The Sudbury Neutrino Observatory (SNO) searched the solar 8^8B neutrino flux for short-period modulations (1/day to 144/day, i.e. periods down to about 10 minutes) motivated by the possibility that solar gravity (g) modes perturb the core temperature where these neutrinos are produced; no signal was found, with sensitivity to sinusoidal modulations only at the 12% (full band) and 10% (SoHO-claimed g-mode bands) amplitude level, and the paper noted that no explicit quantitative theoretical prediction of g-mode-induced flux modulations existed. Later work partially filled the theory gap but left it contested: Lopes and Turck-Chièze (2014) found a resonant amplification of core temperature fluctuations by a factor of about 170 in the 8^8B flux for the dipole g mode of radial order 2 (period near 1.5 hours), while Hatta et al. (2026) find that the first-order flux fluctuation from nonradial g modes vanishes by geometrical cancellation and the second-order time-varying modulation is of order 10−910^{-9} relative, far below any current detector. Experimentally, Super-Kamiokande's 22-year periodicity search (2024) constrains only long periods via 5-day binning. The open problem is to (i) settle the amplitude and spectral content of gravity-mode-induced solar neutrino flux modulations, adjudicating the amplification-versus-cancellation conflict, and (ii) advance short-period searches for such modulations at periods of minutes to hours (frequencies 1/day to 144/day) to a reported amplitude sensitivity that can be compared quantitatively with the settled theoretical prediction, improving on the 12% and 10% amplitude sensitivities reached by SNO.

Background

The Sun produces electron neutrinos in nuclear fusion reactions of the proton–proton chains; the 8^8B neutrinos come from the beta decay of boron-8 nuclei produced only in the hottest central regions, and their production rate is extraordinarily sensitive to the core temperature (roughly as T18T^{18}–T25T^{25} in standard solar models), so even tiny temperature perturbations in the core are amplified into much larger relative changes of the 8^8B neutrino flux. Solar oscillations are conventionally split into pressure (p) modes — sound waves, observed routinely at the surface and the basis of helioseismology — surface gravity (f) modes, and internal gravity (g) modes, buoyancy-restored oscillations trapped in the radiative interior whose amplitudes are largest precisely where 8^8B neutrinos are produced. Because g-mode amplitudes are exponentially damped in the convective envelope, no individual solar g mode has been unambiguously detected from surface brightness or velocity measurements, despite decades of effort with instruments such as GOLF (a Doppler velocity instrument aboard the SOHO satellite) — which is why a core-produced messenger like neutrinos is attractive. Neutrino flavor oscillations (the established phenomenon that electron neutrinos convert among three flavors in flight and in matter, which resolved the historical solar neutrino deficit) must be folded in, since the detected survival probability also depends on the core conditions. The Sudbury Neutrino Observatory (SNO), a heavy-water Cherenkov detector, recorded individual 8^8B neutrino interaction times and performed three high-frequency searches (an open search over 1/day to 144/day, a directed search in frequency bands where g-mode detections had been claimed by SOHO experiments, and a broad-band excess-power search), defining sensitivity as the minimum fractional amplitude AA of a sinusoidal flux modulation detectable at 99% confidence with 90% probability; the corresponding thresholds were A≳12%A \gtrsim 12\% (full band) and A≳10%A \gtrsim 10\% (SoHO bands). All three searches were null, and the authors explicitly noted the absence of a quantitative theory predicting what modulation amplitude realistic g modes would produce, so the comparison of physical expectation to experimental reach was left hanging. Early-1990s studies had qualitatively explored g-mode effects on the neutrino flux in the context of the then-open solar neutrino deficit, but no settled quantitative prediction existed at the time of the SNO analysis, and none is agreed even now: two modern linear-adiabatic calculations reach opposite conclusions about the leading-order effect: Lopes and Turck-Chièze (2014) find a resonant amplification of core temperature fluctuations in the 8^8B flux, while Hatta et al. (2026) find that the first-order term vanishes by geometrical cancellation.

Problem Statement

Establish whether gravity modes of the solar core (or closely related short-timescale core dynamics) induce periodic modulations of the solar neutrino flux that are detectable now or in the foreseeable future. This requires: (1) a definitive quantitative theoretical prediction of the fractional modulation amplitude of the 8^8B (and, where relevant, other) solar neutrino fluxes as a function of oscillation frequency and mode identity — stated for a specified solar model, oscillation eigenfunctions, mode-amplitude convention, and treatment of neutrino flavor conversion — that settles whether the first-order contribution from nonradial (ℓ≠0\ell\neq0) g modes vanishes by geometrical cancellation (Hatta et al. 2026) or is resonantly amplified by the temperature sensitivity of boron production (Lopes and Turck-Chièze 2014); here 'definitive' means settling this amplitude-convention-independent leading-order question and giving the resulting modulation spectrum conditional on the declared convention, not observationally bounding the g-mode amplitudes themselves, which are not observationally constrained; and (2) on the observational side, a short-period modulation search of solar-neutrino event time series over the period range from hours down to about 10 minutes (frequencies 1/day to 144/day, the band in which SNO reached sinusoidal-amplitude sensitivities of 12% for the open search and 10% for the SoHO-claimed g-mode bands): perform the search on the best available solar-neutrino event-time data, or, where no data set of adequate exposure exists, provide a quantitatively justified sensitivity projection, and report the achieved or projected minimum detectable sinusoidal fractional amplitude AA at 99% confidence with 90% probability across the full 1/day–144/day band, with explicit treatment of nonuniform exposure and detector deadtime. The report must state the improvement factor relative to SNO's 12% (open band) and 10% (SoHO-claimed bands), and must state explicitly and quantitatively whether the reported sensitivity reaches the modulation amplitude fixed in part (1) or by what factor it falls short. This part counts as complete once the band-wide minimum detectable amplitude and this comparison are reported; its completion does not depend on whether a signal is detected, on whether SNO's 12%/10% levels are beaten, or on whether the part (1) amplitude is reached. The two directions serve one objective: fixing the physically expected modulation spectrum and bringing real observations to bear on it, so that the detectability of solar core gravity modes through neutrinos is decided rather than left hanging between unconstrained theory and insufficient sensitivity.

References

  1. B. Aharmim et al. (SNO Collaboration), 'Searches for High Frequency Variations in the 8B Solar Neutrino Flux at the Sudbury Neutrino Observatory', The Astrophysical Journal 710, 540–548 (2010). DOI: 10.1088/0004-637X/710/1/540; arXiv:0910.2433; https://arxiv.org/abs/0910.2433
  2. Ilidio Lopes, 'Search for global f-modes and p-modes in the 8B neutrino flux', The Astrophysical Journal Letters 777, L7 (2013). DOI: 10.1088/2041-8205/777/1/L7; arXiv:1310.3467; https://arxiv.org/abs/1310.3467
  3. Ilídio Lopes and Sylvaine Turck-Chièze, 'Detecting gravity modes in the solar 8B neutrino flux', The Astrophysical Journal Letters 792, L35 (2014). DOI: 10.1088/2041-8205/792/2/L35; arXiv:1408.6671; https://arxiv.org/abs/1408.6671
  4. C. Pinçon, T. Appourchaux, G. Buldgen, 'Amplitude of solar gravity modes generated by penetrative plumes', Astronomy & Astrophysics 650, A47 (2021). DOI: 10.1051/0004-6361/202040003; arXiv:2103.03760; https://arxiv.org/abs/2103.03760
  5. K. Abe et al. (Super-Kamiokande Collaboration), 'Search for Periodic Time Variations of the Solar 8B Neutrino Flux between 1996 and 2018 in Super-Kamiokande', Physical Review Letters 132, 241803 (2024). DOI: 10.1103/PhysRevLett.132.241803; arXiv:2311.01159; https://arxiv.org/abs/2311.01159
  6. Yoshiki Hatta, Yuuki Nakano, Sho Sugama, Masanobu Kunitomo, Hiroshi Ito, Takashi Sekii, 'Solar Neutrino Flux Fluctuations Caused by Solar Gravity Modes', preprint (2026). arXiv:2604.06535; https://arxiv.org/abs/2604.06535
  7. Liangliang Ren, Ze-Lin Zhang, Bing Xu, Tian-Cheng Huang, Ran Wang, Jia-Xin Dong, Yan-Ping Wang, 'Comparative Periodogram Analysis of 22 Years of Super-Kamiokande Solar 8B Neutrino Data: Classical, Phase-Based, and Information Theoretic Methods', preprint (2026). arXiv:2607.27979; https://arxiv.org/abs/2607.27979