Comparative analysis of GALLEX-GNO solar neutrino data and SOHO/MDI helioseismology data:: Further evidence for rotational modulation of the solar neutrino flux

Recent histogram analysis of GALLEX-GNO and SAGE data indicates that the solar neutrino flux, in the energy range of gallium experiments, varies on a timescale of weeks. Such variability could be caused by modulation of the neutrino flux by an inhomogeneous magnetic field in the solar interior if neutrinos have a nonzero magnetic moment. We may then expect the detected neutrino flux to oscillate with a frequency set by the synodic rotation frequency in the region of the solar interior that contains the magnetic structure. We investigate this possibility by carrying out a comparative analysis of the GALLEX-GNO solar neutrino data and estimates of the solar internal rotation rate derived from the MDI helioseismology experiment on the SOHO spacecraft. We find that while the Lomb-Scargle spectrum does not show a significant peak in the band appropriate to the radiative zone, it does show two closely spaced peaks in the band appropriate to the convection zone. In order to explore the relationship of these features to the Sun's internal rotation, we introduce a "resonance statistic" that is a measure of the degree of "resonance" of oscillations in the neutrino flux and the solar rotation as a function of radius and latitude. A two-dimensional map of the resonance statistic indicates that the modulation is occurring in the convection zone, near the equator. In order to derive a significance estimate for this result, we next evaluate the integral of this statistic over selected equatorial sections corresponding to the convection zone and the radiative zone. This statistic yields strong evidence that modulation is occurring in the convection zone and no evidence that modulation is occurring in the radiative zone.