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arxiv: 2605.14128 · v1 · submitted 2026-05-13 · 🌌 astro-ph.SR

Recognition: 2 theorem links

· Lean Theorem

Toward a Comprehensive Grid of Cepheid Models with MESA. IV. Modest Effects of Rotation on Blue Loops

R. Smolec , R. Singh Rathour , V. Hocd\'e
Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:06 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords Cepheid starsstellar rotationblue loopsMESA codestellar evolutionmass discrepancyperiod-luminosity relation
0
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The pith

Rotation produces only small luminosity increases in Cepheid blue loops

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

The authors compute stellar evolution tracks from 2 to 8 solar masses using MESA with rotation included for metallicities from 0.002 to 0.014. They show that rotation has modest effects on the blue loops, raising their luminosity by no more than 0.04 dex as the initial rotation rate increases. This effect is much smaller than the luminosity boost from adding main-sequence core overshooting. Consequently, rotation by itself cannot resolve the Cepheid mass discrepancy without also invoking substantial core overshooting. The period-luminosity and period-radius relations stay nearly unchanged, while the period-age relation lengthens ages by only a few percent.

Core claim

Using the fully diffusive approximation for rotationally induced mixing in MESA, the luminosity levels of the blue loops increase by at most 0.04 dex with higher initial rotation rates, without significant changes to their appearance or extent. This is in contrast to results from the Geneva code using an advective-diffusive scheme, where mixing is more efficient and loops are brighter and more extended. The predicted surface velocities exceed observed values.

What carries the argument

The fully diffusive treatment of rotationally induced mixing in evolutionary models of 2-8 solar mass stars.

If this is right

  • Blue loop luminosity and extent remain largely unaffected by rotation.
  • The mass discrepancy cannot be solved by rotation alone.
  • Period-luminosity and period-radius relations are insensitive to rotation.
  • Period-age relations predict ages a few percent longer.
  • Surface rotational velocities are overpredicted compared to observations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Switching to an advective-diffusive mixing scheme could produce larger rotation effects, as seen in other codes.
  • Grids of Cepheid models may need to prioritize core overshooting parameters over rotation for accuracy.
  • Future work could explore intermediate mixing efficiencies to better match observed rotation velocities.
  • Non-rotating models with appropriate overshooting may suffice for most Cepheid property predictions.

Load-bearing premise

The fully diffusive approximation for rotationally induced mixing processes is adequate to capture the effects of rotation on main-sequence and post-main-sequence evolution for these masses and metallicities.

What would settle it

Detection of blue loop luminosities in rotating Cepheids that exceed non-rotating models by more than 0.04 dex, or measurements showing lower surface velocities than predicted, would challenge the findings.

Figures

Figures reproduced from arXiv: 2605.14128 by R. Singh Rathour, R. Smolec, V. Hocd\'e.

Figure 1
Figure 1. Figure 1: Evolutionary tracks for 3, 4, 5, 6, 7, and 8 M⊙ models of the O14 ML4h RA set (with moderate MS core overshooting, fH = 0.01, fenv = 0.04, and ηR = 0.4) for Z = 0.014 (left), Z = 0.006 (middle), and Z = 0.002 (right), and different initial rotation rates coded by color: gray for non-rotating models, then blue for W0 = 0.3, orange for W0 = 0.5, and red for W0 = 0.65. Bottom panels zoom in on the blue loops … view at source ↗
Figure 2
Figure 2. Figure 2: Average surface rotational velocities, vrot, as a function of luminosity during crossings of the IS for 3, 5, and 8 M⊙ models of different metallicities, Z = 0.014 (top), Z = 0.006 (middle), and Z = 0.002 (bottom). Solid, dashed, and dotted lines correspond to models without MS core over￾shooting, and with fH = 0.01, and fH = 0.02, respectively. In all models, the initial ZAMS rotation rate is W0 = 0.3. ti… view at source ↗
Figure 4
Figure 4. Figure 4: Average surface rotational velocities as a func￾tion of luminosity during crossings of the IS for 3, 5, and 8 M⊙ models of Z = 0.002, initialized with a rotation rate of W0 = 0.5. In the top panel, models without magnetic effects and models including magnetic effects are compared. In the middle panel, models with different values of parameters af￾fecting chemical element mixing, fc and fµ, are compared. In… view at source ↗
Figure 3
Figure 3. Figure 3: HRDs for 3−8 M⊙, Z = 0.002 models, initialized with a rotation rate of W0 = 0.5, with different rotation-re￾lated controls aimed at increasing blue loop luminosity. In the top panel, the effects of inclusion of magnetic effects (ST dynamo) in angular momentum (dotted blue tracks) and simultaneously in chemical element mixing (dashed green tracks) are illustrated. In the middle panel, we compare tracks comp… view at source ↗
Figure 5
Figure 5. Figure 5: M − L relations for O24 ML4h RA models (fH = 0.02, fenv = 0.04, ηR = 0.4) with W0 = 0 (gray lines) and the highest initial rotation rate of W0 = 0.65 (blue lines), and for models of the O24 ML8h RA set (with twice as large ηR = 0.8) and W0 = 0.65, for MW, LMC, and SMC metallicities (Z = 0.014, 0.006, and 0.002 in the left, middle, and right panels, respectively). The theoretical relations are confronted wi… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the observed and model P − L relations expressed in terms of the Wesenheit index, WV I = I − 1.55(V − I), for the LMC (left) and SMC (right). OGLE data (Soszy´nski et al. 2015, 2017, 2019) are com￾pared to Z = 0.006 (LMC) and Z = 0.002 (SMC) models of the O24 ML4h RA set without rotation (top) and including rotation (W0 = 0.65, bottom). Model relations are shown for the blue and red edges and… view at source ↗
Figure 7
Figure 7. Figure 7: P − R relations for O24 ML4h RA models (fH = 0.02, fenv = 0.04, ηR = 0.4) and the highest initial rotation rate of W0 = 0.65, for MW, LMC, and SMC metallicities (Z = 0.014, 0.006, and 0.002 in the left, middle, and right panels, respectively), confronted with determinations from Trahin et al. (2021); Gieren et al. (1998, 1999); Gallenne et al. (2017) and Wielg´orski et al. (in prep.). In the first panel, w… view at source ↗
Figure 8
Figure 8. Figure 8: P − Age relations for O24 ML4h RA models (fH = 0.02, fenv = 0.04, ηR = 0.4) without rotation (top panels) and with the highest initial rotation rate of W0 = 0.65 (bottom panels), for MW, LMC, and SMC metallicities (Z = 0.014, 0.006, and 0.002 in the left, middle, and right panels, respectively). Relations are plotted for each crossing; the upper and lower envelopes of the bands correspond to the red and bl… view at source ↗
Figure 9
Figure 9. Figure 9: Evolutionary tracks for 3, 4, 5, and 7 M⊙ from MIST (Choi et al. 2016). Model metallicities, [Fe/H], are +0.0, −0.25, and −0.75 from left to right. Solid lines correspond to models without rotation, while models plotted with blue dashed lines correspond to an initial rotation rate at ZAMS of W0 = 0.4 [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of MESA tracks computed in this study (O14 ML4h RA; blue lines) with models computed with the Geneva code (Georgy et al. 2013) from the SYCLIST database (orange lines). The 3, 5, and 7 M⊙ models are presented with Z = 0.014 (left), Z = 0.006 (middle), and Z = 0.002 (right). Non-rotating models are plotted with solid lines and light color. Models including rotation are plotted with dotted lines … view at source ↗
Figure 11
Figure 11. Figure 11: M − L relations for O14 ML4h RA models (fH=0.01, fenv=0.04, ηR=0.4) with W0 = 0.3 (gray lines) compared with M − L relations from Anderson et al. (2016) (βH = 0.1Hp, ω0 = 0.5; green lines). Comparison is presented for Z = 0.014 (left), 0.006 (middle), and 0.002 (right). The theoretical relations are confronted with determinations from Gallenne et al. (2018, 2025); Pilecki et al. (2018); Evans et al. (2024… view at source ↗
Figure 12
Figure 12. Figure 12: P − Age relations for O14 ML4h RA models (fH=0.01, fenv=0.4, ηR=0.4) with W0 = 0.3 compared with M − L relations from Anderson et al. (2016) (βH = 0.1Hp, ω0 = 0.5; triangles). Comparison is presented for Z = 0.014 (left), 0.006 (middle), and 0.002 (right) [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: HRD (top) and evolution of surface rotational velocity (bottom) for 4 M⊙, Z = 0.002, W0 = 0.3 model computed with MESA’s default rotational mixing prescrip￾tion (solid gray line) and modified prescription from Mar￾tinelli et al. (2025), calibrated to emulate the rotational in￾duced mixing in the Geneva code during MS. Corresponding Geneva track (ω0 = 0.5) is plotted with dashed red line for comparison. In… view at source ↗
Figure 14
Figure 14. Figure 14: Evolutionary tracks computed with MESA-r21.12.1 (solid gray lines) and MESA-25.12.1 (dotted blue lines) from ZAMS until AGB, for models of 3, 4, 5, 6, 7, and 8 M⊙, and different metallicities, Z = 0.014 (left), Z = 0.006 (middle), and Z = 0.002 (right). ACKNOWLEDGMENTS This research is supported by the National Science Cen￾ter, Poland, Sonata BIS project 2018/30/E/ST9/00598. We thank the referee for a car… view at source ↗
Figure 15
Figure 15. Figure 15: Evolutionary tracks computed without core-helium overshooting (O14 ML4h RA model set, solid gray lines) and including core-helium overshooting (fHe=0.01, dotted blue lines) from ZAMS until AGB, for models of 3, 4, 5, 6, 7, and 8 M⊙, and different metallicities, Z = 0.014 (left), Z = 0.006 (middle), and Z = 0.002 (right). In all models W0 = 0.5. helium overshooting is included with the same efficiency as d… view at source ↗
Figure 16
Figure 16. Figure 16: Evolutionary tracks computed with different numerical (spatial and temporal) resolution settings for rotating models of 3, 5, and 7 M⊙ from ZAMS until AGB. The legend is displayed in the top right panel and numerical controls are given in Tab. 11. Models adopt different metallicities, Z = 0.014 (left), Z = 0.006 (middle), and Z = 0.002 (right) and different initial rotation rates, W0 = 0.3 in the top row,… view at source ↗
Figure 17
Figure 17. Figure 17: Positive (top) and negative (bottom) period change rates predicted form evolutionary models of different metallicities (different line styles), including rotation (O14 ML4h RA, W0 = 0.65, dark lines) and non-rotating (bright lines), confronted with determinations for MW Cepheids from Turner et al. (2006) and LMC Cepheids from Rodr´ıguez-Segovia et al. (2022). PCRs were avaluated at the midline of the IS, … view at source ↗
read the original abstract

Evolutionary tracks for $2-8M_\odot$ stars, with metallicities of $Z=0.014$, $0.006$, and $0.002$, including rotation, are computed with Modules for Experiments in Stellar Astrophysics (MESA). We study how rotation impacts the evolutionary properties of classical Cepheids. We examine whether rotation can offer a plausible explanation for the mass discrepancy problem when it is included in the evolutionary code using the fully diffusive approximation for rotationally induced mixing processes. We find that rotation barely influences the appearance and luminosity levels of the blue loops. While luminosity increases with increasing initial rotation rate, the increase does not exceed 0.04 dex, a fraction of the increase resulting from including the main sequence (MS) core overshooting of $0.2H_p$. As a consequence, rotation alone cannot resolve the mass discrepancy problem without simultaneously requiring significant MS core overshooting. Similar to the mass-luminosity relation, the period-radius and period-luminosity relations are barely affected by rotation, while the period-age relation predicts Cepheid ages to be only a few per cent longer compared with models without rotation. The predicted surface rotational velocities are too large compared with observations. These results are in contrast with those obtained with the Geneva code, which implements rotational mixing using the advective-diffusive scheme. In that approach, the luminosity levels of the loops are significantly higher, their luminosity extent increases, and the predicted rotation velocities are lower, compared with MESA models. The differences between the two approaches arise from significantly more efficient rotation-induced mixing during the MS evolution in models computed with the advective-diffusive scheme.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript computes MESA evolutionary tracks for 2–8 M⊙ stars at Z=0.014, 0.006, and 0.002, incorporating rotation via the fully diffusive approximation for rotationally induced mixing. It reports that rotation produces only modest changes to blue-loop morphology and luminosity (increases ≤0.04 dex), insufficient to resolve the Cepheid mass discrepancy without 0.2 Hp main-sequence core overshooting. Period-radius and period-luminosity relations are essentially unaffected while the period-age relation yields ages only a few percent longer; surface velocities are overpredicted relative to observations. Results are contrasted with Geneva-code models that employ an advective-diffusive mixing scheme and produce higher loop luminosities.

Significance. If the quantitative bounds hold, the work supplies useful MESA-specific constraints on the role of rotation in Cepheid progenitors and highlights the sensitivity of blue-loop properties to the choice of rotational-mixing implementation. The direct numerical survey across three metallicities and a range of initial rotation rates, together with the explicit Geneva comparison, provides a clear benchmark for future model grids.

major comments (2)
  1. [Abstract] Abstract: The central quantitative claim that luminosity increases do not exceed 0.04 dex and that rotation alone cannot resolve the mass discrepancy is obtained exclusively under the fully diffusive mixing prescription. The manuscript notes that this prescription overpredicts surface rotational velocities; a test or estimate of how higher mixing efficiency (required to match observed velocities) would affect blue-loop extent and luminosity is needed to establish whether the modest-effect result is robust or prescription-dependent.
  2. [Abstract] Abstract and methods description: The 0.2 Hp core-overshooting value is adopted from prior literature and held fixed. Because the paper states that the luminosity shift from overshooting exceeds that from rotation, a brief sensitivity check varying overshooting together with rotation would clarify the relative contributions and strengthen the claim that rotation is a secondary effect.
minor comments (1)
  1. [Abstract] Abstract: The phrase 'a few per cent longer' for the period-age shift should be replaced by a specific range or mean value derived from the grid.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and positive assessment of the work's significance. We address the two major comments point by point below, with revisions made where they strengthen the manuscript without altering its core conclusions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central quantitative claim that luminosity increases do not exceed 0.04 dex and that rotation alone cannot resolve the mass discrepancy is obtained exclusively under the fully diffusive mixing prescription. The manuscript notes that this prescription overpredicts surface rotational velocities; a test or estimate of how higher mixing efficiency (required to match observed velocities) would affect blue-loop extent and luminosity is needed to establish whether the modest-effect result is robust or prescription-dependent.

    Authors: We agree that the quantitative bounds (≤0.04 dex luminosity increase) are specific to MESA's fully diffusive implementation of rotational mixing. The manuscript already contrasts these results with Geneva-code models that use an advective-diffusive scheme, which produces more efficient main-sequence mixing, higher blue-loop luminosities, and lower surface velocities that better match observations. This comparison provides the requested estimate: even under the higher-efficiency scheme, rotation-induced luminosity shifts remain modest relative to the mass discrepancy and still require substantial overshooting to resolve it. We have revised the abstract and added a clarifying paragraph in the discussion to make this linkage explicit, while retaining the focus on the diffusive case as the primary MESA result. revision: partial

  2. Referee: [Abstract] Abstract and methods description: The 0.2 Hp core-overshooting value is adopted from prior literature and held fixed. Because the paper states that the luminosity shift from overshooting exceeds that from rotation, a brief sensitivity check varying overshooting together with rotation would clarify the relative contributions and strengthen the claim that rotation is a secondary effect.

    Authors: The 0.2 Hp overshooting value is indeed taken from the literature and held fixed, as is standard for such grids. Our calculations already show that the luminosity increase from this overshooting level substantially exceeds the rotation-induced shift (≤0.04 dex) at all masses and metallicities examined. To directly address the request for clarification of relative contributions, we have added a brief sensitivity discussion in the revised methods and results sections, referencing how the separate effects combine and confirming that rotation remains secondary even when overshooting is considered at the adopted level. A full re-grid varying both parameters simultaneously was not performed, as the existing data suffice to support the secondary-role conclusion. revision: partial

Circularity Check

0 steps flagged

No significant circularity in forward MESA evolutionary integrations

full rationale

The paper computes stellar evolutionary tracks for 2-8 solar mass stars using MESA with rotation included via the fully diffusive approximation for mixing. The central results—that rotation increases blue-loop luminosity by at most 0.04 dex and has negligible effect on loop morphology—are direct numerical outputs of these integrations with fixed parameters (overshooting held at 0.2 Hp from prior literature). No predictions reduce to fitted inputs by construction, no self-definitional steps exist, and no load-bearing self-citations make the claims tautological. The contrast with Geneva code results is external. The derivation chain consists of independent forward modeling.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard stellar structure equations plus the specific implementation of rotational mixing inside MESA. No new particles or forces are introduced. The 0.2 Hp overshooting parameter is taken from earlier work and held fixed.

free parameters (1)
  • main-sequence core overshooting
    Fixed at 0.2 pressure scale heights; the paper states that rotation effects are small compared with the luminosity boost from this value.
axioms (2)
  • domain assumption Fully diffusive approximation for rotationally induced mixing is sufficient for 2-8 solar-mass stars
    Invoked when the authors contrast their results with the advective-diffusive scheme used in the Geneva code.
  • standard math Standard MESA input physics (opacities, nuclear rates, equation of state) are adequate for Cepheid blue loops
    Implicit in the use of MESA without additional modifications listed in the abstract.

pith-pipeline@v0.9.0 · 5619 in / 1563 out tokens · 32328 ms · 2026-05-15T02:06:18.047403+00:00 · methodology

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Works this paper leans on

106 extracted references · 106 canonical work pages · 8 internal anchors

  1. [1]

    Aerts, C., Mathis, S., & Rogers, T. M. 2019, ARA&A, 57, 35, doi: 10.1146/annurev-astro-091918-104359

    work page doi:10.1146/annurev-astro-091918-104359 2019

  2. [2]

    2019, A&A, 631, A77, doi: 10.1051/0004-6361/201935160

    Amard, L., Palacios, A., Charbonnel, C., et al. 2019, A&A, 631, A77, doi: 10.1051/0004-6361/201935160

    work page doi:10.1051/0004-6361/201935160 2019

  3. [3]

    Anderson, R. I. 2013, PhD thesis, University of Geneva, Astronomical Observatory

    work page 2013

  4. [4]

    I., Ekstr¨ om, S., Georgy, C., et al

    Anderson, R. I., Ekstr¨ om, S., Georgy, C., et al. 2014, A&A, 564, A100, doi: 10.1051/0004-6361/201322988

    work page doi:10.1051/0004-6361/201322988 2014

  5. [5]

    2016, A&A, 591, A8, doi: 10.1051/0004-6361/201528031

    Meynet, G. 2016, A&A, 591, A8, doi: 10.1051/0004-6361/201528031

    work page doi:10.1051/0004-6361/201528031 2016

  6. [6]

    1999, NuPhA, 656, 3, doi: 10.1016/S0375-9474(99)00030-5

    Angulo, C., Arnould, M., Rayet, M., et al. 1999, NuPhA, 656, 3, doi: 10.1016/S0375-9474(99)00030-5

    work page doi:10.1016/s0375-9474(99)00030-5 1999

  7. [7]

    Asplund, M., Grevesse, N., & Sauval, A. J. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 336, Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis, ed. T. G. Barnes, III & F. N. Bash, 25

    work page 2005

  8. [8]

    J., & Scott, P

    Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481, doi: 10.1146/annurev.astro.46.060407.145222

    work page doi:10.1146/annurev.astro.46.060407.145222 2009

  9. [9]

    C., Nardetto, N., Hocd´ e, V., et al

    Bailleul, M. C., Nardetto, N., Hocd´ e, V., et al. 2026, A&A, 706, A336, doi: 10.1051/0004-6361/202557995

    work page doi:10.1051/0004-6361/202557995 2026

  10. [10]

    1996, A&A, 306, 417

    Bersier, D., & Burki, G. 1996, A&A, 306, 417

    work page 1996

  11. [11]

    E., & Cassinelli, J

    Bjorkman, J. E., & Cassinelli, J. P. 1993, ApJ, 409, 429, doi: 10.1086/172676

    work page doi:10.1086/172676 1993

  12. [12]

    1995, A&A, 297, 727

    Bloecker, T. 1995, A&A, 297, 727

    work page 1995

  13. [13]

    2006, Mem

    Bono, G., Caputo, F., & Castellani, V. 2006, Mem. Soc. Astron. Italiana, 77, 207

    work page 2006

  14. [14]

    E., Cantiello, M., et al

    Brott, I., de Mink, S. E., Cantiello, M., et al. 2011, A&A, 530, A115, doi: 10.1051/0004-6361/201016113

    work page doi:10.1051/0004-6361/201016113 2011

  15. [15]

    2014, ApJ, 788, 93, doi: 10.1088/0004-637X/788/1/93

    Christensen-Dalsgaard, J., & Paxton, B. 2014, ApJ, 788, 93, doi: 10.1088/0004-637X/788/1/93

    work page doi:10.1088/0004-637x/788/1/93 2014

  16. [16]

    2011, ApJL, 728, L43, doi: 10.1088/2041-8205/728/2/L43

    Cassisi, S., & Salaris, M. 2011, ApJL, 728, L43, doi: 10.1088/2041-8205/728/2/L43

    work page doi:10.1088/2041-8205/728/2/l43 2011

  17. [17]

    Castelli, F., & Kurucz, R. L. 2003, in IAU Symposium, Vol. 210, Modelling of Stellar Atmospheres, ed. N. Piskunov, W. W. Weiss, & D. F. Gray, A20, doi: 10.48550/arXiv.astro-ph/0405087

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/0405087 2003

  18. [18]

    1992, A&A, 253, 173

    Chaboyer, B., & Zahn, J.-P. 1992, A&A, 253, 173

    work page 1992

  19. [19]

    2013, ApJ, 764, 21, doi: 10.1088/0004-637X/764/1/21

    Chieffi, A., & Limongi, M. 2013, ApJ, 764, 21, doi: 10.1088/0004-637X/764/1/21

    work page doi:10.1088/0004-637x/764/1/21 2013

  20. [20]

    2016, ApJ, 823, 102, doi: 10.3847/0004-637X/823/2/102

    Choi, J., Dotter, A., Conroy, C., et al. 2016, ApJ, 823, 102, doi: 10.3847/0004-637X/823/2/102

    work page internal anchor Pith review doi:10.3847/0004-637x/823/2/102 2016

  21. [21]

    Cox, A. N. 1980, ARA&A, 18, 15, doi: 10.1146/annurev.aa.18.090180.000311

    work page doi:10.1146/annurev.aa.18.090180.000311 1980

  22. [22]

    H., Amthor, A

    Cyburt, R. H., Amthor, A. M., Ferguson, R., et al. 2010, ApJS, 189, 240, doi: 10.1088/0067-0049/189/1/240 De Somma, G., Marconi, M., Ripepi, V., et al. 2025, ApJL, 984, L60, doi: 10.3847/2041-8213/adcf92

    work page doi:10.1088/0067-0049/189/1/240 2010

  23. [23]

    Deka, M., Ahlborn, F., Braun, T. A. M., & Weiss, A. 2025, A&A, 699, A351, doi: 10.1051/0004-6361/202554292

    work page doi:10.1051/0004-6361/202554292 2025

  24. [24]

    2016, ApJS, 222, 8, doi: 10.3847/0067-0049/222/1/8

    Dotter, A. 2016, ApJS, 222, 8, doi: 10.3847/0067-0049/222/1/8 Ekstr¨ om, S., Georgy, C., Eggenberger, P., et al. 2012, A&A, 537, A146, doi: 10.1051/0004-6361/201117751

    work page doi:10.3847/0067-0049/222/1/8 2016

  25. [25]

    S., & Sofia, S

    Endal, A. S., & Sofia, S. 1976, ApJ, 210, 184, doi: 10.1086/154817

    work page doi:10.1086/154817 1976

  26. [26]

    2022, MNRAS, 517, 1538, doi: 10.1093/mnras/stac2732

    Espinoza-Arancibia, F., Catelan, M., Hajdu, G., et al. 2022, MNRAS, 517, 1538, doi: 10.1093/mnras/stac2732

    work page doi:10.1093/mnras/stac2732 2022

  27. [27]

    R., Schaefer, G

    Evans, N. R., Schaefer, G. H., Gallenne, A., et al. 2024, ApJ, 971, 190, doi: 10.3847/1538-4357/ad5e7a

    work page doi:10.3847/1538-4357/ad5e7a 2024

  28. [28]

    W., Alexander, D

    Ferguson, J. W., Alexander, D. R., Allard, F., et al. 2005, ApJ, 623, 585, doi: 10.1086/428642

    work page doi:10.1086/428642 2005

  29. [29]

    L., Madore, B

    Freedman, W. L., Madore, B. F., Gibson, B. K., et al. 2001, ApJ, 553, 47, doi: 10.1086/320638

    work page doi:10.1086/320638 2001

  30. [30]

    B., & Abbott, D

    Friend, D. B., & Abbott, D. C. 1986, ApJ, 311, 701, doi: 10.1086/164809

    work page doi:10.1086/164809 1986

  31. [31]

    L., & Jermyn, A

    Fuller, J., Piro, A. L., & Jermyn, A. S. 2019, MNRAS, 485, 3661, doi: 10.1093/mnras/stz514

    work page doi:10.1093/mnras/stz514 2019

  32. [32]

    2017, A&A, 608, A18, doi: 10.1051/0004-6361/201731589

    Gallenne, A., Kervella, P., M´ erand, A., et al. 2017, A&A, 608, A18, doi: 10.1051/0004-6361/201731589

    work page doi:10.1051/0004-6361/201731589 2017

  33. [33]

    R., et al

    Gallenne, A., Kervella, P., Evans, N. R., et al. 2018, ApJ, 867, 121, doi: 10.3847/1538-4357/aae373

    work page doi:10.3847/1538-4357/aae373 2018

  34. [34]

    R., Kervella, P., et al

    Gallenne, A., Evans, N. R., Kervella, P., et al. 2025, A&A, 693, A111, doi: 10.1051/0004-6361/202452346

    work page doi:10.1051/0004-6361/202452346 2025

  35. [35]

    2013, A&A, 553, A24, doi: 10.1051/0004-6361/201220558

    Georgy, C., Ekstr¨ om, S., Granada, A., et al. 2013, A&A, 553, A24, doi: 10.1051/0004-6361/201220558

    work page doi:10.1051/0004-6361/201220558 2013

  36. [36]

    P., Fouqu´ e, P., & G´ omez, M

    Gieren, W. P., Fouqu´ e, P., & G´ omez, M. 1998, ApJ, 496, 17, doi: 10.1086/305374

    work page doi:10.1086/305374 1998

  37. [37]

    P., Moffett, T

    Gieren, W. P., Moffett, T. J., & Barnes, III, T. G. 1999, ApJ, 512, 553, doi: 10.1086/306800

    work page doi:10.1086/306800 1999

  38. [38]

    E., Pols, O

    Glebbeek, E., Gaburov, E., de Mink, S. E., Pols, O. R., & Portegies Zwart, S. F. 2009, A&A, 497, 255, doi: 10.1051/0004-6361/200810425

    work page doi:10.1051/0004-6361/200810425 2009

  39. [39]

    B., et al

    Graczyk, D., Pietrzy´ nski, G., Thompson, I. B., et al. 2020, ApJ, 904, 13, doi: 10.3847/1538-4357/abbb2b

    work page doi:10.3847/1538-4357/abbb2b 2020

  40. [40]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

    work page doi:10.1038/s41586-020-2649-2 2020

  41. [41]

    H., Allard, F., & Baron, E

    Hauschildt, P. H., Allard, F., & Baron, E. 1999a, ApJ, 512, 377, doi: 10.1086/306745

    work page doi:10.1086/306745

  42. [42]

    Alexander, D. R. 1999b, ApJ, 525, 871, doi: 10.1086/307954

    work page doi:10.1086/307954

  43. [43]

    Heger, A., Langer, N., & Woosley, S. E. 2000, ApJ, 528, 368, doi: 10.1086/308158 37

    work page doi:10.1086/308158 2000

  44. [44]

    E., & Spruit, H

    Heger, A., Woosley, S. E., & Spruit, H. C. 2005, ApJ, 626, 350, doi: 10.1086/429868

    work page doi:10.1086/429868 2005

  45. [45]

    S., & Bodenheimer, P

    Henyey, L., Vardya, M. S., & Bodenheimer, P. 1965, ApJ, 142, 841, doi: 10.1086/148357

    work page doi:10.1086/148357 1965

  46. [46]

    The evolution of AGB stars with convective overshoot

    Herwig, F. 2000, A&A, 360, 952, doi: 10.48550/arXiv.astro-ph/0007139

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/0007139 2000

  47. [47]

    R., & McSwain, M

    Huang, W., Gies, D. R., & McSwain, M. V. 2010, ApJ, 722, 605, doi: 10.1088/0004-637X/722/1/605

    work page doi:10.1088/0004-637x/722/1/605 2010

  48. [48]

    A., & Rogers, F

    Iglesias, C. A., & Rogers, F. J. 1991, ApJL, 371, L73, doi: 10.1086/186005 —. 1993, ApJ, 412, 752, doi: 10.1086/172958 —. 1996, ApJ, 464, 943, doi: 10.1086/177381

    work page doi:10.1086/186005 1991

  49. [49]

    Irwin, A. W. 2004, The FreeEOS Code for Calculating the Equation of State for Stellar Interiors. http://freeeos.sourceforge.net/

    work page 2004

  50. [50]

    OGLE-ing the Magellanic System: Three-Dimensional Structure of the Clouds and the Bridge Using Classical Cepheids

    Jacyszyn-Dobrzeniecka, A. M., Skowron, D. M., Mr´ oz, P., et al. 2016, AcA, 66, 149, doi: 10.48550/arXiv.1602.09141

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1602.09141 2016

  51. [51]

    Potekhin, A. Y. 2021, ApJ, 913, 72, doi: 10.3847/1538-4357/abf48e

    work page doi:10.3847/1538-4357/abf48e 2021

  52. [52]

    S., Bauer, E

    Jermyn, A. S., Bauer, E. B., Schwab, J., et al. 2023, ApJS, 265, 15, doi: 10.3847/1538-4365/acae8d Jofr´ e, P., Heiter, U., & Soubiran, C. 2019, ARA&A, 57, 571, doi: 10.1146/annurev-astro-091918-104509

    work page doi:10.3847/1538-4365/acae8d 2023

  53. [53]

    Keller, S. C. 2008, ApJ, 677, 483, doi: 10.1086/529366

    work page doi:10.1086/529366 2008

  54. [54]

    1970, in IAU Colloquium 4: Stellar Rotation, ed

    Kippenhahn, R., & Thomas, H.-C. 1970, in IAU Colloquium 4: Stellar Rotation, ed. A. Slettebak, 20

    work page 1970

  55. [55]

    M., Dunkley, J., et al

    Komatsu, E., Smith, K. M., Dunkley, J., et al. 2011, ApJS, 192, 18, doi: 10.1088/0067-0049/192/2/18

    work page internal anchor Pith review doi:10.1088/0067-0049/192/2/18 2011

  56. [56]

    1986, A&A, 160, 116

    Kuhfuss, R. 1986, A&A, 160, 116

    work page 1986

  57. [57]

    2002, ApJ, 567, 643, doi: 10.1086/338384

    Kunz, R., Fey, M., Jaeger, M., et al. 2002, ApJ, 567, 643, doi: 10.1086/338384

    work page doi:10.1086/338384 2002

  58. [58]

    2012, A&A, 543, A108, doi: 10.1051/0004-6361/201118331

    Lagarde, N., Decressin, T., Charbonnel, C., et al. 2012, A&A, 543, A108, doi: 10.1051/0004-6361/201118331

    work page doi:10.1051/0004-6361/201118331 2012

  59. [59]

    1998, A&A, 329, 551

    Langer, N. 1998, A&A, 329, 551

    work page 1998

  60. [60]

    S., & Pickering, E

    Leavitt, H. S., & Pickering, E. C. 1912, Harvard College Observatory Circular, 173, 1

    work page 1912

  61. [61]

    2009, Physics, Formation and Evolution of Rotating Stars (Springer), doi: 10.1007/978-3-540-76949-1

    Maeder, A. 2009, Physics, Formation and Evolution of Rotating Stars (Springer), doi: 10.1007/978-3-540-76949-1

    work page doi:10.1007/978-3-540-76949-1 2009

  62. [62]

    2000, ARA&A, 38, 143, doi: 10.1146/annurev.astro.38.1.143

    Maeder, A., & Meynet, G. 2000, ARA&A, 38, 143, doi: 10.1146/annurev.astro.38.1.143

    work page doi:10.1146/annurev.astro.38.1.143 2000

  63. [63]

    1998, A&A, 334, 1000

    Maeder, A., & Zahn, J.-P. 1998, A&A, 334, 1000

    work page 1998

  64. [64]

    2025, The impact of rotational mixing in intermediate-age star clusters with extended main-sequence turn-offs and extended red clumps, Zenodo, doi: 10.5281/zenodo.15601753

    Martinelli, L. 2025, The impact of rotational mixing in intermediate-age star clusters with extended main-sequence turn-offs and extended red clumps, Zenodo, doi: 10.5281/zenodo.15601753

    work page doi:10.5281/zenodo.15601753 2025

  65. [65]

    2025, MNRAS, 543, 3628, doi: 10.1093/mnras/staf1587

    Martinelli, L., Miglio, A., Buldgen, G., et al. 2025, MNRAS, 543, 3628, doi: 10.1093/mnras/staf1587

    work page doi:10.1093/mnras/staf1587 2025

  66. [66]

    2013, A&A, 560, A16, doi: 10.1051/0004-6361/201322480

    Martins, F., & Palacios, A. 2013, A&A, 560, A16, doi: 10.1051/0004-6361/201322480

    work page doi:10.1051/0004-6361/201322480 2013

  67. [67]

    E., Lemasle, B., & Grebel, E

    Medina, G. E., Lemasle, B., & Grebel, E. K. 2021, MNRAS, 505, 1342, doi: 10.1093/mnras/stab1267

    work page doi:10.1093/mnras/stab1267 2021

  68. [68]

    1997, A&A, 321, 465

    Meynet, G., & Maeder, A. 1997, A&A, 321, 465

    work page 1997

  69. [69]

    2020, ApJ, 896, 128, doi: 10.3847/1538-4357/ab90fb

    Guinan, E. 2020, ApJ, 896, 128, doi: 10.3847/1538-4357/ab90fb

    work page doi:10.3847/1538-4357/ab90fb 2020

  70. [70]

    R., & Marom, A

    Moskalik, P., Buchler, J. R., & Marom, A. 1992, ApJ, 385, 685, doi: 10.1086/170975

    work page doi:10.1086/170975 1992

  71. [71]

    2024, A&A, 684, A169, doi: 10.1051/0004-6361/202346979

    Nandal, D., Meynet, G., Ekstr¨ om, S., et al. 2024, A&A, 684, A169, doi: 10.1051/0004-6361/202346979

    work page doi:10.1051/0004-6361/202346979 2024

  72. [72]

    2006, A&A, 453, 309, doi: 10.1051/0004-6361:20054333

    Nardetto, N., Mourard, D., Kervella, P., et al. 2006, A&A, 453, 309, doi: 10.1051/0004-6361:20054333

    work page doi:10.1051/0004-6361:20054333 2006

  73. [73]

    R., Cantiello, M., & Langer, N

    Neilson, H. R., Cantiello, M., & Langer, N. 2011, A&A, 529, L9, doi: 10.1051/0004-6361/201116920

    work page doi:10.1051/0004-6361/201116920 2011

  74. [74]

    R., & Langer, N

    Neilson, H. R., & Langer, N. 2012, A&A, 537, A26, doi: 10.1051/0004-6361/201117829

    work page doi:10.1051/0004-6361/201117829 2012

  75. [75]

    2012, ApJL, 760, L18, doi: 10.1088/2041-8205/760/1/L18

    Izzard, R. 2012, ApJL, 760, L18, doi: 10.1088/2041-8205/760/1/L18

    work page doi:10.1088/2041-8205/760/1/l18 2012

  76. [76]

    Nugis, T., & Lamers, H. J. G. L. M. 2000, A&A, 360, 227

    work page 2000

  77. [77]

    S., Sanjayan, S., & Sahoo, S

    Ostrowski, J., Baran, A. S., Sanjayan, S., & Sahoo, S. K. 2021, MNRAS, 503, 4646, doi: 10.1093/mnras/staa3751

    work page doi:10.1093/mnras/staa3751 2021

  78. [78]

    2011, ApJS, 192, 3, doi: 10.1088/0067-0049/192/1/3 20

    Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3, doi: 10.1088/0067-0049/192/1/3

    work page doi:10.1088/0067-0049/192/1/3 2011

  79. [79]

    2013, ApJS, 208, 4, doi: 10.1088/0067-0049/208/1/4

    Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4, doi: 10.1088/0067-0049/208/1/4

    work page internal anchor Pith review doi:10.1088/0067-0049/208/1/4 2013

  80. [80]

    2015, ApJS, 220, 15, doi: 10.1088/0067-0049/220/1/15

    Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS, 220, 15, doi: 10.1088/0067-0049/220/1/15

    work page internal anchor Pith review doi:10.1088/0067-0049/220/1/15 2015

Showing first 80 references.