Power-Spectrum Analysis of Super-Kamiokande Solar Neutrino Data, Taking into Account Asymmetry in the Error Estimates
The purpose of this article is to carry out a power-spectrum analysis of the Super-Kamiokande five-day dataset that takes account of the asymmetry in the error estimates. Whereas for symmetrical error estimates the likelihood analysis involves a linear optimization procedure, for asymmetrical error estimates it involves a nonlinear optimization procedure. For most frequencies there is little difference between the power spectra derived from analyses of symmetrized error estimates and from asymmetrical error estimates, but this is not the case for the principal peak in the power spectrum at 9.43 yr −1. A likelihood analysis that takes account of the error asymmetry leads to a peak with power 13.24 at that frequency, and a Monte Carlo analysis shows that there is a chance of only 0.1% of finding a peak this big or bigger in the search band 1 – 36 yr −1. From this perspective, power-spectrum analysis that takes account of asymmetry of the error estimates gives evidence for variability that is significant at the 99.9% level. We comment briefly on an apparent discrepancy between power-spectrum analyses of the Super-Kamiokande and SNO solar neutrino experiments.
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