Solar Neutrino Flux Fluctuations Caused by Solar Gravity Modes

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.