pith. machine review for the scientific record. sign in

arxiv: 1301.0319 · v2 · submitted 2013-01-02 · 🌌 astro-ph.SR · astro-ph.IM

Recognition: 1 theorem link

Modules for Experiments in Stellar Astrophysics (MESA): Giant Planets, Oscillations, Rotation, and Massive Stars

Bill Paxton , Matteo Cantiello , Phil Arras , Lars Bildsten , Edward F. Brown , Aaron Dotter , Christopher Mankovich , M. H. Montgomery , Dennis Stello , F. X. Timmes , Richard Townsend

Authors on Pith no claims yet

Pith reviewed 2026-05-10 21:36 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.IM
keywords stellar evolutionMESAmassive starssupernova progenitorsasteroseismologyrotating starsgiant planetsLedoux criterion
0
0 comments X

The pith

MESA now models the full evolution of massive stars to core collapse via a new radiation-dominated envelope treatment.

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

The paper updates the open-source MESA stellar evolution code with several new capabilities. It lowers the mass limit for giant planet models, fully couples an adiabatic pulsation code for asteroseismology, adds diffusion of angular momentum and chemicals for rotating stars, and improves the numerical solver for multi-core performance. The central advance is a new handling of radiation-dominated envelopes that lets massive-star models run continuously from the main sequence through core collapse without interruption. This change directly supports creation of updated grids for supernova, long gamma-ray burst, and pair-instability supernova progenitors. Updates to opacities, equations of state, nuclear rates, and boundary conditions are included along with a software development kit for reproducible builds.

Core claim

The authors introduce a new treatment of radiation-dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse. Combined with a numerical recasting of the Ledoux criterion for multi-species mixing, this change enables generation of new sets of supernovae, long gamma-ray burst, and pair-instability progenitor models while also extending the code to lower-mass giant planets and rotating stars.

What carries the argument

The new treatment of radiation-dominated envelopes, which recasts the coupled stellar structure and composition equations to prevent numerical breakdown in high-radiation zones and thereby permits continuous evolution to core collapse.

If this is right

  • New grids of supernova and pair-instability supernova progenitor models can now be produced without manual intervention at the envelope stage.
  • Long gamma-ray burst progenitor calculations become feasible for the first time within the same code framework.
  • Rotating-star models with consistent angular-momentum and chemical diffusion can be compared directly to earlier non-diffusive calculations.
  • Asteroseismic frequencies for 3-8 solar-mass stars can be computed self-consistently from the same evolutionary sequences.
  • Performance scaling on multi-core machines improves, allowing larger parameter surveys of planet and star models.

Where Pith is reading between the lines

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

  • The uninterrupted massive-star tracks could be used to map how envelope stripping affects the final black-hole mass distribution.
  • Coupling the new pulsation module to the rotating models would allow tests of how differential rotation alters mode frequencies observable by Kepler.
  • Extending the low-mass planet module to include the new envelope treatment might permit consistent modeling of highly irradiated hot Jupiters.
  • The performance gains suggest the code could now run statistical ensembles of massive-star models to quantify uncertainties in core-collapse outcomes.

Load-bearing premise

The numerical recasting of the Ledoux criterion and the envelope treatment accurately capture the underlying physics of mixing and structure without introducing significant artifacts when solving the full set of stellar equations.

What would settle it

Comparison of the new massive-star tracks against observed supernova progenitor masses or core-collapse timing inferred from light curves; if the models still halt or produce unphysical envelope masses, the treatment fails.

read the original abstract

We substantially update the capabilities of the open source software package Modules for Experiments in Stellar Astrophysics (MESA), and its one-dimensional stellar evolution module, MESA Star. Improvements in MESA Star's ability to model the evolution of giant planets now extends its applicability down to masses as low as one-tenth that of Jupiter. The dramatic improvement in asteroseismology enabled by the space-based Kepler and CoRoT missions motivates our full coupling of the ADIPLS adiabatic pulsation code with MESA Star. This also motivates a numerical recasting of the Ledoux criterion that is more easily implemented when many nuclei are present at non-negligible abundances. This impacts the way in which MESA Star calculates semi-convective and thermohaline mixing. We exhibit the evolution of 3-8 Msun stars through the end of core He burning, the onset of He thermal pulses, and arrival on the white dwarf cooling sequence. We implement diffusion of angular momentum and chemical abundances that enable calculations of rotating-star models, which we compare thoroughly with earlier work. We introduce a new treatment of radiation-dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse. This enables the generation of new sets of supernovae, long gamma-ray burst, and pair-instability progenitor models. We substantially modify the way in which MESA Star solves the fully coupled stellar structure and composition equations, and we show how this has improved MESA's performance scaling on multi-core processors. Updates to the modules for equation of state, opacity, nuclear reaction rates, and atmospheric boundary conditions are also provided. We describe the MESA Software Development Kit (SDK) that packages all the required components needed to form a unified and maintained build environment for MESA. [Abridged]

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 / 3 minor

Summary. The paper presents substantial updates to the open-source MESA stellar evolution code and its MESA Star module. Key advances include extending giant-planet modeling to 0.1 Jupiter masses, full coupling to the ADIPLS pulsation code, a numerical recasting of the Ledoux criterion for multi-species mixing, diffusion of angular momentum and abundances for rotating stars with comparisons to prior literature, a new treatment of radiation-dominated envelopes that permits uninterrupted evolution of massive stars to core collapse (enabling new supernova, GRB, and pair-instability progenitor sets), solver modifications for improved multi-core scaling, and updates to EOS, opacities, nuclear rates, boundary conditions, plus the MESA SDK for reproducible builds.

Significance. If the new envelope treatment and Ledoux recasting function as described without introducing artifacts, the work is significant because it directly enables previously inaccessible progenitor models for core-collapse events and rotating massive stars. The open-source release, thorough comparisons for rotating models, and provision of the SDK for a unified build environment are explicit strengths that promote reproducibility and community use. These contributions advance the field by lowering barriers to complex stellar modeling.

major comments (2)
  1. [New treatment of radiation-dominated envelopes] The section describing the new treatment of radiation-dominated envelopes: the central claim that this modification permits uninterrupted evolution to core collapse (and thus new progenitor sets) is load-bearing, yet the manuscript provides no quantitative validation such as convergence tests, stability metrics through the radiation-dominated phase, or direct comparisons of final core properties against codes that previously failed. This leaves open whether the coupled structure-composition solver remains accurate.
  2. [Recasting of the Ledoux criterion] The section on the numerical recasting of the Ledoux criterion: while motivated by the presence of many nuclei, the explicit modified form of the criterion (presumably given as an equation) is not shown to reduce exactly to the standard Ledoux limit or to preserve the correct semi-convective/thermohaline behavior; without this demonstration the impact on mixing calculations for the exhibited 3-8 Msun tracks cannot be fully assessed.
minor comments (3)
  1. [Abstract] The abstract lists many updates but does not indicate what specific output (e.g., HR-diagram tracks or abundance profiles) is shown for the 3-8 Msun models; a single clarifying sentence would improve readability.
  2. [Rotating-star models] The rotating-star comparisons are described as 'thorough,' yet no table or figure quantifies differences in key observables (surface velocities, core rotation, or surface abundances) relative to the cited earlier work; adding such a summary would strengthen the claim.
  3. [Solver modifications] The solver scaling improvements are stated without accompanying performance data (e.g., wall-clock time vs. core count); a brief table or plot would make the multi-core benefit concrete.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive overall assessment and for the constructive major comments, which help strengthen the presentation of the new capabilities. We address each point below and will incorporate revisions in the next version of the manuscript.

read point-by-point responses
  1. Referee: [New treatment of radiation-dominated envelopes] The section describing the new treatment of radiation-dominated envelopes: the central claim that this modification permits uninterrupted evolution to core collapse (and thus new progenitor sets) is load-bearing, yet the manuscript provides no quantitative validation such as convergence tests, stability metrics through the radiation-dominated phase, or direct comparisons of final core properties against codes that previously failed. This leaves open whether the coupled structure-composition solver remains accurate.

    Authors: We agree that additional quantitative validation would strengthen the manuscript for this central new feature. In the revised version we will add a dedicated subsection presenting convergence tests with respect to spatial and temporal resolution during the radiation-dominated phase, including stability metrics for the coupled structure-composition solver. We will also include direct comparisons of final core properties (central density, temperature, and composition at the onset of collapse) against earlier MESA models that terminated prematurely under the previous envelope treatment. These additions will confirm that the solver remains accurate and does not introduce artifacts. revision: yes

  2. Referee: [Recasting of the Ledoux criterion] The section on the numerical recasting of the Ledoux criterion: while motivated by the presence of many nuclei, the explicit modified form of the criterion (presumably given as an equation) is not shown to reduce exactly to the standard Ledoux limit or to preserve the correct semi-convective/thermohaline behavior; without this demonstration the impact on mixing calculations for the exhibited 3-8 Msun tracks cannot be fully assessed.

    Authors: We acknowledge that an explicit demonstration of the limiting behavior is needed. The revised manuscript will include a new subsection (or short appendix) showing analytically that the numerical form reduces exactly to the classical Ledoux criterion when only a single composition variable is present or when composition gradients are negligible. We will also add test calculations confirming that the semi-convective and thermohaline mixing rates are unchanged in their standard regimes, with direct side-by-side comparisons of the resulting mixing profiles in the 3-8 solar-mass tracks. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper is a software methods description of numerical updates to the MESA stellar evolution code, including new implementations for radiation-dominated envelopes, angular momentum diffusion, and solver modifications. Central claims concern the practical effects of these code changes (e.g., uninterrupted evolution to core collapse) and are supported by direct comparisons to earlier independent literature rather than by any internal derivation chain. No equations, fitted parameters, or self-citations are presented as load-bearing predictions that reduce to the paper's own inputs by construction; the work is self-contained against external benchmarks and prior results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the correctness of numerical implementations of standard stellar structure equations and physical models drawn from prior literature, with no new free parameters, ad hoc axioms, or invented entities introduced in the described updates.

axioms (1)
  • standard math Standard equations of stellar structure, energy transport, and nuclear burning
    The code solves these with updated numerical methods and boundary conditions.

pith-pipeline@v0.9.0 · 5673 in / 1319 out tokens · 59961 ms · 2026-05-10T21:36:37.286352+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 26 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The Tale of a Hungry Subgiant and Its Brown Dwarf: Interior Radiative Damping Dominates the Tidal Evolution of TOI-5882

    astro-ph.SR 2026-05 unverdicted novelty 7.0

    Radiative damping of internal gravity waves dominates tidal evolution in TOI-5882, shortening the brown dwarf's engulfment timescale by a factor of 2-6 relative to classical models.

  2. Type Ib Supernovae are bluer than Type Ic Supernovae

    astro-ph.HE 2026-05 unverdicted novelty 7.0

    Type Ib supernovae are systematically bluer than Type Ic supernovae in optical colors, likely due to helium-rich versus helium-poor progenitors.

  3. Hyperaccreting Neutron Stars inside Massive Envelopes: The Implausibility of Thorne-\.Zytkow Objects

    astro-ph.HE 2026-04 unverdicted novelty 7.0

    Hypercritical accretion onto neutron stars embedded in massive envelopes leads to rapid collapse into black holes rather than stable Thorne-Zytkow objects.

  4. White dwarf + M dwarf Detached Binaries in Long Period Radio Transients: Observed Binary Parameters, Evolution, and Population Constraints

    astro-ph.SR 2026-04 unverdicted novelty 7.0

    Two long period radio transients are detached white dwarf-M dwarf binaries with matching periods, massive cool crystallized white dwarfs, low inclinations, and an estimated population of 100-2000 such systems within 2 kpc.

  5. Irregularly Sampled Time Series Interpolation for Binary Evolution Simulations Using Dynamic Time Warping

    astro-ph.SR 2026-04 unverdicted novelty 7.0

    Dynamic Time Warping with a shared warping path across parameters aligns binary stellar tracks for accurate interpolation while preserving physical relationships such as the Stefan-Boltzmann law.

  6. The Black Hole Mass Gap as a New Probe of Millicharged Particles

    hep-ph 2026-04 unverdicted novelty 7.0

    Millicharged particles weaken pulsational pair-instability in massive stars, shifting the lower edge of the black hole mass gap upward and turning gravitational wave observations into a probe for particles with masses...

  7. The Distribution of Blue Straggler Stars in the Color-Magnitude Diagrams of Old Open Clusters

    astro-ph.SR 2026-05 unverdicted novelty 6.0

    Blue straggler stars in old open clusters predominantly appear near the terminal-age main sequence because mass transfer from asymptotic giant branch donors enriches their cores with helium.

  8. Double Neutron Star Delay Times Across Cosmic Metallicities: The Role of Helium Star Progenitors

    astro-ph.SR 2026-05 unverdicted novelty 6.0

    Simulations show double neutron star mergers peak 80-250 million years after star formation across metallicities, with 15% quick mergers and over 20% delayed over a billion years.

  9. Revisiting Turner Window Axions: The Untapped Potential of NaI Dark Matter Detectors

    hep-ph 2026-04 unverdicted novelty 6.0

    Revised supernova opacity modeling reopens the Turner window for hadronically coupled axions, enabling resonant absorption searches in NaI detectors for couplings |g_app| between 10^{-6.5} and 10^{-2}.

  10. Hot blue progenitors of stellar-mass black holes

    astro-ph.SR 2026-04 unverdicted novelty 6.0

    Black hole progenitors are predominantly hot and blue at pre-collapse, often Wolf-Rayet stars luminous in ultraviolet, with only a minority as red supergiants, and a direct-collapse rate of about 0.4 per century for a...

  11. Spectroscopic Disentangling Revealed the Tertiary Component in the Multiple System EM Boo

    astro-ph.SR 2026-05 unverdicted novelty 5.0

    Tertiary in EM Boo is A-F type with Teff=7000K; system distance ~300 pc indicates Gaia DR3 underestimates true distance due to multiplicity.

  12. A Theoretical Study of the Structure and Elemental Abundances of HD 20794

    astro-ph.SR 2026-04 unverdicted novelty 5.0

    MESA grid models find HD 20794 is a 0.80 solar-mass star aged ~9 Gyr whose observed abundances match core-collapse supernova enrichment and are preserved over Gyr timescales.

  13. The Effect of Mass Loss and Convective Overshooting on the Pre-Collapse Structure, Composition, and Neutrino Emission of Red Supergiants

    astro-ph.SR 2026-04 unverdicted novelty 5.0

    Varying mass loss and overshooting in RSG models shows core contraction and heating interrupted by silicon burning, shifting pre-SN neutrino flux to higher energies and beta-process dominance hours before collapse.

  14. The First Infrared Portrait of A Solar-Like Host Star with Debris Disk: Pioneering High-Resolution H- and K-Band Spectroscopy of HD115617 with Comparative Optical Spectrum Analysis

    astro-ph.SR 2026-04 unverdicted novelty 5.0

    The first NIR high-resolution spectroscopy of solar analog HD115617 shows a 250 K temperature discrepancy with optical data but confirms solar composition, main-sequence status, and no chemical signature of planetary ...

  15. The T16 Planet Hunt: 10,000 New Planet Candidates from TESS Cycle 1 and the Confirmation of a Hot Jupiter Around TIC 183374187

    astro-ph.EP 2026-04 conditional novelty 5.0

    A transit search on TESS Cycle 1 full-frame images produced 10,091 new planet candidates down to T=16 mag, more than doubling the known TESS total, with one hot Jupiter confirmed by radial velocity.

  16. Sensitivity of Dry Lava Planet Atmospheric Emission Spectra to Changes in Lava Compositions

    astro-ph.EP 2026-04 unverdicted novelty 5.0

    Simulations indicate that order-of-magnitude changes in TiO2 and SiO2 abundances in lava melts produce distinguishable TiO, SiO, and SiO2 features in dry lava planet emission spectra, potentially observable with 12 JW...

  17. Impacts of Multidimensional Progenitor Perturbations on Core-Collapse Supernova Explosions

    astro-ph.SR 2026-04 unverdicted novelty 5.0

    2D core-collapse supernova simulations of 15 solar-mass progenitors with varied multi-D initial structures show similar explosion dynamics, with no detectable impact from progenitor turbulence due to saturation by pos...

  18. Adiabatic Mass Loss In Binary Stars. VI. Massive Helium Binary Stars

    astro-ph.SR 2026-04 unverdicted novelty 5.0

    Adiabatic mass-loss models for massive helium stars give critical mass ratios 0.7-3.0 on the main sequence and 1.5-27 on the Hertzsprung gap, lowered by winds and adjusted by isotropic re-emission.

  19. Deep Adaptive Optics Imaging Rules Out a Helium Star Companion to PSR J1928+1815

    astro-ph.SR 2026-04 accept novelty 5.0

    Deep Keck/NIRC2 adaptive optics imaging rules out a helium star companion to PSR J1928+1815, supporting a massive white dwarf with possible wind-driven eclipses.

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

    astro-ph.SR 2026-05 unverdicted novelty 4.0

    Rotation produces only modest changes to blue loop luminosity and extent in MESA Cepheid models and cannot fix the mass discrepancy without substantial main-sequence overshooting.

  21. Analysis of DQZ White Dwarf Evolution through Procyon

    astro-ph.SR 2026-05 unverdicted novelty 4.0

    MESA grid models of Procyon A and B give a system age of 2.23 Gyr, white dwarf cooling age of 1.20 Gyr, and map the progenitor to the 1.9-2.6 solar mass range with higher core overshoot than standard.

  22. On the origin of variability in $\alpha$ Cygni variable $\epsilon$ Ori (HD 37128) using TESS observations and modelling

    astro-ph.SR 2026-05 conditional novelty 4.0

    Linear stability analysis and non-linear hydrodynamical simulations link the stochastic low-frequency variability of ε Ori to strange-mode instabilities that excite finite-amplitude pulsations.

  23. Modeling of the magnetic stellar wind braking of the ssrAp 33 Lib (HD137949)

    astro-ph.SR 2026-04 unverdicted novelty 4.0

    Magnetic wind braking can slow ssrAp stars like 33 Lib to rotation periods of 80 years or more according to MESA evolution models that include magnetic field and wind changes.

  24. Probing Red Giant Interiors with G-Dominated Mixed Modes I: The Cases of KIC 9145955, KIC 9970396, KIC 9882316 and KIC 11968334

    astro-ph.SR 2026-04 unverdicted novelty 4.0

    Asteroseismic fits to g-dominated mixed modes in four red giants suggest convective overshooting rises with mass and yield a core rotation rate of 0.7409 μHz for KIC 11968334.

  25. A Path to Constraints on Common Envelope Ejection in Massive Binaries: Full Evolutionary Reconstruction of Three Black Hole X-ray Binaries

    astro-ph.SR 2026-04 unverdicted novelty 4.0

    Reconstruction of GRO J1655-40, SAX J1819.3-2525 and 4U 1543-47 requires CE efficiencies α_0.5U ≳6.7, α_U ≳4.2, α_H ≳1.7 with no solutions below unity, implying need for additional energy or formalism changes plus nat...

  26. Binary Star Evolution Modules in REBOUNDx

    astro-ph.SR 2026-04 unverdicted novelty 4.0

    REBOUNDx now includes interoperable modules implementing standard binary evolution physics including RLOF, CE drag, winds, magnetic braking, and post-Newtonian corrections.

Reference graph

Works this paper leans on

197 extracted references · 197 canonical work pages · cited by 26 Pith papers

  1. [1]

    2011, A&A, 526, A63

    Alibert, Y ., Mordasini, C., & Benz, W. 2011, A&A, 526, A63

  2. [2]

    H., Alexander, D

    Allard, F., Hauschildt, P. H., Alexander, D. R., Tamanai, A., & Schweitzer, A. 2001, ApJ, 556, 357

  3. [3]

    G., Serenelli, A

    Althaus, L. G., Serenelli, A. M., C´orsico, A. H., & Montgomery, M. H. 2003, A&A, 404, 593

  4. [4]

    1999, Nuclear Physics A, 656, 3

    Angulo, C., et al. 1999, Nuclear Physics A, 656, 3

  5. [5]

    1980, ApJ, 242, 1208

    Arcoragi, J.-P., & Fontaine, G. 1980, ApJ, 242, 1208

  6. [6]

    Arnett, D., Meakin, C., & Young, P. A. 2010, ApJ, 710, 1619 B¨ohm-Vitense, E. 1958, Zeitschrift f¨ur Astrophysik, 46, 108

  7. [7]

    2009, in IAU Symposium, V ol

    Baglin, A., Auvergne, M., Barge, P., Deleuil, M., Michel, E., & CoRoT Exoplanet Science Team. 2009, in IAU Symposium, V ol. 253, IAU Symposium, 71–81

  8. [8]

    N., Basu, S., & Pinsonneault, M

    Bahcall, J. N., Basu, S., & Pinsonneault, M. H. 1998, Physics Letters B, 433, 1

  9. [9]

    A., Latter, H., & Weiss, N

    Balbus, S. A., Latter, H., & Weiss, N. 2012, MNRAS, 420, 2457

  10. [10]

    A., Welsh, W

    Bass, G., Orosz, J. A., Welsh, W. F., Windmiller, G., Ames Gregg, T., Fetherolf, T., Wade, R. A., & Quinn, S. N. 2012, ArXiv e-prints

  11. [11]

    G., et al

    Beck, P. G., et al. 2012, Nature, 481, 55

  12. [12]

    A., & Allard, N

    Bergeron, P., Wesemael, F., Lamontagne, R., Fontaine, G., Saffer, R. A., & Allard, N. F. 1995, ApJ, 449, 258

  13. [13]

    Bildsten, L., Paxton, B., Moore, K., & Macias, P. J. 2012, ApJ, 744, L6

  14. [14]

    S., & Dorodnitsyn, A

    Bisnovatyi-Kogan, G. S., & Dorodnitsyn, A. V . 1999, A&A, 344, 647

  15. [15]

    1995, A&A, 297, 727 B¨ohm, K

    Bloecker, T. 1995, A&A, 297, 727 B¨ohm, K. H., & Cassinelli, J. 1971, A&A, 12, 21

  16. [16]

    2007, A&A, 462, 1031

    Bonanno, A., K¨uker, M., & Patern`o, L. 2007, A&A, 462, 1031

  17. [17]

    2009, in IAU Symposium, V ol

    Borucki, W., et al. 2009, in IAU Symposium, V ol. 253, IAU Symposium, 289–299

  18. [18]

    Boss, A. P. 2011, ApJ, 731, 74

  19. [19]

    2006, A&A, 449, 451

    Braithwaite, J. 2006, A&A, 449, 451

  20. [20]

    Braithwaite, J., & Spruit, H. C. 2004, Nature, 431, 819

  21. [21]

    2005, Phys

    Brandenburg, A., & Subramanian, K. 2005, Phys. Rep., 417, 1

  22. [22]

    D., & Tassoul, M

    Brassard, P., Fontaine, G., Wesemael, F., Kawaler, S. D., & Tassoul, M. 1991, ApJ, 367, 601

  23. [23]

    2007, MNRAS, 381, 1482

    Briquet, M., Morel, T., Thoul, A., Scuflaire, R., Miglio, A., Montalb´an, J., Dupret, M.-A., & Aerts, C. 2007, MNRAS, 381, 1482

  24. [24]

    2011, A&A, 530, A115

    Brott, I., et al. 2011, A&A, 530, A115

  25. [25]

    M., Garaud, P., & Stellmach, S

    Brown, J. M., Garaud, P., & Stellmach, S. 2013, ApJ, 768, 34

  26. [26]

    M., Christensen-Dalsgaard, J., Dziembowski, W

    Brown, T. M., Christensen-Dalsgaard, J., Dziembowski, W. A., Goode, P., Gough, D. O., & Morrow, C. A. 1989, ApJ, 343, 526

  27. [27]

    M., Gilliland, R

    Brown, T. M., Gilliland, R. L., Noyes, R. W., & Ramsey, L. W. 1991, ApJ, 368, 599

  28. [28]

    C., et al

    Calder, A. C., et al. 2007, ApJ, 656, 313

  29. [29]

    2011, A&A, 534, A140

    Cantiello, M., & Braithwaite, J. 2011, A&A, 534, A140

  30. [30]

    2010, A&A, 521, A9 14 Avaliable fromhttp://www.astro.wisc.edu/˜townsend/static.php?ref=mesasdk

    Cantiello, M., & Langer, N. 2010, A&A, 521, A9 14 Avaliable fromhttp://www.astro.wisc.edu/˜townsend/static.php?ref=mesasdk. Modules for Experiments in Stellar Astrophysics (MESA) 43

  31. [31]

    2009, A&A, 499, 279

    Cantiello, M., et al. 2009, A&A, 499, 279

  32. [32]

    K., Cunha, K., Smith, V

    Carlberg, J. K., Cunha, K., Smith, V . V ., & Majewski, S. R. 2012, ApJ, 757, 109

  33. [33]

    A., et al

    Carter, J. A., et al. 2011, Science, 331, 562

  34. [34]

    Y ., Pietrinferni, A., Catelan, M., & Salaris, M

    Cassisi, S., Potekhin, A. Y ., Pietrinferni, A., Catelan, M., & Salaris, M. 2007, ApJ, 661, 1094

  35. [35]

    2011, ApJ, 732, 25

    Chang, P., & Hui, L. 2011, ApJ, 732, 25

  36. [36]

    2005, Science, 309, 2189

    Charbonnel, C., & Talon, S. 2005, Science, 309, 2189

  37. [37]

    2007, A&A, 467, L15

    Charbonnel, C., & Zahn, J.-P. 2007, A&A, 467, L15

  38. [38]

    L., & Wheeler, J

    Chatzopoulos, E., Robinson, E. L., & Wheeler, J. C. 2012, ApJ, 755, 95

  39. [39]

    Chatzopoulos, E., & Wheeler, J. C. 2012, ApJ, 748, 42

  40. [40]

    Christensen-Dalsgaard, J., & Thompson, M. J. 1997, MNRAS, 284, 527

  41. [41]

    1996, Science, 272, 1286

    Christensen-Dalsgaard, J., et al. 1996, Science, 272, 1286

  42. [42]

    2007, A&A, 475, 1019

    Claret, A. 2007, A&A, 475, 1019

  43. [43]

    P., & Giuli, R

    Cox, J. P., & Giuli, R. T. 1968, Principles of stellar structure (New York: Gordon and Breach)

  44. [44]

    H., et al

    Cyburt, R. H., et al. 2010, ApJS, 189, 240

  45. [45]

    A., Sakstein, J., & Shaw, D

    Davis, A.-C., Lim, E. A., Sakstein, J., & Shaw, D. J. 2012, Phys. Rev. D, 85, 123006 de Bruijne, J. H. J. 2012, Ap&SS, 341, 31 de Jager, C., Nieuwenhuijzen, H., & van der Hucht, K. A. 1988, A&AS, 72, 259

  46. [46]

    2011, A&A, 535, A91

    Deheuvels, S., & Michel, E. 2011, A&A, 535, A91

  47. [47]

    2010, A&A, 515, 87

    Deheuvels, S., et al. 2010, A&A, 515, 87

  48. [48]

    Denissenkov, P. A. 2010, ApJ, 723, 563 —. 2012, ApJ, 753, L3

  49. [49]

    A., Herwig, F., Bildsten, L., & Paxton, B

    Denissenkov, P. A., Herwig, F., Bildsten, L., & Paxton, B. 2013, ApJ, 762, 8

  50. [50]

    A., & Pinsonneault, M

    Denissenkov, P. A., & Pinsonneault, M. 2007, ApJ, 655, 1157 —. 2008, ApJ, 684, 626

  51. [51]

    A., Pinsonneault, M., Terndrup, D

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

  52. [52]

    Dotter, A., Chaboyer, B., Jevremovi´c, D., Kostov, V ., Baron, E., & Ferguson, J. W. 2008, ApJS, 178, 89

  53. [53]

    2004, A&A, 415, 251

    Dupret, M.-A., Thoul, A., Scuflaire, R., Daszy´nska-Daszkiewicz, J., Aerts, C., Bourge, P.-O., Waelkens, C., & Noels, A. 2004, A&A, 415, 251

  54. [54]

    2008, Ap&SS, 316, 43

    Eggenberger, P., Meynet, G., Maeder, A., Hirschi, R., Charbonnel, C., Talon, S., & Ekstr¨om, S. 2008, Ap&SS, 316, 43

  55. [55]

    2012, A&A, 544, L4 Ekstr¨om, S., et al

    Eggenberger, P., Montalb´an, J., & Miglio, A. 2012, A&A, 544, L4 Ekstr¨om, S., et al. 2012, A&A, 537, A146

  56. [56]

    S., & Sofia, S

    Endal, A. S., & Sofia, S. 1976, ApJ, 210, 184 —. 1978, ApJ, 220, 279

  57. [57]

    J., et al

    Evans, C. J., et al. 2011, A&A, 530, A108

  58. [58]

    W., Alexander, D

    Ferguson, J. W., Alexander, D. R., Allard, F., Barman, T., Bodnarik, J. G., Hauschildt, P. H., Heffner-Wong, A., & Tamanai, A. 2005, ApJ, 623, 585

  59. [59]

    A., & Valenti, J

    Fischer, D. A., & Valenti, J. 2005, ApJ, 622, 1102

  60. [60]

    J., Saumon, D., Marley, M

    Fortney, J. J., Saumon, D., Marley, M. S., Lodders, K., & Freedman, R. S. 2006, ApJ, 642, 495

  61. [61]

    S., Marley, M

    Freedman, R. S., Marley, M. S., & Lodders, K. 2008, ApJS, 174, 504

  62. [62]

    B., & Abbott, D

    Friend, D. B., & Abbott, D. C. 1986, ApJ, 311, 701

  63. [63]

    2010, Molecular Physics, 108, 2265

    Frommhold, L., Abel, M., Wang, F., Gustafsson, M., Li, X., & Hunt, K. 2010, Molecular Physics, 108, 2265

  64. [64]

    M., Hirschi, R., Eggenberger, P., & Maeder, A

    Georgy, C., Ekstr¨om, S., Meynet, G., Massey, P., Levesque, E. M., Hirschi, R., Eggenberger, P., & Maeder, A. 2012, A&A, 542, A29

  65. [65]

    2011, A&A, 527, A52

    Georgy, C., Meynet, G., & Maeder, A. 2011, A&A, 527, A52

  66. [66]

    2012, ArXiv e-prints

    Giannotti, M., Wise, M., & Mohammed, A. 2012, ArXiv e-prints

  67. [67]

    E., Pols, O

    Glebbeek, E., Gaburov, E., de Mink, S. E., Pols, O. R., & Portegies Zwart, S. F. 2009, A&A, 497, 255

  68. [68]

    Gough, D. O. 1986, in Hydrodynamic and Magnetodynamic Problems in the Sun and Stars, ed. Y . Osaki, 117

  69. [69]

    1993, in Origin and Evolution of the Elements, ed

    Grevesse, N., & Noels, A. 1993, in Origin and Evolution of the Elements, ed. N. Prantzos, E. Vangioni-Flam, & M. Casse, 15–25

  70. [70]

    Grevesse, N., & Sauval, A. J. 1998, Space Sci. Rev., 85, 161

  71. [71]

    2005, Annual Review of Earth and Planetary Sciences, 33, 493 —

    Guillot, T. 2005, Annual Review of Earth and Planetary Sciences, 33, 493 —. 2010, A&A, 520, A27

  72. [72]

    1995, A&AS, 109, 109

    Guillot, T., & Morel, P. 1995, A&AS, 109, 109

  73. [73]

    1996, Solving Ordinary Differential Equations

    Hairer, E., & Wanner, G. 1996, Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems, 2nd edn. (Berlin: Springer)

  74. [74]

    1997, A&A, 327, 224

    Heger, A., Jeannin, L., Langer, N., & Baraffe, I. 1997, A&A, 327, 224

  75. [75]

    1998, A&A, 334, 210 —

    Heger, A., & Langer, N. 1998, A&A, 334, 210 —. 2000, ApJ, 544, 1016

  76. [76]

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

  77. [77]

    E., & Spruit, H

    Heger, A., Woosley, S. E., & Spruit, H. C. 2005, ApJ, 626, 350

  78. [78]

    S., & Bodenheimer, P

    Henyey, L., Vardya, M. S., & Bodenheimer, P. 1965, ApJ, 142, 841

  79. [79]

    2000a, A&A, 360, 952 —

    Herwig, F. 2000a, A&A, 360, 952 —. 2000b, A&A, 360, 952 —. 2004, ApJS, 155, 651

  80. [80]

    1997, A&A, 324, L81

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

Showing first 80 references.