. doi:10.1086/519295

    2007 doi

  7. [15]

    & Antia, H

    Basu, S. & Antia, H. M.\ 2008, , 457, 217. doi:10.1016/j.physrep.2007.12.002

    2008 doi

  8. [16]

    G., do Nascimento, J.-D., Duarte, T., et al.\ 2017, , 602, A63

    Beck, P. G., do Nascimento, J.-D., Duarte, T., et al.\ 2017, , 602, A63. doi:10.1051/0004-6361/201629820

    2017 doi

  9. [17]

    doi:10.1093/mnras/stv1493

    Benomar, O., Takata, M., Shibahashi, H., et al.\ 2015, , 452, 2654. doi:10.1093/mnras/stv1493

    2015 doi

  10. [18]

    Boesgaard, A. M. & Steigman, G.\ 1985, , 23, 319. doi:10.1146/annurev.aa.23.090185.001535

    1985

  11. [19]

    Boesgaard, A. M. & Tripicco, M. J.\ 1986, , 302, L49. doi:10.1086/184635

    1986 doi

  12. [20]

    M.\ 1987, , 99, 1067

    Boesgaard, A. M.\ 1987, , 99, 1067. doi:10.1086/132078

    1987 doi

  13. [21]

    M., Budge, K

    Boesgaard, A. M., Budge, K. G., & Ramsay, M. E.\ 1988, , 327, 389. doi:10.1086/166201

    1988 doi

  14. [22]

    doi:10.1051/0004-6361/202451321

    Borisov, S., Prantzos, N., & Charbonnel, C.\ 2024, , 691, A142. doi:10.1051/0004-6361/202451321

    2024 doi

  15. [23]

    doi:10.1051/0004-6361/201834693

    Bossini, D., Vallenari, A., Bragaglia, A., et al.\ 2019, , 623, A108. doi:10.1051/0004-6361/201834693

    2019 doi

  16. [24]

    M., et al.\ 2025, arXiv:2501.03723

    Buldgen, G., Noels, A., Amarsi, A. M., et al.\ 2025, arXiv:2501.03723. doi:10.48550/arXiv.2501.03723

    2025 doi arXiv

  17. [25]

    E., & Mel \'e ndez, J.\ 2016, , 587, A100

    Carlos, M., Nissen, P. E., & Mel \'e ndez, J.\ 2016, , 587, A100. doi:10.1051/0004-6361/201527478

    2016 doi

  18. [26]

    doi:10.1093/mnras/stz681

    Carlos, M., Mel \'e ndez, J., Spina, L., et al.\ 2019, , 485, 4052. doi:10.1093/mnras/stz681

    2019 doi

  19. [27]

    doi:10.1051/0004-6361:20078928

    Castro, M., Vauclair, S., Richard, O., et al.\ 2009, , 494, 663. doi:10.1051/0004-6361:20078928

    2009 doi

  20. [28]

    & Molaro, P.\ 2019, , 482, 4372

    Cescutti, G. & Molaro, P.\ 2019, , 482, 4372. doi:10.1093/mnras/sty2967

    2019 doi

  21. [29]

    D., Deliyannis, C

    Cummings, J. D., Deliyannis, C. P., Maderak, R. M., et al.\ 2017, , 153, 128. doi:10.3847/1538-3881/aa5b86

    2017 doi

  22. [30]

    H., Fields, B

    Cyburt, R. H., Fields, B. D., & Olive, K. A.\ 2008, , 2008, 012. doi:10.1088/1475-7516/2008/11/012

    2008 doi

  23. [31]

    & Michaud, G.\ 1988, , 334, 746

    Charbonneau, P. & Michaud, G.\ 1988, , 334, 746. doi:10.1086/166875

    1988 doi

  24. [32]

    R.\ 1989, , 347, 821

    Charbonneau, P., Michaud, G., & Proffitt, C. R.\ 1989, , 347, 821. doi:10.1086/168172

    1989 doi

  25. [33]

    Charbonnel, C., Vauclair, S., & Zahn, J.-P.\ 1992, , 255, 191

    1992

  26. [34]

    & Talon, S.\ 2005, Science, 309, 2189

    Charbonnel, C. & Talon, S.\ 2005, Science, 309, 2189. doi:10.1126/science.1116849

    2005 doi

  27. [35]

    doi:10.1103/RevModPhys.74.1073

    Christensen-Dalsgaard, J.\ 2002, Reviews of Modern Physics, 74, 1073. doi:10.1103/RevModPhys.74.1073

    2002 doi

  28. [36]

    doi:10.1051/0004-6361:200810665

    Decressin, T., Mathis, S., Palacios, A., et al.\ 2009, , 495, 271. doi:10.1051/0004-6361:200810665

    2009 doi

  29. [37]

    Z., et al.\ 2015, , 576, A69

    Delgado Mena, E., Bertr \'a n de Lis, S., Adibekyan, V. Z., et al.\ 2015, , 576, A69. doi:10.1051/0004-6361/201425433

    2015 doi

  30. [38]

    doi:10.1051/0004-6361/202141094

    Dumont, T., Charbonnel, C., Palacios, A., et al.\ 2021, , 654, A46. doi:10.1051/0004-6361/202141094

    2021 doi

  31. [39]

    S.\ 1925, The Observatory, 48, 73

    Eddington, A. S.\ 1925, The Observatory, 48, 73

    1925

  32. [40]

    Endal, A. S. & Sofia, S.\ 1981, , 243, 625. doi:10.1086/158628

    1981 doi

  33. [41]

    Epstein, C. R. & Pinsonneault, M. H.\ 2014, , 780, 159. doi:10.1088/0004-637X/780/2/159

    2014 doi

  34. [42]

    D.\ 2011, Annual Review of Nuclear and Particle Science, 61, 47

    Fields, B. D.\ 2011, Annual Review of Nuclear and Particle Science, 61, 47. doi:10.1146/annurev-nucl-102010-130445

    2011 doi

  35. [43]

    doi:10.1051/0004-6361/201731677

    Fu, X., Romano, D., Bragaglia, A., et al.\ 2018, , 610, A38. doi:10.1051/0004-6361/201731677

    2018 doi

  36. [44]

    doi:10.3847/1538-4365/ab505c

    Gao, Q., Shi, J.-R., Yan, H.-L., et al.\ 2019, , 245, 33. doi:10.3847/1538-4365/ab505c

    2019 doi

  37. [45]

    Garcia Lopez, R. J. & Spruit, H. C.\ 1991, , 377, 268. doi:10.1086/170356

    1991 doi

  38. [46]

    & Sauval, A

    Grevesse, N. & Sauval, A. J.\ 1998, , 85, 161. doi:10.1023/A:1005161325181

    1998 doi

  39. [47]

    Hobbs, L. M. & Pilachowski, C.\ 1986, , 309, L17. doi:10.1086/184752

    1986 doi

  40. [48]

    R., et al.\ 2020, , 491, 3, 3586

    Li, G., Van Reeth, T., Bedding, T. R., et al.\ 2020, , 491, 3, 3586. doi:10.1093/mnras/stz2906

    2020 doi

  41. [49]

    doi:10.1093/mnras/stae639

    Li, X.-F., Shi, J.-R., Li, Y., et al.\ 2024, , 529, 1423. doi:10.1093/mnras/stae639

    2024 doi

  42. [50]

    doi:10.3847/2041-8213/adb833

    Li, X.-F., Shi, J.-R., Li, Y., et al.\ 2025, , 982, L4. doi:10.3847/2041-8213/adb833

    2025 doi

  43. [51]

    Jackson, R. J. & Jeffries, R. D.\ 2014, , The effect of star-spots on the ages of low-mass stars determined from the lithium depletion boundary, 445, 4, 4306. doi:10.1093/mnras/stu2076

    2014 doi

  44. [52]

    S., Tayar, J., & Fuller, J.\ 2020, , 491, 1, 690

    Jermyn, A. S., Tayar, J., & Fuller, J.\ 2020, , 491, 1, 690. doi:10.1093/mnras/stz2983

    2020 doi

  45. [53]

    & Chaboyer, B.\ 2018, , 856, 1, 10

    Joyce, M. & Chaboyer, B.\ 2018, , 856, 1, 10. doi:10.3847/1538-4357/aab200

    2018 doi

  46. [54]

    & Tayar, J.\ 2023, Galaxies, 11, 3, 75

    Joyce, M. & Tayar, J.\ 2023, Galaxies, 11, 3, 75. doi:10.3390/galaxies11030075

    2023 doi

  47. [55]

    R., Deliyannis, C

    King, J. R., Deliyannis, C. P., Hiltgen, D. D., et al.\ 1997, , 113, 1871. doi:10.1086/118399

    1997 doi

  48. [56]

    ISBN 978-3-540-76948-4

    Maeder, A.\ 2009, Physics, Formation and Evolution of Rotating Stars. ISBN 978-3-540-76948-4. Springer Berlin Heidelberg, 2009. doi:10.1007/978-3-540-76949-1

    2009 doi

  49. [57]

    L., Simpson, J

    Martell, S. L., Simpson, J. D., Balasubramaniam, A. G., et al.\ 2021, , 505, 5340. doi:10.1093/mnras/stab1356

    2021 doi

  50. [58]

    doi:10.1093/mnras/stad1177

    Martos, G., Mel \'e ndez, J., Rathsam, A., et al.\ 2023, , 522, 3217. doi:10.1093/mnras/stad1177

    2023 doi

  51. [59]

    S., et al.\ 2021, , 505, 200

    Matteucci, F., Molero, M., Aguado, D. S., et al.\ 2021, , 505, 200. doi:10.1093/mnras/stab1234

    2021 doi

  52. [60]

    doi:10.1007/s00159-021-00133-8

    Matteucci, F.\ 2021, , 29, 5. doi:10.1007/s00159-021-00133-8

    2021 doi

  53. [61]

    & Maeder, A.\ 2002, , 390, 561

    Meynet, G. & Maeder, A.\ 2002, , 390, 561. doi:10.1051/0004-6361:20020755

    2002 doi

  54. [62]

    doi:10.1086/164025

    Michaud, G.\ 1986, , 302, 650. doi:10.1086/164025

    1986 doi

  55. [63]

    Montalban, J.\ 1994, , 281, 421

    1994

  56. [64]

    & Schatzman, E.\ 1996, , 305, 513

    Montalban, J. & Schatzman, E.\ 1996, , 305, 513

    1996

  57. [65]

    & Rebolo, R.\ 2002, , 386, 1039

    Montalb \'a n, J. & Rebolo, R.\ 2002, , 386, 1039. doi:10.1051/0004-6361:20020338

    2002 doi

  58. [66]

    doi:10.1051/0004-6361/201526370

    Netopil, M., Paunzen, E., Heiter, U., et al.\ 2016, , 585, A150. doi:10.1051/0004-6361/201526370

    2016 doi

  59. [67]

    B., et al.\ 2018, , 234, 2, 34

    Paxton, B., Schwab, J., Bauer, E. B., et al.\ 2018, , 234, 2, 34. doi:10.3847/1538-4365/aaa5a8

    2018 doi

  60. [68]

    doi:10.1051/0004-6361:20030891

    Piau, L., Randich, S., & Palla, F.\ 2003, , 408, 1037. doi:10.1051/0004-6361:20030891

    2003 doi

  61. [69]

    doi:10.1146/annurev.astro.35.1.557

    Pinsonneault, M.\ 1997, , 35, 557. doi:10.1146/annurev.astro.35.1.557

    1997 doi

  62. [70]

    doi:10.1051/0004-6361/202038688

    Randich, S., Pasquini, L., Franciosini, E., et al.\ 2020, , 640, L1. doi:10.1051/0004-6361/202038688

    2020 doi

  63. [71]

    & Magrini, L.\ 2021, Frontiers in Astronomy and Space Sciences, 8, 6

    Randich, S. & Magrini, L.\ 2021, Frontiers in Astronomy and Space Sciences, 8, 6. doi:10.3389/fspas.2021.616201

    2021

  64. [72]

    doi:10.1093/mnras/stad2589

    Rathsam, A., Mel \'e ndez, J., & Carvalho Silva, G.\ 2023, , 525, 4642. doi:10.1093/mnras/stad2589

    2023 doi

  65. [73]

    M., Stauffer, J

    Rebull, L. M., Stauffer, J. R., Cody, A. M., et al.\ 2018, , 155, 5, 196. doi:10.3847/1538-3881/aab605

    2018 doi

  66. [74]

    Y., Lorenzo-Oliveira, D., et al.\ 2024, arXiv:2408.10999

    Reggiani, H., Galarza, J. Y., Lorenzo-Oliveira, D., et al.\ 2024, arXiv:2408.10999. doi:10.48550/arXiv.2408.10999

    2024 doi arXiv

  67. [75]

    & Michaud, G.\ 1993, , 416, 312

    Richer, J. & Michaud, G.\ 1993, , 416, 312. doi:10.1086/173237

    1993 doi

  68. [76]

    doi:10.1051/0004-6361/200913282

    Sbordone, L., Bonifacio, P., Caffau, E., et al.\ 2010, , 522, A26. doi:10.1051/0004-6361/200913282

    2010 doi

  69. [77]

    & Weiss, A.\ 1999, , 347, 272

    Schlattl, H. & Weiss, A.\ 1999, , 347, 272

    1999

  70. [78]

    N., Steigman, G., & Dearborn, D

    Schramm, D. N., Steigman, G., & Dearborn, D. S. P.\ 1990, , 359, L55. doi:10.1086/185794

    1990 doi

  71. [79]

    doi:10.1086/146297

    Schwarzschild, M., Howard, R., & H \"a rm, R.\ 1957, , 125, 233. doi:10.1086/146297

    1957 doi

  72. [80]

    R., Fedele, S

    Soderblom, D. R., Fedele, S. B., Jones, B. F., et al.\ 1993, , 106, 1080. doi:10.1086/116705

    1993 doi

  73. [81]

    & Pinsonneault, M

    Somers, G. & Pinsonneault, M. H.\ 2015, , Older and Colder: The Impact of Starspots on Pre-main-sequence Stellar Evolution, 807, 2, 174. doi:10.1088/0004-637X/807/2/174

    2015 doi

  74. [82]

    & Pinsonneault, M

    Somers, G. & Pinsonneault, M. H.\ 2016, , 829, 32. doi:10.3847/0004-637X/829/1/32

    2016 doi

  75. [83]

    & Spite, M.\ 1982, , 115, 357

    Spite, F. & Spite, M.\ 1982, , 115, 357

    1982

  76. [84]

    P., Steinhauer, A., et al.\ 2023, , 952, 71

    Sun, Q., Deliyannis, C. P., Steinhauer, A., et al.\ 2023, , 952, 71. doi:10.3847/1538-4357/acc5e3

    2023 doi

  77. [85]

    A.\ 1950, , 110, 548

    Sweet, P. A.\ 1950, , 110, 548. doi:10.1093/mnras/110.6.548

    1950 doi

  78. [86]

    Sweigart, A. V. & Mengel, J. G.\ 1979, , 229, 624. doi:10.1086/156996

    1979 doi

  79. [87]

    Swenson, F. J. & Faulkner, J.\ 1992, , 395, 654. doi:10.1086/171686

    1992 doi

  80. [88]

    doi:10.1051/0004-6361/200913897

    Takeda, Y., Honda, S., Kawanomoto, S., et al.\ 2010, , 515, A93. doi:10.1051/0004-6361/200913897

    2010 doi

  81. [89]

    & Tassoul, M.\ 1982, , 49, 317

    Tassoul, J.-L. & Tassoul, M.\ 1982, , 49, 317. doi:10.1086/190801

    1982 doi

  82. [90]

    & Tassoul, J.-L.\ 1983, , 267, 334

    Tassoul, M. & Tassoul, J.-L.\ 1983, , 267, 334. doi:10.1086/160872

    1983 doi

  83. [91]

    Cambridge ; New York : Cambridge University Press, 2000

    Tassoul, J.-L.\ 2000, Stellar rotation / Jean-Louis Tassoul. Cambridge ; New York : Cambridge University Press, 2000. (Cambridge astrophysics series ; 36)

    2000

  84. [92]

    doi:10.1086/306056

    Turcotte, S., Richer, J., & Michaud, G.\ 1998, , 504, 559. doi:10.1086/306056

    1998 doi

  85. [93]

    doi:10.1051/0004-6361/201628616

    Van Reeth, T., Tkachenko, A., & Aerts, C.\ 2016, , 593, A120. doi:10.1051/0004-6361/201628616

    2016 doi

  86. [94]

    doi:10.1051/0004-6361/202142921

    Van Reeth, T., De Cat, P., Van Beeck, J., et al.\ 2022, , 662, A58. doi:10.1051/0004-6361/202142921

    2022 doi

  87. [95]

    & Sears, R

    Weymann, R. & Sears, R. L.\ 1965, , 142, 174. doi:10.1086/148274

    1965 doi

  88. [96]

    doi:10.48550/arXiv.2410.17590

    Yana Galarza, J., Lorenzo-Oliveira, D., Ferreira, T., et al.\ 2024, arXiv:2410.17590. doi:10.48550/arXiv.2410.17590

    2024 doi arXiv

  89. [97]

    Zahn, J.-P.\ 1992, , 265, 115

    1992

  90. [98]

    doi:10.3847/1538-4357/ab2f77

    Zhang, Q.-S., Li, Y., & Christensen-Dalsgaard, J.\ 2019, , 881, 103. doi:10.3847/1538-4357/ab2f77

    2019 doi

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