pith. sign in

arxiv: 2605.20366 · v1 · pith:KT2CMDI6new · submitted 2026-05-19 · 🌌 astro-ph.SR

Investigating the impact of Solar Fusion III reaction rates on helioseismic constraints and solar neutrino fluxes

T. Sandron , G. Buldgen , A. Noels , M.A. Dupret , R. Scuflaire This is my paper

Pith reviewed 2026-05-21 06:58 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar modelsnuclear reaction rateshelioseismologysolar neutrinosSolar Fusion IIIstandard solar modelneutrino fluxes
0
0 comments X

The pith

Solar Fusion III reaction rates slightly improve helioseismic agreement in solar models but lower predicted beryllium, boron, and CNO neutrino fluxes.

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

The paper tests the latest Solar Fusion III nuclear reaction rates as inputs to both standard and non-standard solar models. These updated rates produce a modest improvement in how well the models match data from sound waves propagating through the Sun. At the same time the rates reduce the expected fluxes of beryllium, boron, and CNO neutrinos. Even when the rates of key reactions are varied within their stated uncertainties the models still fail to match observed neutrino fluxes, pointing to the possible need for additional physical processes.

Core claim

Using the Solar Fusion III reaction rates significantly impacts the agreement of solar models with both helioseismic constraints and neutrino flux measurements. For helioseismic constraints there is a slight improvement, but the rates lower the beryllium, boron and CNO neutrino fluxes. Changes to key reaction rates within their quoted uncertainties prove insufficient to reconcile the models with observations.

What carries the argument

Solar Fusion III reaction rates as the updated set of nuclear cross-sections governing energy generation and neutrino production in the solar core.

If this is right

  • Solar models built with Solar Fusion III rates achieve closer agreement with helioseismic inversion results.
  • Predicted fluxes for beryllium, boron, and CNO neutrinos decrease relative to models using earlier rate compilations.
  • Adjustments to individual reaction rates within their uncertainties do not eliminate the mismatch with measured neutrino fluxes.
  • Additional mechanisms such as those linked to planetary formation may be required to bring models into full consistency with observations.

Where Pith is reading between the lines

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

  • If the lowered neutrino fluxes prove accurate, upcoming detectors could record signals below previous theoretical expectations.
  • Similar rate updates could shift predicted neutrino outputs in models of other main-sequence stars.
  • Further tests could examine whether the new rates interact differently with opacity or initial abundance changes.

Load-bearing premise

Non-standard solar models can reproduce observed lithium and beryllium depletion by varying abundances, nuclear reaction rates, and opacities and still serve as valid tests of the new rates against helioseismic and neutrino data.

What would settle it

A precise measurement of the solar boron neutrino flux lying well outside the lowered range predicted by Solar Fusion III models would show that rate uncertainties alone cannot account for the discrepancy.

Figures

Figures reproduced from arXiv: 2605.20366 by A. Noels, G. Buldgen, M.A. Dupret, R. Scuflaire, T. Sandron.

Figure 1
Figure 1. Figure 1: Left panel: Relative differences in squared adiabatic sound speed profile (c2 ) between the Sun and various SSMs of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: Relative differences in squared adiabatic sound speed profile (c2 ) between the Sun and various NSSMs as a function of normalized radius, as determined from an SOLA inversion of helioseismic data. Right panel: Relative differences in entropy proxy profile (S) between the Sun and various NSSMs as a function of normalized radius, as determined from an SOLA inversion of helioseismic data. pp[£10 1… view at source ↗
Figure 3
Figure 3. Figure 3: Predicted neutrino fluxes (pp, 7Be, 8B, CNO) by various SSMs in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Left panel: Relative differences in squared adiabatic sound speed profile (c2 ) between the Sun and various NSSMs using the AAG21 abundances, including macroscopic mixing and modifications to both the 7Be(p, γ) 8B and 14N(p, γ) 15O reaction rates. as a function of normalized radius, as determined from an SOLA inversion of helioseismic data. Right panel: Same as the left panel but for relative differences i… view at source ↗
Figure 6
Figure 6. Figure 6: Predicted neutrino fluxes (pp, 7Be, 8B, CNO) by various NSSMs including macroscopic mixing in [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Arguments of the integrals described in Eqs. [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

Nuclear reaction rates are crucial ingredients of solar and stellar models, they directly impact the duration of the life of stars and the energy they produce. In the solar case, the tight observational constraints put on models (Mass, Radius, Luminosity and chemical composition) coupled to our capabilities to probe the solar interior thanks to helioseismology and solar neutrinos provide an exquisite testbed for such physical ingredients. With the recent publication of the Solar Fusion III reaction rates, a new generation of solar models may be computed and put to the test. We aim to investigate the impact of the new Solar Fusion III reaction rates on solar models, both standard and non-standard, as well as the impact of the current uncertainties on some key solar reactions on the predicted neutrino fluxes for boron and the so-called CNO cycle. We compute various theoretical standard solar models as well as non-standard models reproducing the depletion of lithium and beryllium for various abundances, nuclear reaction rates and opacities. We focus on the impact of the solar fusion III reaction rates on both helioseismic inversion results and neutrino fluxes. We find that using the Solar Fusion III reaction rates significantly impact the agreement of solar models both with helioseismic constraints and neutrino flux measurements. While for helioseismic constraints it seems that there is a slight improvement, for neutrino fluxes, the use of the SFIII reaction rates induces a lowering of the beryllium, boron and CNO neutrino fluxes. When investigating the impact of changes on the rates of key reactions within their quoted uncertainties, we find that these changes are far from sufficient to reconcile models and observations, potentially hinting at other processes (e.g. planetary formation as found in other studies).

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

3 major / 2 minor

Summary. The paper computes standard and non-standard solar models incorporating the Solar Fusion III (SFIII) nuclear reaction rates and compares the resulting helioseismic inversions and neutrino flux predictions (7Be, 8B, and CNO) against observations. It reports a modest improvement in helioseismic agreement but a systematic lowering of the neutrino fluxes when SFIII rates are adopted; variations of key rates within their quoted 1-sigma uncertainties are stated to be insufficient to restore agreement with measured fluxes, suggesting possible additional physics such as planetary formation effects.

Significance. If the quantitative mapping from rate changes to core temperature, composition profiles, and fluxes is robustly demonstrated, the work would provide a timely test of the SFIII compilation against the tightest available solar constraints. It would strengthen the case that nuclear-rate updates alone cannot resolve current neutrino-flux discrepancies and would motivate further exploration of non-standard solar physics.

major comments (3)
  1. [Abstract / methods summary paragraph] Abstract and methods summary: the central claim that SFIII-induced lowering of 7Be, 8B and CNO fluxes lies outside the range reachable by rate variations within quoted uncertainties is not supported by any explicit tabulation or figure showing the magnitude of the central-temperature shift or the 3He/4He profile adjustment after recalibration to fixed luminosity, radius and surface Z/X. Without this mapping the statement that the changes are “far from sufficient” cannot be verified.
  2. [Non-standard models] Non-standard models section: the assumption that models tuned to reproduce observed lithium and beryllium depletion (by varying abundances, rates and opacities) remain valid benchmarks for testing SFIII rates against helioseismic and neutrino data requires explicit demonstration that the same models still satisfy the helioseismic inversion constraints used elsewhere in the paper.
  3. [Neutrino flux predictions] Neutrino-flux results: no covariance matrix or sensitivity table is provided that quantifies how the flux changes induced by the SFIII rates correlate with the simultaneous adjustments to opacity tables and initial abundances that are also varied in the non-standard runs.
minor comments (2)
  1. [Throughout] Notation for the key reactions (e.g., 3He(3He,2p)4He and 7Be(p,γ)8B) should be standardized throughout the text and tables.
  2. [Figures] Figure captions should explicitly state whether error bars include only rate uncertainties or also the propagated uncertainties from abundance and opacity variations.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive report. The comments highlight areas where additional clarity and supporting material would strengthen the presentation. We address each major comment below and indicate the revisions planned for the manuscript.

read point-by-point responses

  1. Referee: [Abstract / methods summary paragraph] Abstract and methods summary: the central claim that SFIII-induced lowering of 7Be, 8B and CNO fluxes lies outside the range reachable by rate variations within quoted uncertainties is not supported by any explicit tabulation or figure showing the magnitude of the central-temperature shift or the 3He/4He profile adjustment after recalibration to fixed luminosity, radius and surface Z/X. Without this mapping the statement that the changes are “far from sufficient” cannot be verified.

    Authors: We agree that an explicit tabulation or figure quantifying the central-temperature shift and 3He/4He adjustment after recalibration would make the argument more verifiable. In the revised manuscript we will add a table (or supplementary figure) reporting these structural changes for the SFIII models relative to the prior rate compilation, together with the resulting neutrino-flux shifts. This will directly support the statement that variations within the quoted 1-sigma uncertainties remain insufficient. revision: yes

  2. Referee: [Non-standard models] Non-standard models section: the assumption that models tuned to reproduce observed lithium and beryllium depletion (by varying abundances, rates and opacities) remain valid benchmarks for testing SFIII rates against helioseismic and neutrino data requires explicit demonstration that the same models still satisfy the helioseismic inversion constraints used elsewhere in the paper.

    Authors: The non-standard models were constructed to simultaneously match the observed Li and Be depletions while remaining as close as possible to the helioseismic inversions. To make this explicit, we will add a short paragraph and a supplementary table in the revised version that compares the sound-speed and density inversion residuals for the non-standard SFIII models against the standard solar model and against the observational uncertainties, confirming that the helioseismic agreement is preserved at the level reported in the abstract. revision: yes

  3. Referee: [Neutrino flux predictions] Neutrino-flux results: no covariance matrix or sensitivity table is provided that quantifies how the flux changes induced by the SFIII rates correlate with the simultaneous adjustments to opacity tables and initial abundances that are also varied in the non-standard runs.

    Authors: A full covariance matrix would require a dedicated Monte-Carlo ensemble that lies outside the scope of the present study. However, we can supply a sensitivity table that isolates the flux response to individual changes in opacity and initial abundances for the SFIII-based models. We will include this table in the revision to quantify the dominant correlations to the extent permitted by the existing model grid. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results derive from external rates and independent observations

full rationale

The paper imports the Solar Fusion III reaction rates from an external compilation and computes standard and non-standard solar models whose outputs are compared directly to independent helioseismic inversions and measured neutrino fluxes. The reported lowering of 7Be, 8B and CNO fluxes, as well as the conclusion that rate variations within quoted uncertainties remain insufficient, follow from numerical solution of the stellar-structure equations after the rate substitution; no equation or parameter in the study is defined in terms of the target fluxes or helioseismic quantities themselves. Non-standard models that reproduce Li and Be depletion are constructed by varying abundances, rates and opacities and then tested against the same external constraints, without any self-definitional loop or fitted-input-called-prediction pattern. No load-bearing self-citation, uniqueness theorem, or ansatz smuggling is present in the provided text.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard solar model assumptions plus the ability to vary abundances, opacities, and rates to match lithium/beryllium depletion while testing against external data.

free parameters (2)
  • initial abundances
    Varied across models to reproduce lithium and beryllium depletion
  • opacity tables
    Adjusted in non-standard models
axioms (1)
  • domain assumption Standard solar model boundary conditions (mass, radius, luminosity, surface composition) are correctly imposed
    Invoked when computing theoretical standard solar models

pith-pipeline@v0.9.0 · 5860 in / 1389 out tokens · 36320 ms · 2026-05-21T06:58:51.643206+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages · 1 internal anchor

  1. [1]

    B., et al

    Acharya, B., Aliotta, M., Balantekin, A. B., et al. 2025, Rev. Mod. Phys., 97, 035002

    work page 2025

  2. [2]

    G., García, A., Robertson, R

    Adelberger, E. G., García, A., Robertson, R. G. H., et al. 2011, Reviews of Mod- ern Physics, 83, 195

    work page 2011

  3. [3]

    M., Ogneva, D., Buldgen, G., et al

    Amarsi, A. M., Ogneva, D., Buldgen, G., et al. 2024, A&A, 690, A128

    work page 2024

  4. [4]

    1999, Nucl

    Angulo, C., Arnould, M., Rayet, M., et al. 1999, Nucl. Phys. A, 656, 3

    work page 1999

  5. [5]

    M., & Grevesse, N

    Asplund, M., Amarsi, A. M., & Grevesse, N. 2021, A&A, 653, A141

    work page 2021

  6. [6]

    Bahcall, J. N. 1989, Neutrino Astrophysics

    work page 1989

  7. [7]

    N., Huebner, W

    Bahcall, J. N., Huebner, W. F., Lubow, S. H., Parker, P . D., & Ulrich, R. K. 1982, Reviews of Modern Physics, 54, 767

    work page 1982

  8. [8]

    Bahcall, J. N. & Shaviv, G. 1968, ApJ, 153, 113

    work page 1968

  9. [9]

    Bahcall, J. N. & Ulrich, R. K. 1988, Reviews of Modern Physics, 60, 297

    work page 1988

  10. [10]

    2023, Phys

    Basilico, D., Bellini, G., Benziger, J., et al. 2023, Phys. Rev. D, 108, 102005

    work page 2023

  11. [11]

    & Antia, H

    Basu, S. & Antia, H. M. 2004, ApJ, 606, L85

    work page 2004

  12. [12]

    J., Elsworth, Y ., New, R., & Serenelli, A

    Basu, S., Chaplin, W. J., Elsworth, Y ., New, R., & Serenelli, A. M. 2009, ApJ, 699, 1403 Borexino Collaboration, Agostini, M., Altenmüller, K., et al. 2018, Nature, 562, 505 Borexino Collaboration, Agostini, M., Altenmüller, K., Appel, S., et al. 2020, Nature, 587, 577

    work page 2009

  13. [13]

    2010, Annual Review of Nuclear and Particle Science, 60, 53

    Broggini, C., Bemmerer, D., Guglielmetti, A., & Menegazzo, R. 2010, Annual Review of Nuclear and Particle Science, 60, 53

    work page 2010

  14. [14]

    2023, A&A, 669, L9

    Buldgen, G., Eggenberger, P ., Noels, A., et al. 2023, A&A, 669, L9

    work page 2023

  15. [15]

    Buldgen, G., Salmon, S. J. A. J., Noels, A., et al. 2019, A&A, 621, A33

    work page 2019

  16. [16]

    P ., et al

    Chen, X., Su, J., Shen, Y . P ., et al. 2025, Phys. Rev. Lett., 135, 232701

    work page 2025

  17. [17]

    2021, Living Reviews in Solar Physics, 18, 2

    Christensen-Dalsgaard, J. 2021, Living Reviews in Solar Physics, 18, 2

    work page 2021

  18. [18]

    V ., et al

    Christensen-Dalsgaard, J., Dappen, W., Ajukov, S. V ., et al. 1996, Science, 272, 1286

    work page 1996

  19. [19]

    O., & Thompson, M

    Christensen-Dalsgaard, J., Gough, D. O., & Thompson, M. J. 1991, ApJ, 378, 413

    work page 1991

  20. [20]

    P ., Magee, N

    Colgan, J., Kilcrease, D. P ., Magee, N. H., et al. 2016, ApJ, 817, 116

    work page 2016

  21. [21]

    Cox, J. P . & Giuli, R. T. 1968, Principles of stellar structure (Gordon and Breach) Däppen, W. 2024, Sol. Phys., 299, 128

    work page 1968

  22. [22]

    R., Broomhall, A

    Davies, G. R., Broomhall, A. M., Chaplin, W. J., Elsworth, Y ., & Hale, S. J. 2014, MNRAS, 439, 2025

    work page 2014

  23. [23]

    2025, Sol

    Deal, M., Buldgen, G., Manchon, L., et al. 2025, Sol. Phys., 300, 96 Di Mauro, M. P ., Christensen-Dalsgaard, J., Rabello-Soares, M. C., & Basu, S. 2002, A&A, 384, 666

    work page 2025

  24. [24]

    A., Pamiatnykh, A

    Dziembowski, W. A., Pamiatnykh, A. A., & Sienkiewicz, R. . 1991, MNRAS, 249, 602

    work page 1991

  25. [25]

    2004, Physics Letters B, 591, 61

    Formicola, A., Imbriani, G., Costantini, H., et al. 2004, Physics Letters B, 591, 61

    work page 2004

  26. [26]

    2022, Phys

    Frentz, B., Aprahamian, A., Boeltzig, A., et al. 2022, Phys. Rev. C, 106, 065803

    work page 2022

  27. [27]

    Guzik, J. A. & Mussack, K. 2010, ApJ, 713, 1108

    work page 2010

  28. [28]

    C., Hamish Robertson, R

    Haxton, W. C., Hamish Robertson, R. G., & Serenelli, A. M. 2013, ARA&A, 51, 21

    work page 2013

  29. [29]

    Iglesias, C. A. & Rogers, F. J. 1996, ApJ, 464, 943 Article number, page 7 of 8 A&A proofs: manuscript no. aa60005-26 Fig. 8: Arguments of the integrals described in Eqs. 3,4,5 and 6 for the NSSM model using the AAG21 abundances and either the SFIII or the combination of NACRE II and SFII reaction rates used in our previous publications. Upper left panel:...

    work page 1996

  30. [30]

    2005, European Physical Jour- nal A, 25, 455

    Imbriani, G., Costantini, H., Formicola, A., et al. 2005, European Physical Jour- nal A, 25, 455

    work page 2005

  31. [31]

    Kosovichev, A. G. & Fedorova, A. V . 1991, Soviet Ast., 35, 507

    work page 1991

  32. [32]

    2025, A&A, 702, A167

    Kunitomo, M., Buldgen, G., & Guillot, T. 2025, A&A, 702, A167

    work page 2025

  33. [33]

    & Guillot, T

    Kunitomo, M. & Guillot, T. 2021, A&A, 655, A51

    work page 2021

  34. [34]

    2022, A&A, 667, L2 Le Pennec, M., Turck-Chièze, S., Salmon, S., et al

    Kunitomo, M., Guillot, T., & Buldgen, G. 2022, A&A, 667, L2 Le Pennec, M., Turck-Chièze, S., Salmon, S., et al. 2015, ApJ, 813, L42

    work page 2022

  35. [35]

    2022, A&A, 661, A140

    Magg, E., Bergemann, M., Serenelli, A., et al. 2022, A&A, 661, A140

    work page 2022

  36. [36]

    IAU 2015 Resolution B3 on Recommended Nominal Conversion Constants for Selected Solar and Planetary Properties

    Mamajek, E. E., Prsa, A., Torres, G., et al. 2015, arXiv e-prints, arXiv:1510.07674

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  37. [37]

    2009, ApJ, 701, 1204

    Mao, D., Mussack, K., & Däppen, W. 2009, ApJ, 701, 1204

    work page 2009

  38. [38]

    2011, Phys

    Marta, M., Formicola, A., Bemmerer, D., et al. 2011, Phys. Rev. C, 83, 045804

    work page 2011

  39. [39]

    2008, Phys

    Marta, M., Formicola, A., Gyürky, G., et al. 2008, Phys. Rev. C, 78, 022802

    work page 2008

  40. [40]

    2015, ApJs, 220, 2

    Mondet, G., Blancard, C., Cossé, P ., & Faussurier, G. 2015, ApJs, 220, 2

    work page 2015

  41. [41]

    2011, Ap&SS, 336, 111

    Mussack, K. 2011, Ap&SS, 336, 111

    work page 2011

  42. [42]

    & Däppen, W

    Mussack, K. & Däppen, W. 2011, ApJ, 729, 96 Orebi Gann, G. D., Zuber, K., Bemmerer, D., & Serenelli, A. 2021, Annual Re- view of Nuclear and Particle Science, 71, 491

    work page 2011

  43. [43]

    1986, ApJS, 61, 177

    Paquette, C., Pelletier, C., Fontaine, G., & Michaud, G. 1986, ApJS, 61, 177

    work page 1986

  44. [44]

    Pijpers, F. P . & Thompson, M. J. 1994, A&A, 281, 231 Proffitt, C. R. & Michaud, G. 1991, ApJ, 380, 238

    work page 1994

  45. [45]

    C., Basu, S., & Christensen-Dalsgaard, J

    Rabello-Soares, M. C., Basu, S., & Christensen-Dalsgaard, J. 1999, MNRAS, 309, 35

    work page 1999

  46. [46]

    2025, Experimental Astronomy, 59, 26

    Rauer, H., Aerts, C., Cabrera, J., et al. 2025, Experimental Astronomy, 59, 26

    work page 2025

  47. [47]

    A., Sienkiewicz, R., & Goode, P

    Richard, O., Dziembowski, W. A., Sienkiewicz, R., & Goode, P . R. 1998, A&A, 338, 756 Scuflaire, R., Théado, S., Montalbán, J., et al. 2008, ApSS, 316, 83

    work page 1998

  48. [48]

    Shaviv, N. J. & Shaviv, G. 2001, ApJ, 558, 925

    work page 2001

  49. [49]

    A., Bahcall, J

    Thoul, A. A., Bahcall, J. N., & Loeb, A. 1994, ApJ, 421, 828 V ernazza, J. E., Avrett, E. H., & Loeser, R. 1981, ApJS, 45, 635

    work page 1994

  50. [50]

    Villante, F. L. & Serenelli, A. 2021, Frontiers in Astronomy and Space Sciences, 7, 112 V orontsov, S. V ., Baturin, V . A., & Pamiatnykh, A. A. 1991, Nature, 349, 49

    work page 2021

  51. [51]

    2018, Phys

    Wagner, L., Akhmadaliev, S., Anders, M., et al. 2018, Phys. Rev. C, 97, 015801

    work page 2018

  52. [52]

    X., Nordlander, T., Asplund, M., et al

    Wang, E. X., Nordlander, T., Asplund, M., et al. 2021, MNRAS, 500, 2159

    work page 2021

  53. [53]

    2013, Nucl

    Xu, Y ., Takahashi, K., Goriely, S., et al. 2013, Nucl. Phys. A, 918, 61

    work page 2013

  54. [54]

    2019, ApJ, 881, 103 Article number, page 8 of 8

    Zhang, Q.-S., Li, Y ., & Christensen-Dalsgaard, J. 2019, ApJ, 881, 103 Article number, page 8 of 8

    work page 2019