pith. sign in

arxiv: 2604.06535 · v1 · submitted 2026-04-08 · 🌌 astro-ph.SR · hep-ex

Solar Neutrino Flux Fluctuations Caused by Solar Gravity Modes

Yoshiki Hatta , Yuuki Nakano , Sho Sugama , Masanobu Kunitomo , Hiroshi Ito , Takashi Sekii This is my paper

Pith reviewed 2026-05-10 18:41 UTC · model grok-4.3

classification 🌌 astro-ph.SR hep-ex
keywords solar neutrinosgravity modesg-modesneutrino fluxsolar magnetic activitysolar oscillations8B neutrinos
0
0 comments X

The pith

Solar gravity modes produce a net increase in mean neutrino flux that varies with the 11-year activity cycle.

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

The paper calculates neutrino flux changes from solar g-modes using linear adiabatic oscillations of a spherical star. First-order fluctuations cancel out completely due to geometric symmetry. Second-order terms survive and split into a small oscillating part and a steady part that raises the average flux level. This steady rise scales with the square of the mode amplitude. Because the amplitude may track convection strength, which itself changes with the solar magnetic cycle, the mean neutrino output should show an 11-year modulation detectable in long-term data.

Core claim

Linear adiabatic oscillation analysis shows that g-modes produce zero first-order fluctuation in neutrino flux because of geometrical cancellation across the solar sphere. The second-order fluctuation is nonzero and contains both time-varying and time-independent components. For an assumed maximum relative temperature perturbation of 10^{-5}, the time-varying piece reaches only about 10^{-9} relative amplitude in 8B neutrinos, while the time-independent piece raises the mean flux by an amount proportional to A_{nℓ}^2. If A_{nℓ} follows convection amplitude and therefore varies with solar magnetic activity, the mean flux exhibits an approximately 11-year variation that could be compared with

What carries the argument

Second-order term in the neutrino production rate expansion under small temperature and density perturbations from g-modes, after first-order terms cancel by spherical symmetry.

If this is right

  • The mean neutrino flux rises by an amount proportional to the square of the g-mode amplitude.
  • This mean-flux increase modulates on an 11-year timescale matching the solar magnetic cycle.
  • Long-term neutrino measurements can constrain models of g-mode excitation mechanisms.
  • A detected cyclic variation would constitute indirect evidence for the presence of solar g-modes.

Where Pith is reading between the lines

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

  • Neutrino observations could serve as a probe of how magnetic fields influence convection deep inside the Sun.
  • Improved long-baseline flux monitoring might detect the effect without resolving any individual g-mode.
  • The mechanism supplies an independent test of standard solar model predictions for average neutrino rates.

Load-bearing premise

The g-mode amplitude parameter is directly tied to convection strength and therefore changes with the solar magnetic activity cycle.

What would settle it

A multi-year record of solar neutrino flux that shows no 11-year periodic variation at the amplitude level implied by A_{nℓ} near 10^{-5}.

Figures

Figures reproduced from arXiv: 2604.06535 by Hiroshi Ito, Masanobu Kunitomo, Sho Sugama, Takashi Sekii, Yoshiki Hatta, Yuuki Nakano.

Figure 1
Figure 1. Figure 1: Flux per unit length, i.e., ϕ(r) × 4πr2ρ, of 8B (left) and 7Be (right) neutrinos as a function of the fractional radius. Different colors represent the four solar models used in this study, namely, SSM-GS98 in black, SSM-A09 in grey, K2-A2-12 in yellow, and K2- MZvar-A2-12 in red. (See the main text for more information on the models.) A primary difference among the models is in the abundance of heavier el… view at source ↗
Figure 2
Figure 2. Figure 2: Eigenfunctions of the temperature perturbations (δ ln T)nℓ as a function of the fractional radius. The left and right panel show dipole (ℓ = 1) and quadrupole (ℓ = 2) modes, respectively, where radial orders are indicated by different colors. These eigenfunctions are obtained by solving linear adiabatic oscillation of the fiducial model, i.e. K2-MZvar-A2-12. The maximum amplitude is normalized to be unity.… view at source ↗
Figure 3
Figure 3. Figure 3: Relative fluctuation in the neutrino flux ∆Φnℓ/Φ0, that is caused by a single g-mode labeled with (n, ℓ), as a function of the g-mode period (see, for instance, the first term in the right-hand side of Equation (21)), for 8B (left) and 7Be (right) neutrinos. The numerical evaluations are carried out based on the four solar models described in Section 3.1, which are represented by circles (SSM-A09), crosses… view at source ↗
Figure 4
Figure 4. Figure 4: Results of numerical evaluation of Equation (20) in which about 100 g-modes (−8 ≤ n ≤ −1, ℓ = 1, 2, 3, −ℓ ≤ m ≤ +ℓ) are assumed to be contributing to the 8B neutrino flux fluctuations. For the numerical evaluation, the value of Anℓ is assumed to be 10−5 . The left panel shows the relative flux fluctuation ∆Φg-mode/Φ0 as a function of time, and the middle panel shows the power spectral density of ∆Φg-mode/Φ… view at source ↗
Figure 5
Figure 5. Figure 5: Constraint on the number of g-mode oscillations inside the Sun. The thick lines show the upper limit of the number of g-mode oscillations at 90% C.L. by considering the amplitude of the solar 8B neutrinos detected by the Super-Kamiokande detector (in red), and the Homestake experiment (in light green), and the solar 7Be neutrinos by the SAGE experiment (in magenta), and the GALLEX/GNO experiments (in black… view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The radial profiles of the functions Qi (nℓ),(nℓ) (r) (defined in Equations (B6) to (B9)) in the case of dipole (ℓ = 1) modes with different radial orders (n = −8 to −1, represented by different colors). The left and right panels show the cases of 8B and 13N neutrinos, respectively. Although we have seen a clear difference in flux density profiles of 8B and 13N (see [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Eigenfunctions ξr, ξh, and δ ln T (from top to bottom) in the case of a g-mode with (n, ℓ) = (−20, 1) obtained by numerically solving linear adiabatic oscillation via GYRE (black solid curves) and those obtained based on the asymptotic approach described in the main text (orange dotted curves). Note that the asymptotic eigenfunctions diverge around r/R⊙ ∼ 0.71, which corresponds to the outer turning point … view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the non-time-varying component π R Q(nℓ),(nℓ)dr in the flux fluctuation of 8B neutrino that are evaluated with the eigenfunctions computed via GYRE (red, blue, and lime circles) and those evaluated with the asymptotic eigenfunctions (pink, turquoise, and moss green stars) as a function of the g-mode periods. The fiducial model (K2-MZvar-A2-12, see the main text) is used for the evaluations. … view at source ↗
Figure 11
Figure 11. Figure 11: Asymptotic evaluations of the non-time varying component ∆Φnℓ/Φ0 = π R Q(nℓ),(nℓ)dr as a function of the corresponding g-mode period (in hours) in the case of 8B neutrinos. The ranges of the radial order and the spherical degree are 1 ≤ n ≤ 501 and 1 ≤ ℓ ≤ 501. For clarity, every twenty-five n and every fifty ℓ are shown in the figure. The amplitude parameter Anℓ is assumed to be 10−5 for all the modes. R… view at source ↗
Figure 12
Figure 12. Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
read the original abstract

We have evaluated fluctuations in neutrino fluxes caused by solar gravity (g) modes based on the analysis of linear adiabatic oscillation of a spherically symmetric star. We find that the first-order fluctuation is zero due to geometrical cancellation. We still find that the second-order fluctuation is non-zero, which consists of time-varying and non-time-varying components. The amplitude of the time-varying component is small (${\sim} 10^{-9}$ in relative difference, in the case of $\mathrm{^{8}B}$ neutrino) and well below the detection limits of the current neutrino detectors, when we assume the g-mode amplitude parameter $A_{n \ell}$ to be $10^{-5}$, which corresponds to the assumed maximum relative temperature perturbation inside the Sun. Thus, it is at the moment fair to say that detecting individual solar g-modes via the solar neutrino flux measurement is almost impossible. However, the net increase in the mean neutrino flux that originates from the non-time-varying component could be non-negligible. In particular, since $A_{n \ell}$ may be related to convection amplitude, which could change in accordance with the solar magnetic activity, the total net increase in the neutrino flux, which is proportional to $A_{n \ell}^2$, should also change with the solar activity cycle. Such a long-period variation~(${\sim} 11$~years) in the neutrino flux could thus be interpreted as evidence for a bunch of solar g-modes. Comparison of the theoretical prediction with the solar neutrino measurements by, e.g., Super-Kamiokande, may have a potential to put constraints on the theory of the excitation mechanism of solar g-modes.

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 / 2 minor

Summary. The paper claims that solar gravity modes induce neutrino flux fluctuations where the first-order term vanishes due to geometrical cancellation over the sphere. The second-order term is non-zero and contains both time-varying and time-independent components; the latter produces a net increase in the mean flux proportional to A_{nℓ}^2. Assuming A_{nℓ} tracks convection amplitude and therefore varies with the solar magnetic cycle, the authors argue this yields an observable ~11-year modulation in the ^{8}B neutrino flux that could be detected by Super-Kamiokande and interpreted as evidence for g-modes.

Significance. If the second-order calculation and the A_{nℓ}–convection link can be placed on a firmer quantitative footing, the work would offer a novel, mean-flux-based probe of g-mode amplitudes and excitation that complements helioseismology. The approach rests on standard linear adiabatic theory, which is a methodological strength, but the absence of explicit derivations and cycle-amplitude predictions currently limits its impact on solar-interior or neutrino astrophysics.

major comments (2)
  1. [Abstract and central derivation] The abstract asserts a clean separation into first- and second-order terms with geometrical cancellation, yet the manuscript does not supply the explicit derivation of the second-order perturbation, the integration over the mode spectrum, or the quantitative evaluation of the time-averaged mean component. Without these steps the support for the stated amplitudes (∼10^{-9} for the time-varying part) and the claim that the mean increase “could be non-negligible” remains unsubstantiated.
  2. [Interpretation of solar-cycle variation] The central interpretive claim—that the mean flux increase varies with the solar cycle—rests on the unshown assumption that A_{nℓ} is directly related to convection amplitude and therefore changes with magnetic activity. No scaling relation, excitation model, or numerical estimate of ΔA_{nℓ} over the 11-year cycle is provided, nor is the resulting mean-flux shift computed for ^{8}B neutrinos, leaving the proposed observational test without a falsifiable amplitude.
minor comments (2)
  1. [Assumed amplitude] The numerical choice A_{nℓ}=10^{-5} as the maximum relative temperature perturbation is load-bearing for the detectability conclusion but is introduced without a clear mapping to velocity or density perturbations.
  2. [Notation] Notation for the mode indices (n,ℓ) and the precise definition of the neutrino flux perturbation should be stated explicitly at the first use rather than assumed from context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of the potential significance of our work and for the detailed comments that will help improve the manuscript. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and central derivation] The abstract asserts a clean separation into first- and second-order terms with geometrical cancellation, yet the manuscript does not supply the explicit derivation of the second-order perturbation, the integration over the mode spectrum, or the quantitative evaluation of the time-averaged mean component. Without these steps the support for the stated amplitudes (∼10^{-9} for the time-varying part) and the claim that the mean increase “could be non-negligible” remains unsubstantiated.

    Authors: We agree with the referee that the manuscript would benefit from a more explicit presentation of the derivations. Although the analysis is based on standard linear adiabatic theory as stated, the step-by-step calculation of the second-order term and the spherical integration were omitted for brevity. In the revised version, we will add an appendix containing the full derivation of the first-order cancellation (due to integration of spherical harmonics over the sphere) and the second-order contribution, including the separation into time-varying and time-independent parts. We will also show the explicit integration over the mode spectrum and compute the numerical value of the time-averaged mean flux increase for the assumed A_{nℓ} = 10^{-5}, thereby substantiating the amplitude estimates and the claim regarding the mean increase. revision: yes

  2. Referee: [Interpretation of solar-cycle variation] The central interpretive claim—that the mean flux increase varies with the solar cycle—rests on the unshown assumption that A_{nℓ} is directly related to convection amplitude and therefore changes with magnetic activity. No scaling relation, excitation model, or numerical estimate of ΔA_{nℓ} over the 11-year cycle is provided, nor is the resulting mean-flux shift computed for ^{8}B neutrinos, leaving the proposed observational test without a falsifiable amplitude.

    Authors: The connection between g-mode amplitudes and convective activity is indeed an assumption, grounded in the prevailing theory that solar g-modes are stochastically excited by convection (as discussed in the manuscript's introduction and references). We did not include a specific scaling relation or cycle variation estimate because a detailed excitation model lies outside the primary scope of this work, which focuses on the neutrino flux perturbation calculation. However, to address this, we will revise the manuscript to include a new subsection discussing this assumption, providing a simple scaling estimate based on observed variations in convective velocities or granulation over the solar cycle, and computing the corresponding modulation in the mean ^{8}B neutrino flux. This will make the observational prediction more quantitative and falsifiable, while clearly stating the limitations of the estimate. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper computes neutrino flux perturbations from standard linear adiabatic oscillation theory applied to a spherically symmetric star. First-order terms cancel by geometrical symmetry, while the second-order terms (time-varying and constant) follow directly from the assumed g-mode amplitude parameter A_{nℓ} via the oscillation equations; the constant component yields a net mean-flux shift proportional to A_{nℓ}² by algebraic expansion, not by redefinition or fitting. The suggestion that this shift could vary over the solar cycle is explicitly framed as a hypothesis resting on an external possible link to convection amplitude, without any self-citation, uniqueness theorem, or input parameter being renamed as an output prediction. No load-bearing step reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard stellar oscillation theory plus an assumed numerical amplitude for g-modes; no new physical entities are postulated.

free parameters (1)
  • A_{n ℓ} = 10^{-5}
    G-mode amplitude parameter set to 10^{-5} to represent the maximum plausible relative temperature perturbation inside the Sun.
axioms (2)
  • standard math Linear adiabatic oscillation of a spherically symmetric star
    Basis for evaluating neutrino flux fluctuations as stated in the abstract.
  • domain assumption Geometrical cancellation produces zero first-order fluctuation
    Invoked to explain why only second-order terms survive.

pith-pipeline@v0.9.0 · 5624 in / 1519 out tokens · 49302 ms · 2026-05-10T18:41:49.239731+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

15 extracted references · 15 canonical work pages

  1. [1]

    N., Gavrin, V

    Abdurashitov, J. N., Gavrin, V. N., Gorbachev, V. V., et al. 2009, PhRvC, 80, 015807, doi: 10.1103/PhysRevC.80.015807 Abe, K., Abe, K., Aihara, H., et al. 2018, arXiv e-prints, arXiv:1805.04163, doi: 10.48550/arXiv.1805.04163 Abe, K., et al. 2022, Astropart. Phys., 139, 102702, doi: 10.1016/j.astropartphys.2022.102702 Abe, K., Bronner, C., Hayato, Y., et ...

    work page doi:10.1103/physrevc.80.015807 2009

  2. [2]

    Acciarri et al

    https://arxiv.org/abs/2511.14590 Acciarri, R., Acero, M. A., Adamowski, M., et al. 2015, arXiv e-prints, arXiv:1512.06148, doi: 10.48550/arXiv.1512.06148 Aerts, C., Christensen-Dalsgaard, J., & Kurtz, D. W. 2010, Asteroseismology, doi: 10.1007/978-1-4020-5803-5 Agostini, M., et al. 2017, PhRvD, 96, 091103, doi: 10.1103/PhysRevD.96.091103 —. 2018, Nature, ...

    work page doi:10.48550/arxiv.1512.06148 2015

  3. [3]

    Figure 7.Same as Figure 3 but for the CNO neutrinos, i.e., 13N, 15O, and 17F (from left to right). D.ASYMPTOTIC EVALUATION OF THE NON-TIME-VARYING COMPONENT IN THE NEUTRINO FLUX FLUCTUATION In this appendix, we show that the non-time varying component (π R Q(nℓ),(nℓ)dr) is positive for g-modes with 1≤n≤500 and 1≤ℓ≤500. For evaluating the integration, we n...

    work page 1989

  4. [4]

    and smoothN 2 with which we compute the eigenfunctions basically following the formulations in Unno et al. (1989). We will describe the procedure in more detail in the following paragraphs. As we see little differences among the different solar models, we will show the case of our fiducial model (K2-MZvar-A2-12 in the main text). Please see Unno et al. (1...

    work page 1989

  5. [5]

    = 1; GYRE = 2; asymp

    = 1; asymp. = 1; GYRE = 2; asymp. = 2; GYRE = 3; asymp. = 3; GYRE Figure 10.Comparison of the non-time-varying componentπ R Q(nℓ),(nℓ)drin the flux fluctuation of 8B neutrino that are evaluated with the eigenfunctions computed via GYRE (red, blue, and lime circles) and those evaluated with the asymptotic eigenfunctions (pink, turquoise, and moss green sta...

    work page 1998

  6. [6]

    Because of the reaction threshold, flux intensities, and the energy dependence of the cross section, the reaction predominantly occurs by solar 8B neutrons (Bahcall et al

    The detector contains 615 tons of C 2Cl4 as a target of solar neutrinos detection, and utilizes the absorption reaction, 37Cl +ν e → 37Ar +e − with the reaction threshold is 0.814 MeV. Because of the reaction threshold, flux intensities, and the energy dependence of the cross section, the reaction predominantly occurs by solar 8B neutrons (Bahcall et al. ...

    work page 1996

  7. [7]

    2009), the GALLEX experiment used 30.3 tons in Italy from 1991 to 1997 (Hampel et al

    E.2.SAGE, GALLEX, and GNO experiments Three experiments have used Gallium to confirm the solar neutrino problem: the SAGE experiment used 50 tons of metallic gallium in Russia from 1990 to 2007 (Abdurashitov et al. 2009), the GALLEX experiment used 30.3 tons in Italy from 1991 to 1997 (Hampel et al. 1999), and the GNO experiment followed the complete of t...

    work page 1990

  8. [8]

    2003), started its operation in

    E.3.Super-Kamiokande experiment The Super-Kamiokande experiment, which is a water Cherenkov detector in Japan (Fukuda et al. 2003), started its operation in

    work page 2003

  9. [9]

    This detector observes solar 8B neutrinos via the neutrino-electron elastic scattering (Fukuda et al. 1998). However, the distinction between solar neutrino signals and background events is difficult because the energy 27 of such events overlaps with that of other background events, such as radioactive impurities in purified water (Nakano et al

    work page 1998

  10. [10]

    and the spallation products by cosmic-ray muons (Zhang et al. 2016). On the other hand, the Cherenkov light from the recoil electron after the elastic interaction can preserve the direction of the incoming neutrinos. Hence, the solar neutrino events are clearly observed over the background rate from the direction of the Sun. The public data from the Super...

    work page 2016

  11. [11]

    2009), started its operation on 2007 and completed on

    E.4.Borexino experiment The Borexino experiment, which is the organic liquid scintillator detector in Italy (Alimonti et al. 2009), started its operation on 2007 and completed on

    work page 2009

  12. [12]

    2011; Bellini et al

    The Borexino detector has observed many kinds of solar neutrinos (Bellini et al. 2011; Bellini et al. 2012; Agostini et al. 2020, 2018; Agostini et al

    work page 2011

  13. [13]

    2009; Asplund et al

    and contributed to solve the inner composition problem (Serenelli et al. 2009; Asplund et al. 2009; Serenelli 2010; Buldgen et al. 2019; Orebi Gann et al. 2021; Magg et al. 2022). The Borexino detector has reduced its internal background with several techniques, and the count rate of solar 7Be neutrino interactions clearly demonstrates the annual modulati...

    work page 2009

  14. [14]

    2000), started in 1999 and completed its operation in

    E.5.SNO experiment The SNO experiment, which is the heavy water Cherenkov detector in Canada (Boger et al. 2000), started in 1999 and completed its operation in

    work page 2000

  15. [15]

    As a consequence, the SNO detector can measure not only the pure electron neutrino flux but also the total solar neutrino flux including all neutrino flavors (Aharmim et al

    The SNO experiment uses deuterons ( 2H) as a target for the neutrino interactions (Chen 1985), and solar neutrinos undergo three different kinds of interactions, such as elastic scattering, charged current, and neutral current interactions. As a consequence, the SNO detector can measure not only the pure electron neutrino flux but also the total solar neu...

    work page 1985