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The s process in rotating low-mass AGB stars. Nucleosynthesis calculations in models matching asteroseismic constraints

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Rotation matching asteroseismic observations leaves s-process yields unchanged.

desk verdict First rotating AGB s-process models forced to match asteroseismic core rates; yields match non-rotating models, but the artificial viscosity's unknown mixing efficiency is the load-bearing caveat. read the letter →

arxiv 1908.09160 v1 pith:XFVU2ZFT submitted 2019-08-24 astro-ph.SR

J.W. den Hartogh , R. Hirschi , M. Lugaro , C.L. Doherty , U. Battino , F. Herwig , M. Pignatari , P. Eggenberger This is my paper · ORCID
classification astro-ph.SR
keywords sprocessAGBstarsstellarrotationasteroseismologynucleosynthesis13Cpocketlow-massevolution
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 asks whether stellar rotation changes the slow neutron capture process (s process) in low-mass asymptotic giant branch (AGB) stars, which are major producers of heavy elements beyond iron. The authors compute $2\,M_\odot$, $Z=0.01$ models with initial rotation speeds of 0, 125, and 250 km/s, and add an artificial viscosity that slows the core to match rotation rates inferred from asteroseismology. They find that once the core rotates at observed rates, rotationally induced mixing is too weak to perturb the $^{13}\mathrm{C}$ pocket where the s-process neutrons are released, so the s-process yields are indistinguishable from those of non-rotating models. This holds even when the core rotates one order of magnitude faster than the observed upper limit, and it is independent of the initial rotation rate. If correct, rotation does not explain the observed spread in s-process abundances among AGB stars.

What carries the argument

The key device is the split between angular momentum transport and chemical mixing. The artificial viscosity $\nu_{\mathrm{add}}$, a constant calibrated to asteroseismic core rotation rates, is added to the angular momentum diffusion coefficient $D_{\mathrm{am}}$ but not to the chemical mixing coefficient $D_{\mathrm{mix}}$, so the core is slowed while composition is untouched. The diagnostic object is the $^{13}\mathrm{C}$ pocket, a thin layer of carbon-13 formed at the top of the helium intershell after each third dredge-up; during the interpulse period it releases neutrons via $^{13}\mathrm{C}(\alpha,n)^{16}\mathrm{O}$ and drives the s process. The paper shows that in the slowly rotating cores the residual instabilities—mainly the Eddington-Sweet circulation, which scales as $\Omega^2$ and is inhibited by the molecular weight gradient—are too weak to change the pocket, while the secular shear is discontinuous and therefore does not mix composition smoothly. This explains why the s-process yields match the non-rotating case.

What would settle it

The claim fails if a physically motivated angular momentum transport mechanism that also mixes chemical elements is implemented in the same stellar evolution code and produces s-process yields different from non-rotating models; the authors themselves show that adding $\nu_{\mathrm{add}}$ to the chemical mixing coefficient erases the $^{13}\mathrm{C}$ pocket entirely, so the threshold chemical mixing efficiency could be bracketed with a parameter study.

Watch

Extended reading notes

Core claim

The central discovery, stated on the paper's own terms, is that the missing angular momentum transport process required to match asteroseismic observations also suppresses rotationally induced mixing to the point of irrelevance for s-process nucleosynthesis. Using a constant artificial viscosity $\nu_{\mathrm{add}}$ added only to the angular momentum diffusion equation, and calibrated to observed core rotation rates, the authors construct $2\,M_\odot$, $Z=0.01$ AGB models whose cores spin at the observed rates during the main sequence, core helium burning, and the white dwarf phase. In these models the Eddington-Sweet circulation, the only continuously acting rotational mixing process, has a diffusion coefficient in the $^{13}\mathrm{C}$ pocket region that is too small to alter the abundance profiles, and the secular shear instability produces only discontinuous mixing with little effect. The resulting surface enrichment of s-process elements is comparable to the non-rotating model, including in a model rotating an order of magnitude faster than the asteroseismic upper limit. The authors conclude that rotation consistent with asteroseismology has no effect on s-process production, independent of the initial rotation rate.

Load-bearing premise

The conclusion rests on the assumption that the real, still unidentified process that removes angular momentum from stellar cores, here represented by the artificial viscosity, does not also mix chemical elements; if it mixed chemicals at even a fraction of its angular momentum efficiency, the $^{13}\mathrm{C}$ pocket and the s-process yields would change.

Editorial extensions

If this is right

  • Observed run-to-run spreads in s-process abundances among AGB stars of similar metallicity should not be attributed to rotation; other processes such as convective boundary mixing must be responsible.
  • Non-rotating AGB models can be used for heavy-element yield grids in galactic chemical evolution without losing accuracy due to rotation.
  • The initial rotation rate of a star, at least up to 250 km/s, does not determine its s-process outcome once the core spin is slowed to observed values.
  • Even a core rotating one order of magnitude faster than the asteroseismic upper limit still yields s-process enrichments matching non-rotating models, giving a wide safety margin.
  • The missing angular momentum transport mechanism is constrained: it must not mix chemical elements at the same rate as it transports angular momentum, otherwise chemically homogeneous stars would result.

Reading between the lines

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

  • If the result extends to other masses and metallicities, rotating AGB models may be dropped from yield grids entirely, freeing computational resources for multi-dimensional mixing studies.
  • Asteroseismic core rotation rates could be used as a boundary condition to calibrate the chemical mixing side of rotational instabilities: any candidate transport mechanism must reproduce both the observed spins and the observed s-process patterns.
  • The paper's exclusion of the GSF instability rests on arguments from other stellar contexts; if GSF operates in the AGB intershell, the $^{13}\mathrm{C}$ pocket could be affected, although the appendix suggests even including it does not change the yields.
  • A direct observational test would be to compare s-process abundances of asteroseismically characterized post-AGB stars with their core rotation rates; the paper predicts no correlation.
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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 / 5 minor

Summary. The paper investigates whether rotational mixing affects s-process nucleosynthesis in low-mass AGB stars when the stellar models are forced to match asteroseismically measured core rotation rates. The authors construct 2 Msun, Z=0.01 MESA models with initial rotation rates of 0, 125, and 250 km/s, and add an artificial viscosity nu_add (calibrated in Paper I) to the angular momentum transport equation to slow the core. They compute s-process yields with the NuGrid post-processing tool MPPNP. For models with nu_add=10^6 cm^2/s, which match the upper limit of observed core rotation rates during core He burning and the white dwarf phase, the surface enrichment of s-process elements is comparable to that of the non-rotating model. A conservative model rotating an order of magnitude faster than observed ('250 5') also shows comparable s-process production. The authors conclude that once rotation rates are consistent with asteroseismic constraints, rotationally induced mixing has no effect on s-process nucleosynthesis, and that this result is independent of the initial rotation rate.

Significance. If the central claim holds, this is an important and timely result: it connects asteroseismic constraints on internal rotation to nucleosynthesis yields, suggesting that non-rotating AGB models may be adequate for galactic chemical evolution studies, at least for the masses and metallicities considered. The paper is computationally substantial, uses established codes (MESA, MPPNP), and compares against a broad set of observed rotation rates across several evolutionary phases. It also includes a conservative upper-limit model and an appendix exploring the role of additional rotational instabilities. These are genuine strengths. However, the headline conclusion rests on the assumption that the unidentified angular momentum transport process, here represented by nu_add, does not mix chemical elements at levels relevant to 13C-pocket formation. The paper's own tests only rule out equal efficiency for angular momentum and chemical mixing, not partial efficiencies, so the universal phrasing of the conclusion is stronger than the evidence currently supports.

major comments (3)
  1. [Sect. 2.2, Eqs. (5)-(6), and Sect. 4] The decision to add nu_add only to Dam and not to Dmix is the main load-bearing assumption of the paper. The test described in Sect. 4, in which nu_add is also added to Dmix at the same value and produces chemically homogeneous stars, rules out only the case where the missing process mixes chemicals with the same efficiency as it transports angular momentum. It does not constrain intermediate efficiencies. Since the physical nature of the missing process is unknown, a mechanism such as internal gravity waves or a magnetic instability could, in principle, mix chemicals at a fraction of the angular momentum transport rate. The 13C pocket is sensitive to weak diffusive mixing, and even a modest extra diffusion coefficient in the pocket region could change the 13C/14N ratio and the resulting neutron capture path. I therefore request either a parametric study varying the ratio of chemical to angular momentum diffusion (e.g., D_mix = fc * D_rot + epsilon * nu_add with 0 < epsilon < 1) or a clear restriction of the conclusion to models in which the missing process does not mix chemicals.
  2. [Abstract and Sect. 4, bullet list] The statement that the result is 'independent of the initial rotation rate' is not supported by the model grid. The main s-process comparison includes only two initial rotation rates, 125 and 250 km/s, both typical of young B stars. The additional 10 km/s model mentioned in Sect. 2.5 is used only to show that low initial rotation cannot reproduce observed core rotation rates; no s-process yields are shown for it. Two initial rates are insufficient to establish independence over the full relevant range. The claim should be weakened to 'for the initial rotation rates considered here' or supported with models spanning a wider range, including a low-rotation case for which yields are actually computed.
  3. [Sect. 3.1 and Fig. 3] The detailed comparison of 13C-pocket abundance and diffusion profiles is presented for the '250 5' model, which rotates an order of magnitude faster than the asteroseismic upper limit, rather than for the '250 6' model that actually matches the observed rotation rates. While Fig. 5 shows that the surface enrichment of '250 6' overlaps with the non-rotating model, the paper does not show the pocket structure for the asteroseismically matched model. Given that the 13C pocket is the primary neutron source and that the authors emphasize the importance of small differences in the pocket, I ask that the pocket profiles for the '250 6' model (or an explicit statement of why they are not shown) be included to directly support the central conclusion.
minor comments (5)
  1. [Sect. 2, paragraph on mass loss] The text reads 'ad discussed by Wood & Faulkner 1986'; this should be 'as discussed by'.
  2. [Fig. 2] The x-axis label appears as 'log10(g/cm s□2)', which looks like a corrupted rendering; it should presumably be a density or log g label. Please correct the typesetting.
  3. [Sect. 3.1, paragraph on ES circulation] The text states both that the Eddington-Sweet circulation is present with values between 10^1 and 10^2 g^2 s^-1 in the 13C-pocket region and that the molecular weight gradient prevents this mixing process from being active within the pocket. These statements appear contradictory and should be clarified.
  4. [Table 1 caption] The caption begins 'Names of the models are a combination...'; this should be 'Names of the models are combinations...' or 'The model names are a combination...'.
  5. [Sect. 4, paragraph on f parameters] The authors state that the conclusions remain the same when testing the Yoon et al. (2006) and Brott et al. (2011) values of fc and fmu, but no results or figures are shown for this test. A sentence with the resulting yields or a figure reference would make this verifiable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the s-process yields are independent outputs of models calibrated only to asteroseismic rotation data.

full rationale

The paper's central claim is that rotating AGB models whose cores are forced (via an artificial viscosity nu_add) to match asteroseismically measured rotation rates produce s-process yields comparable to non-rotating models. The derivation chain is: (i) nu_add is calibrated to asteroseismic core and surface rotation-rate observations (Fig. 2), an external dataset; (ii) with this nu_add, MESA computes rotation profiles with slower, more solid-body cores; (iii) rotational mixing coefficients DES and DSSI are then computed from those profiles via the standard Heger et al. (2000) prescriptions, with fc and fmu taken from independent calibrations and not from any s-process data; (iv) MPPNP post-processing converts the resulting thermal and diffusion histories into s-process yields. The s-process yields are never used to adjust nu_add, fc, fmu, or any other parameter, so the headline result is an output rather than a fitted quantity. The main self-citation, Paper I, provides the nu_add method, but this paper independently re-anchors nu_add to asteroseismic rotation rates and directly compares to observations, so the self-citation is not load-bearing. The caveat that nu_add is added to Dam (Eq. 5) but not to Dmix (Eq. 6) is an explicit assumption about the physics of the missing angular-momentum process; the paper tests the equal-efficiency extreme and acknowledges that partial-efficiency mixing would remain a concern, but this is an uncertainty in model input, not a circular derivation of the conclusion. Thus no circular step is present.

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

The central claim is a numerical experiment. The key free parameters are the artificial viscosity nu_add, calibrated to asteroseismology, and the inherited rotation-mixing and CBM parameters. No new physical entities are introduced; nu_add is explicitly described as non-physical, so it is listed as a free parameter rather than an invented entity.

free parameters (5)
  • nu_add (additional viscosity) = 10^6 cm^2 s^-1 for models 125 6 and 250 6; 10^5 for model 250 5
    Artificial viscosity added to angular momentum transport only, calibrated so model core rotation matches asteroseismic observations. It has no physical meaning and directly sets the rotation profile during the AGB phase.
  • fc (rotational mixing efficiency) = 1/30
    Scales the contribution of rotationally induced instabilities to chemical mixing in Eq. 6. Value from Heger et al. 2000, originally calibrated to main-sequence nitrogen enrichment, not to s-process data.
  • fmu (molecular weight gradient factor) = 0.05
    Reduces the stabilizing effect of the mean molecular weight gradient in shear and Eddington-Sweet instabilities. Inherited from Heger et al. 2000; the authors test the Yoon/Brott values and report similar conclusions.
  • CBM parameters (D0, D2, f1HP0, f2HP0, z2) = Values from Herwig et al. 1997 and Battino et al. 2016
    Convective boundary mixing prescription that creates the 13C pocket. Calibrated in prior work to gravity-wave and 3D hydrodynamics simulations, not fitted here, but it directly sets the neutron source for the s-process.
  • Initial rotation rates = 125 and 250 km/s at ZAMS
    Chosen to match young B star observations from Huang et al. 2010 and to allow comparison with earlier AGB rotation studies. Not fitted to s-process abundances.
assumptions (5)
  • domain assumption The 13C pocket created by convective boundary mixing is the dominant neutron source for the s-process in these models.
    The exact mixing process that forms the 13C pocket is unknown, as stated in Section 1. The paper adopts the CBM prescription of Battino et al. 2016, and the whole s-process analysis is built around the properties of this pocket.
  • domain assumption The missing angular momentum transport, modeled as nu_add, does not mix chemical elements.
    nu_add appears in Dam (Eq. 5) but not in Dmix (Eq. 6). The authors test adding it to chemical mixing and find homogeneous evolution, which they use as evidence, but this remains an assumption about an unknown physical mechanism.
  • domain assumption The excluded rotational instabilities GSF, DSI, and SH are negligible in these stars.
    Section 2.2.1 excludes GSF based on Hirschi & Maeder 2010 and Caleo et al. 2016, and excludes DSI and SH as not transporting angular momentum. The appendix explores their inclusion, but the implementation is acknowledged to be uncertain.
  • domain assumption Asteroseismic core rotation observations of MS, RGB, core He-burning, and WD stars are representative constraints for AGB progenitors and successors.
    Section 2.5 compares model rotation to observed samples, selecting single stars in the 1.4-3.0 Msun mass range. If the observed rotation rates are biased, the enforced core rotation in the models would be incorrect.
  • standard math The standard MESA diffusion treatment of rotation and mixing (Eqs. 3-7) correctly captures the included physics.
    The implementation follows Heger et al. 2000 and is standard for stellar evolution codes. No new mathematical claim is made.

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Cite this review

Pith. "Pith review of The s process in rotating low-mass AGB stars. Nucleosynthesis calculations in models matching asteroseismic constraints." pith.science (2026). https://pith.science/paper/XFVU2ZFT

@misc{pith2026190809160,
  author       = {Pith},
  title        = {Pith review of: The s process in rotating low-mass AGB stars. Nucleosynthesis calculations in models matching asteroseismic constraints},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XFVU2ZFT}},
  note         = {Machine review of arXiv:1908.09160}
}
abstract

Aims. We investigate the s-process during the AGB phase of stellar models whose cores are enforced to rotate at rates consistent with asteroseismology observations of their progenitors and successors. Methods. We calculated new 2M$_{\odot}$, Z=0.01 models, rotating at 0, 125, and 250 km/s at the start of main sequence. An artificial, additional viscosity was added to enhance the transport of angular momentum in order to reduce the core rotation rates to be in agreement with asteroseismology observations. We compared rotation rates of our models with observed rotation rates during the MS up to the end of core He burning, and the white dwarf phase. Results. We present nucleosynthesis calculations for these rotating AGB models that were enforced to match the asteroseismic constraints on rotation rates of MS, RGB, He-burning, and WD stars. In particular, we calculated one model that matches the upper limit of observed rotation rates of core He-burning stars and we also included a model that rotates one order of magnitude faster than the upper limit of the observations. The s-process production in both of these models is comparable to that of non-rotating models. Conclusions. Slowing down the core rotation rate in stars to match the above mentioned asteroseismic constraints reduces the rotationally induced mixing processes to the point that they have no effect on the s-process nucleosynthesis. This result is independent of the initial rotation rate of the stellar evolution model. However, there are uncertainties remaining in the treatment of rotation in stellar evolution, which need to be reduced in order to confirm our conclusions, including the physical nature of our approach to reduce the core rotation rates of our models, and magnetic processes.

Figures

Figures reproduced from arXiv: 1908.09160 by the authors.

Figure 1
Figure 1. The HRDs of all our non-rotating and rotating models, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Evolution of core (Ωc) and surface rotation (Ωs) rates. Four of the models listed in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Abundance and diffusion profiles within 13C-pocket regions. These regions fall within the same interpulse period as the fifth TDU (from our MPPNP results). The left panels show the abundance profiles of the non-rotating model, and the middle and right panels show the abundance and diffusion profiles of the ‘250 5’ model. The top panels correspond to the maximum extent of the TDU, the middle panels correspond to the … view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Time evolution of Ω. The Ω profile is taken from the inter￾pulse of the ‘250 5’ model that is shown in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Surface enrichment of ‘noR’, ‘250 5’ and ‘250 6’. This [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

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Works this paper leans on

99 extracted references · 48 canonical work pages

  1. [1]

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

    ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

  3. [3]

    1966, in Stellar Evolution, ed.\ R

    Baker, N. 1966, in Stellar Evolution, ed.\ R. F. Stein,& A. G. W. Cameron (Plenum, New York) 333

    1966

  4. [4]

    1988, A&A, 200, 58

    Balluch, M. 1988, A&A, 200, 58

    1988

  5. [5]

    Cox, J. P. 1980, Theory of Stellar Pulsation (Princeton University Press, Princeton) 165

    1980

  6. [6]

    N.,& Stewart, J

    Cox, A. N.,& Stewart, J. N. 1969, Academia Nauk, Scientific Information 15, 1

    1969

  7. [7]

    1980, Prog

    Mizuno H. 1980, Prog. Theor. Phys., 64, 544

    1980

  8. [8]

    Tscharnuter W. M. 1987, A&A, 188, 55

    1987

Show all 99 references
  1. [9]

    1992, in ASP Conf

    Terlevich, R. 1992, in ASP Conf. Ser. 31, Relationships between Active Galactic Nuclei and Starburst Galaxies, ed. A. V. Filippenko, 13

    1992

  2. [10]

    Yorke, H. W. 1980a, A&A, 86, 286

  3. [11]

    F., Tytler, D

    Zheng, W., Davidsen, A. F., Tytler, D. & Kriss, G. A. 1997, preprint

    1997

  4. [12]

    2002, , 579, 817

    Abia , C., Dom \' nguez , I., Gallino , R., et al. 2002, , 579, 817

    2002

  5. [13]

    Aerts, C., Mathis, S., & Rogers, T. M. 2019, , 57, null

    2019

  6. [14]

    2018, , 237, 15

    Aerts , C., Molenberghs , G., Michielsen , M., et al. 2018, , 237, 15

    2018

  7. [15]

    V., & Tkachenko, A

    Aerts, C., Reeth, T. V., & Tkachenko, A. 2017, , 847, L7

    2017

  8. [16]

    2016, , 827, 30

    Battino, U., Pignatari, M., Ritter, C., et al. 2016, , 827, 30

    2016

  9. [17]

    2019, arXiv e-prints, arXiv:1906.01952

    Battino , U., Tattersall , A., Lederer-Woods , C., et al. 2019, arXiv e-prints, arXiv:1906.01952

    2019 arXiv

  10. [18]

    E., Hirschi , R., Pignatari , M., et al

    Bennett , M. E., Hirschi , R., Pignatari , M., et al. 2012, , 420, 3047

    2012

  11. [19]

    2017, , 835, 97

    Bisterzo, S., Travaglio, C., Wiescher, M., Käppeler, F., & Gallino, R. 2017, , 835, 97

    2017

  12. [20]

    1995, , 297, 727

    Bloecker , T. 1995, , 297, 727

    1995

  13. [21]

    J., Koch , D., Basri , G., et al

    Borucki , W. J., Koch , D., Basri , G., et al. 2010, Science, 327, 977

    2010

  14. [22]

    E., Cantiello , M., et al

    Brott , I., de Mink , S. E., Cantiello , M., et al. 2011, , 530, A115

    2011

  15. [23]

    F., Doherty , C

    Buntain , J. F., Doherty , C. L., Lugaro , M., et al. 2017, , 471, 824

    2017

  16. [24]

    M., Burbidge, G

    Burbidge, E. M., Burbidge, G. R., Fowler, W. A., & Hoyle, F. 1957, Rev. Mod. Phys., 29, 547

    1957

  17. [25]

    A., & Tognelli , E

    Caleo , A., Balbus , S. A., & Tognelli , E. 2016, , 460, 338

    2016

  18. [26]

    2014, , 788, 93

    Cantiello , M., Mankovich , C., Bildsten , L., Christensen-Dalsgaard , J., & Paxton , B. 2014, , 788, 93

    2014

  19. [27]

    2017, , 605, A111

    Ceillier , T., Tayar , J., Mathur , S., et al. 2017, , 605, A111

    2017

  20. [28]

    Chaboyer , B., Demarque , P., & Pinsonneault , M. H. 1995, , 441, 865

    1995

  21. [29]

    & Zahn , J.-P

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

    1992

  22. [30]

    B., Pereira , C

    de Castro , D. B., Pereira , C. B., Roig , F., et al. 2016, , 459, 4299

    2016

  23. [31]

    2015, A&A, 580

    Deheuvels, S., Ballot, J., Beck, P., & Mosser, B. 2015, A&A, 580

    2015

  24. [32]

    J., et al

    Deheuvels, S., Do g an, G., Goupil, M. J., et al. 2014, , 564, A27

    2014

  25. [33]

    A., Chaplin, W

    Deheuvels, S., Garc \' a, R. A., Chaplin, W. J., et al. 2012, , 756, 19

    2012

  26. [34]

    W., Eggenberger , P., & Hirschi , R

    den Hartogh , J. W., Eggenberger , P., & Hirschi , R. 2019, , 622, A187

    2019

  27. [35]

    A., Pinsonneault, M., Terndrup, D

    Denissenkov, P. A., Pinsonneault, M., Terndrup, D. M., & Newsham, G. 2010, ApJ, 716, 1269

    2010

  28. [36]

    Denissenkov , P. A. & Tout , C. A. 2003, , 340, 722

    2003

  29. [37]

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

    1925

  30. [38]

    Eggenberger , P., Buldgen , G., & Salmon , S. J. A. J. 2019, , 626, L1

    2019

  31. [39]

    2019, , 621, A66

    Eggenberger, P., Deheuvels, S., Miglio, A., et al. 2019, , 621, A66

    2019

  32. [40]

    2017, , 599, A18

    Eggenberger, P., Lagarde, N., Miglio, A., et al. 2017, , 599, A18

    2017

  33. [41]

    2005, , 440, L9

    Eggenberger , P., Maeder , A., & Meynet , G. 2005, , 440, L9

    2005

  34. [42]

    2012, , 544, L4

    Eggenberger, P., Montalb \'a n, J., & Miglio, A. 2012, , 544, L4

    2012

  35. [43]

    Endal , A. S. & Sofia , S. 1978, , 220, 279

    1978

  36. [44]

    1968, , 68, 317

    Fricke , K. 1968, , 68, 317

    1968

  37. [45]

    L., & Jermyn , A

    Fuller , J., Piro , A. L., & Jermyn , A. S. 2019, , 485, 3661

    2019

  38. [46]

    1998, , 497, 388

    Gallino , R., Arlandini , C., Busso , M., et al. 1998, , 497, 388

    1998

  39. [47]

    & Schubert , G

    Goldreich , P. & Schubert , G. 1967, , 150, 571

    1967

  40. [48]

    & Siess, L

    Goriely, S. & Siess, L. 2018, , 609, A29

    2018

  41. [49]

    & Noels , A

    Grevesse , N. & Noels , A. 1993, in Perfectionnement de l'Association Vaudoise des Chercheurs en Physique, ed. B. Hauck , S. Paltani , & D. Raboud , 205--257

    1993

  42. [50]

    Heger , A., Langer , N., & Woosley , S. E. 2000, , 528, 368

    2000

  43. [51]

    J., Gänsicke, B

    Hermes, J. J., Gänsicke, B. T., Kawaler, S. D., et al. 2017, The Astrophysical Journal Supplement Series, 232, 23

    2017

  44. [52]

    2000, , 360, 952

    Herwig , F. 2000, , 360, 952

    2000

  45. [53]

    2001, Astrophysics and Space Science, 275, 15

    Herwig, F. 2001, Astrophysics and Space Science, 275, 15

    2001

  46. [54]

    2005, , 43, 435

    Herwig , F. 2005, , 43, 435

    2005

  47. [55]

    1997, , 324, L81

    Herwig , F., Bloecker , T., Schoenberner , D., & El Eid , M. 1997, , 324, L81

    1997

  48. [56]

    2007, in Astronomical Society of the Pacific Conference Series, Vol

    Herwig , F., Freytag , B., Fuchs , T., et al. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 378, Why Galaxies Care About AGB Stars: Their Importance as Actors and Probes, ed. F. Kerschbaum , C. Charbonnel , & R. F. Wing , 43

    2007

  49. [57]

    2003, , 593, 1056

    Herwig , F., Langer , N., & Lugaro , M. 2003, , 593, 1056

    2003

  50. [58]

    & Maeder , A

    Hirschi , R. & Maeder , A. 2010, , 519, A16

    2010

  51. [59]

    & Iben , Icko, J

    Hollowell , D. & Iben , Icko, J. 1988, , 333, L25

    1988

  52. [60]

    R., & McSwain , M

    Huang , W., Gies , D. R., & McSwain , M. V. 2010, , 722, 605

    2010

  53. [61]

    & Renzini , A

    Iben , I., J. & Renzini , A. 1982, , 263, L23

    1982

  54. [62]

    James , H. A. & Kahn , F. D. 1970, , 5, 232

    1970

  55. [63]

    James , R. A. & Kahn , F. D. 1971, , 12, 332

    1971

  56. [64]

    2011, Rev

    K\"appeler, F., Gallino, R., Bisterzo, S., & Aoki, W. 2011, Rev. Mod. Phys., 83, 157

    2011

  57. [65]

    Karakas , A. I. & Lattanzio , J. C. 2014, , 31, e030

    2014

  58. [66]

    Kawaler , S. D. 2015, in Astronomical Society of the Pacific Conference Series, Vol. 493, 19th European Workshop on White Dwarfs, ed. P. Dufour , P. Bergeron , & G. Fontaine , 65

    2015

  59. [67]

    1974, in IAU Symposium, Vol

    Kippenhahn , R. 1974, in IAU Symposium, Vol. 66, Late Stages of Stellar Evolution, ed. R. J. Tayler & J. E. Hesser , 20

    1974

  60. [68]

    1999, , 346, L37

    Langer, N., Heger, A., Wellstein, S., & Herwig, F. 1999, , 346, L37

    1999

  61. [69]

    Lau, H. H. B., Gil-Pons, P., Doherty, C., & Lattanzio, J. 2012, , 542, A1

    2012

  62. [70]

    1987, , 178, 159

    Maeder , A. 1987, , 178, 159

    1987

  63. [71]

    & Meynet, G

    Maeder, A. & Meynet, G. 2000, , 38, 143

    2000

  64. [72]

    & Meynet, G

    Maeder, A. & Meynet, G. 2012, Rev. Mod. Phys., 84, 25

    2012

  65. [73]

    P., Goupil, M

    Marques, J. P., Goupil, M. J., Lebreton, Y., et al. 2013, , 549, A74

    2013

  66. [74]

    J., Belkacem , K., et al

    Mosser , B., Goupil , M. J., Belkacem , K., et al. 2012, , 548, A10

    2012

  67. [75]

    Nucci , M. C. & Busso , M. 2014, , 787, 141

    2014

  68. [76]

    2011, , 192, 3

    Paxton , B., Bildsten , L., Dotter , A., et al. 2011, , 192, 3

    2011

  69. [77]

    2013, , 208, 4

    Paxton , B., Cantiello , M., Arras , P., et al. 2013, , 208, 4

    2013

  70. [78]

    2013, , 774, 98

    Piersanti , L., Cristallo , S., & Straniero , O. 2013, , 774, 98

    2013

  71. [79]

    2016, , 225, 24

    Pignatari , M., Herwig , F., Hirschi , R., et al. 2016, , 225, 24

    2016

  72. [80]

    H., Kawaler , S

    Pinsonneault , M. H., Kawaler , S. D., Sofia , S., & Demarque , P. 1989, , 338, 424

    1989

  73. [81]

    2018, , 476, 3432

    Prantzos , N., Abia , C., Limongi , M., Chieffi , A., & Cristallo , S. 2018, , 476, 3432

    2018

  74. [82]

    2004, , 415, 1089

    Siess , L., Goriely , S., & Langer , N. 2004, , 415, 1089

    2004

  75. [83]

    2016, , 589, A23

    Spada , F., Gellert , M., Arlt , R., & Deheuvels , S. 2016, , 589, A23

    2016

  76. [84]

    1995, , 440, L85

    Straniero , O., Gallino , R., Busso , M., et al. 1995, , 440, L85

    1995

  77. [85]

    2006, Nuclear Physics A, 777, 311

    Straniero , O., Gallino , R., & Cristallo , S. 2006, Nuclear Physics A, 777, 311

    2006

  78. [86]

    Suijs , M. P. L., Langer , N., Poelarends , A.-J., et al. 2008, , 481, L87

    2008

  79. [87]

    Sweigart, A. V. 1999, in IAU Symposium, Vol. 190, New Views of the Magellanic Clouds, ed. Y.-H. Chu , N. Suntzeff , J. Hesser , & D. Bohlender , 370

    1999

  80. [88]

    & Pinsonneault , M

    Tayar , J. & Pinsonneault , M. H. 2013, , 775, L1

    2013

  81. [89]

    & Pinsonneault , M

    Tayar , J. & Pinsonneault , M. H. 2018, , 868, 150

    2018

  82. [90]

    2004, , 601, 864

    Travaglio , C., Gallino , R., Arnone , E., et al. 2004, , 601, 864

    2004

  83. [91]

    1924, , 84, 665

    von Zeipel, H. 1924, , 84, 665

    1924

  84. [92]

    2016, , 93, 045803

    Wallner , A., Bichler , M., Buczak , K., et al. 2016, , 93, 045803

    2016

  85. [93]

    1946, Astrophysica Norvegica, 4, 1

    Wasiutynski , J. 1946, Astrophysica Norvegica, 4, 1

    1946

  86. [94]

    Wood, P. R. & Faulkner, D. J. 1986, , 307, 659

    1986

  87. [95]

    C., Langer , N., & Norman , C

    Yoon , S. C., Langer , N., & Norman , C. 2006, , 460, 199

    2006

  88. [96]

    1974, in IAU Symposium, Vol

    Zahn , J.-P. 1974, in IAU Symposium, Vol. 59, Stellar Instability and Evolution, ed. P. Ledoux , A. Noels , & A. W. Rodgers , 185--194

    1974

  89. [97]

    @esa (Ref

    \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command natbib from the document \@ifclassloaded aguplus natbib The aguplus class already includes natbib codin...

  90. [98]

    @stdbsttrue NAT@ctr \@lbibitem[ NAT@ctr ] \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 [ @natanchorstart #2\@extra@b@citeb \@biblabel @num @natanchorend] @ifc...

  91. [99]

    n>5 X=pf, U x6P YEs > 88Y ZhL !|ӷ ! SE:udg:@:8 ( ); t iױE 't p,!W,@G܏@2 !Zx3^ FE Ջ #Ǒ) # dC)|AW# GU#d ն

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    2001 arXiv

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