The usual procedure for estimating the significance of a peak in a power spectrum is to calculate the probability of obtaining that value or a larger value by chance, on the assumption that the time series contains only noise (e.g. that the measurements were derived from random samplings of a Gaussian distribution). However, it is known that one should regard this ?P-Value? approach with caution. As an alternative, we here examine a Bayesian approach to estimating the significance of a peak in a power spectrum. This approach requires that we consider explicitly the hypothesis that the time series contains a periodic signal as well as noise. The challenge is to identify a probability distribution function for the power that is appropriate for this hypothesis. We propose what seem to be reasonable and minimally restrictive conditions to require of this function, and then propose a simple function that meets these requirements. We also identify a consistency condition, and check to see that our function satisfies this condition. We find that the Bayesian significance estimates are considerably more conservative than the conventional estimates. We apply this procedure to three recent analyses of solar neutrino data: (a) bimodality of GALLEX data; (b) power spectrum analysis of Super-Kamiokande data; and (c) the combined analysis of radiochemical neutrino data and irradiance data.

Authors: P.A. Sturrock
Projects: None

Publication Status: Solar Physics (submitted)
Last Modified: 2008-12-11 10:29

Solar neutrino variability and its implications for solar physics and neutrino physics

Recent coordinated power-spectrum analyses of radiochemical solar neutrino data and the solar irradiance have revealed a highly significant, high-Q common modulation at 11.85 yr-1. Since the stability of this frequency points to an explanation in terms of rotation, this result may be attributable to non-spherically-symmetric nuclear burning in a solar core with sidereal rotation frequency 12.85 yr-1. The variability of the amplitude (on a timescale of years) suggests that the relevant nuclear burning is variable as well as asymmetric. Recent analysis of Super-Kamiokande solar neutrino data has revealed r-mode-type modulations with frequencies corresponding to a region with sidereal rotation frequency 13.97 yr-1. If this modulation is attributed to the RSFP (Resonant Spin Flavor Precession) process, it provides a measurement of the rotation rate deep in the radiative zone. These two results suggest that the core rotates significantly more slowly than the radiative zone. If one accepts an upper limit of 7 MG for the Sun's internal magnetic field, an RSFP interpretation of the Super-Kamiokande results leads to a lower limit of 10-12 Bohr magnetons for the neutrino transition magnetic moment.

Abstract. Time-frequency analysis of data from the GALLEX and GNO solar neutrino experiments shows that some features in power-spectrum analyses of those datasets are due to aliasing (a result of the fact that run durations tend to be small multiples of one week). Displays formed from the published GALLEX data show a sharp discontinuity that we attribute to some systematic effect. We therefore normalize data for each of the four experiments in the GALLEX series and concatenate the resulting normalized data. This step effectively removes the presumed systematic effect. To help understand the effect of aliasing, we form time-frequency displays of the two principal modulations found in the data, at 11.87 yr-1 and at 13.63 yr-1. We also form time-frequency displays of datasets formed by subtracting these modulations from the actual (normalized) data. The results suggest that the true principal modulation is that at 11.87 yr-1. Comparison with helioseismology data suggests that modulation is occurring in the core, due perhaps to inhomogeneities and fluctuations in the nuclear-burning process, and that the sidereal rotation rate of the core is 12.87 yr-1, or 408 nHz.

Authors: P.A. Sturrock
Projects: None

Publication Status: Solar Physics (in press)
Last Modified: 2008-09-23 20:51

Evidence for R-Mode Oscillations in Super-Kamiokande Solar Neutrino Data

There has for some time been evidence of variability in radiochemical solar neutrino measurements, but this evidence has seemed suspect since the cerenkov experiments have not shown similar evidence of variability. The present re-analysis of Super-Kamiokande data shows strong evidence of r-mode oscillations. The frequencies of these oscillations correspond to a region with a sidereal rotation rate of 13.97 year-1. This estimate is incompatible with the rotation rate in the convection zone, but compatible with current estimates of the rotation rate in the radiative zone. The excitation of r-modes in the radiative zone may be due to a velocity field originating in or related to the nuclear-burning core.

Authors: P.A. Sturrock
Projects: None

Publication Status: Solar Physics (in press)
Last Modified: 2008-09-23 20:51

Combined analysis of solar neutrino and solar irradiance data: further evidence for variability of the solar neutrino flux and its implications concerning the solar core

A search for any particular feature in any single solar neutrino dataset is unlikely to establish variability of the solar neutrino flux since the count rates are very low. It helps to combine datasets, and in this article we examine data from both the Homestake and GALLEX experiments. These show evidence of modulation with a frequency of 11.85 yr-1, which could be indicative of rotational modulation originating in the solar core. We find that precisely the same frequency is prominent in power spectrum analyses of the ACRIM irradiance data for both the Homestake and GALLEX time intervals. These results suggest that the solar core is inhomogeneous and rotates with sidereal frequency 12.85 yr-1. We find, by Monte Carlo calculations, that the probability that the neutrino data would by chance match the irradiance data in this way is only 2 parts in 10,000. This rotation rate is significantly lower than that of the inner radiative zone (13.97 yr-1) as recently inferred from analysis of Super-Kamiokande data, suggesting that there may be a second, inner tachocline separating the core from the radiative zone. This opens up the possibility that there may be an inner dynamo that could produce a strong internal magnetic field and a second solar cycle.

Authors: P.A. Sturrock
Projects: None

Publication Status: Solar Physics (in press)
Last Modified: 2008-09-23 20:51