Search for Periodicities in the Homestake Solar Neutrino Data

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Abstract
We evaluate a χ2 statistic to test against the Homestake data the hypothesis that the neutrino flux from the Sun is constant. We use estimates of standard deviations derived 1000 simulations of the sequence of 108 runs, and we also use two procedures for deriving proxies for the standard deviation from the experimental data. All tests indicate that the hypothesis should be rejected; the significance level ranges from 5.8% to 0.1%. We also search for evidence of periodicities in the neutrino flux by evaluating the log likelihood of finding the actual count rates in a model in which the neutrino flux is modulated with a sinusoidal term. We consider a range of values of the frequency (0-20 cycles yr-1) and, for each frequency, adjust the modulation parameters to maximize the likelihood. We find no evidence of modulation at the frequency of the solar cycle. A 1000 shuffle test and 1000 simulations using error estimates taken from the simulations yield no evidence for either the quasi-biennial (2.2 yr) periodicity or the Rieger (157 day) periodicity. However, simulations based on the experimental error estimates yield significance levels of 1% and 2.7% for the quasi-biennial periodicity, and 2% and 0.2% for the Rieger periodicity. We have also looked for evidence of modulation at a frequency that might be related to the solar rotation frequency. We have adopted a search band of 12.4-13.1 cycles yr-1, corresponding to the 1 year lower sideband (synodic frequency) of the rotation frequency of the Sun's radiative zone, as estimated from helioseismology. There is indeed a peak in that band, at 12.88 cycles yr-1, that according to the simulation test is significant at the 3% level. However, we also find evidence of four sidebands near 10.88, 11.88, 13.88, and 14.88 cycles yr-1 that may be due to the departure of the rotational axis from the normal to the ecliptic. We introduce a correlation measure formed from the powers at a "fundamental" and at four sidebands. None of 1000 shuffle tests, and only one of 1000 simulations, yield values of the correlation measure as large as that formed from the experimental data. These tests offer support, at the 0.1% and 0.2% significance level, respectively, for the proposition that the neutrino flux is modulated at a frequency that could be the synodic frequency corresponding to a sidereal rotational frequency of 13.88 cycles yr-1 (440 nHz) of the Sun's radiative zone.