Search for sub-percent periodic modulations of the solar $^7$Be neutrino flux and the amplitude of the helioseismic g-mode coupling

The solar $^7$Be neutrino line at 0.862 MeV is an unusually sensitive probe of the solar core: standard solar models give a flux scaling roughly with the 11th power of the core temperature, so coherent temperature perturbations of the fusion region — such as those associated with solar gravity (g) modes — would imprint amplified periodic modulations on the neutrino rate. A 2011 sensitivity study for the proposed LENA liquid-scintillator observatory (Wurm et al., Phys. Rev. D 83, 032010) showed that a 35-kiloton detector with Borexino-level radiopurity could search the $^7$Be rate for periodic modulations at the sub-percent amplitude level over periods from minutes (the g-mode range) to decades, an improvement of more than an order of magnitude over existing limits, while flagging as open the missing quantitative mechanism linking g-modes to the neutrino flux and the demands on detector stability and analysis methods. Developments since that study: the seasonal (geometric) modulation is now measured by Borexino, SNO's $^8$B high-frequency search (amplitude sensitivity about 10%) remains the only neutrino periodicity search in the g-mode band, JUNO — taking physics data since 2025 — is projected to reach 0.3–2.5% on $^7$Be, and a recent second-order calculation (Hatta et al., 2026) finds the first-order g-mode effect identically zero by geometrical cancellation and second-order time-varying amplitudes of order $10^{-10}$–$10^{-9}$, far below detection. Both the empirical sub-percent search and the quantitative theoretical amplitude are therefore still open, and the theory side has become genuinely contested.

Background

In the proton–proton (pp) chain that powers the Sun, electron capture on beryllium-7 produces a monoenergetic electron-neutrino line at 0.862 MeV (the 90% branch). Because these neutrinos are low in energy, they cannot be detected efficiently by water Cherenkov detectors; instead they are observed in real time through neutrino–electron elastic scattering in large volumes of organic liquid scintillator, a medium that converts the recoil electron's energy into a light flash. The Borexino detector at Gran Sasso pioneered this measurement at the 100-ton scale and demonstrated the extreme radiopurity it requires.

The scientific interest of the $^7$Be flux lies in its temperature sensitivity. Standard solar model calculations give power-law scalings of the neutrino fluxes with core temperature, $\phi_{^7\mathrm{Be}}\propto T_\mathrm{c}^{11}$ and $\phi_{^8\mathrm{B}}\propto T_\mathrm{c}^{25}$ (Bahcall–Ulmer exponents). A coherent relative temperature perturbation $\delta T/T$ of the fusion region therefore maps onto a relative flux modulation of roughly $11\,\delta T/T$ for $^7$Be, so a percent-level flux search is, in effect, a $10^{-4}$-level search for periodic core temperature fluctuations.

The physically motivated source of such fluctuations is solar gravity modes. Helioseismology has mapped the solar interior with pressure-driven (p) modes, which are acoustic waves trapped near the surface. Buoyancy-driven gravity (g) modes, in contrast, are confined to the radiative interior and are evanescent in the convective envelope; their surface velocity amplitudes are predicted to be below a few mm/s, and despite repeated claims no g-mode detection has been accepted by the helioseismology community. Since g modes have their largest displacement amplitudes precisely in the core where the fusion reactions occur, with typical periods from several minutes to a few hours, a periodic modulation of the neutrino flux at the corresponding periods would be the only direct observation of core dynamics on those timescales.

Wurm et al. (2011) assessed this program prospectively for LENA, a proposed next-generation liquid-scintillator observatory with a 35-kiloton fiducial mass in which solar $^7$Be neutrinos would yield about $1.7\times 10^4$ electron-recoil events per day. Using Monte-Carlo studies analyzed with the Lomb–Scargle periodogram — a standard least-squares technique for detecting sinusoidal modulations, $N(t)=N_0(1+A\sin(2\pi t/T+\varphi))$, in binned, unevenly sampled rate data — they projected sensitivities to relative amplitudes of roughly 0.5% for periods between 10 minutes and 1 day (one year of data) and 0.3% for periods between 1 day and 10 years (ten years of data), surpassing then-running detectors by at least a factor of 20. They also identified the analysis caveats that the proposed $^7$Be modulation search inherits: sub-percent sensitivity requires stable detector response and radiopurity — in particular control of drifts in the beta-emitting contaminants $^{210}$Bi and $^{85}$Kr — over years; binned periodograms lose power at high frequencies, where unbinned maximum-likelihood methods are needed; for modulation periods beyond about twice the measurement time the sensitivity depends strongly on the unknown oscillation phase; and, most fundamentally, the study assumed but could not quantify a mechanism converting g-mode amplitudes into neutrino flux modulations. The best existing experimental limit at the time came from the Sudbury Neutrino Observatory (SNO), which searched its $^8$B solar neutrino data for high-frequency (1–144 cycles/day) variations and found none at amplitudes of 10–12% or larger.

Two developments define the current frontier. First, the theoretical mechanism has been computed, with conflicting results: a first-order perturbative formulation by Lopes and Turck-Chièze (2014) found resonant amplification of temperature fluctuations in the $^8$B flux, while a second-order analysis by Hatta et al. (2026) shows that the first-order flux fluctuation from any nonradial mode vanishes identically by geometrical cancellation and that the second-order, time-varying signal is of order $10^{-10}$–$10^{-9}$ for standard assumed g-mode amplitudes. Second, LENA was never built, but its modulation program passed to JUNO, a 20-kiloton liquid-scintillator detector in China that began physics data taking in August 2025 and whose published sensitivity study projects percent-to-sub-percent reach on $^7$Be modulations depending on the achieved radiopurity.

Problem Statement

The problem has two jointly supporting parts that together decide whether the solar core is time-variable on measurable scales:

1. (Empirical search) Determine whether the interaction rate of solar $^7$Be neutrinos is periodically modulated, with relative amplitude at the percent-to-sub-percent level, over periods from several minutes (the helioseismic g-mode range) to tens of years — beyond the known geometric annual modulation due to Earth's orbital eccentricity. An admissible answer is a detection (with period, amplitude, phase and significance, and rejection of instrumental and background origins), an upper limit on the modulation amplitude as a function of period, or — no sub-percent $^7$Be rate series having yet been taken, so that the search remains prospective — a quantitative determination, from detector specifications and published backgrounds, of the projected sub-percent sensitivity/reach of a JUNO-class $^7$Be measurement, together with the detector-stability and time-dependent-background requirements (notably $^{210}$Bi and $^{85}$Kr drifts) that a sub-percent amplitude claim would demand. For periods comparable to or below the analysis bin width, binned periodograms lose sensitivity, so the analysis must control the bin-width limitation — for example through sufficiently fine binning or through unbinned maximum-likelihood methods — and for periods much longer than the measurement time the answer must address the oscillation-phase degeneracy.

2. (Theoretical mechanism) Establish quantitatively the relative amplitude with which solar g-mode oscillations modulate the $^7$Be (and, for comparison, $^8$B) neutrino flux — through coherent temperature perturbations of the fusion region, changes of the matter potential (the neutrino–electron forward-scattering interaction that modifies flavor oscillations inside the Sun), or second-order mode coupling — and determine whether any such channel can produce modulations at or above the percent-to-sub-percent detection level given present constraints on g-mode amplitudes. Because the published first-order and second-order coupling treatments disagree by orders of magnitude on this amplitude, an answer to this part must resolve that disagreement rather than adopt either existing calculation as settled. This prediction is what converts a future detection or limit into a statement about the solar core and about g-mode excitation.

The single overarching objective is to establish whether the solar $^7$Be neutrino flux varies periodically at the percent-to-sub-percent level and whether helioseismic g-modes can cause such variation. Both parts are required for completion and neither alone resolves the task: part 2 supplies the interpretive theory linking part 1's outcome to g-mode amplitudes and their excitation, while part 1 retains independent solar-physics meaning without any specific g-mode model, bounding coherent temperature fluctuations of the fusion region at the $10^{-4}$ level implied by the $\phi_{^7\mathrm{Be}}\propto T_\mathrm{c}^{11}$ scaling.

References

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