A heuristic remark on the periodic variation in the number of solar neutrinos detected on Earth

Four operating neutrino observatories confirm the long standing discrepancy between detected and predicted solar neutrino flux. Among these four experiments the Homestake experiment is taking data for almost 25 years. The reliability of the radiochemical method for detecting solar neutrinos has been tested recently by the GALLEX experiment. All efforts to solve the solar neutrino problem by improving solar, nuclear, and neutrino physics have failed so far. This may also mean that the average solar neutrino flux extracted from the four experiments may not be the proper quantity to explain the production of neutrinos in the deep interior of the Sun. Occasionally it has been emphasized that the solar neutrino flux may vary over time. In this paper we do address relations among specific neutrino fluxes produced in the proton-proton chain that are imposed by the coupled systems of nonlinear partial differential equations of solar structure and kinetic equations by focusing our attention on a statistical interpretation of selected kinetic equations of PPII/PPIII branch reactions of the protonproton chain. A fresh look at the statistical implications for the outcome of kinetic equations for nuclear reactions may shed light on recent claims that the⁷ Be-neutrino flux of the Sun is suppressed in comparison to the pp- and⁸B neutrino fluxes and may hint at that the solar neutrino flux is indeed varying over time as shown by the Homestake experiment.     

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 year⁻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 a sidereal frequency of 12.85 year⁻¹. From Monte Carlo calculations, it is found 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 year⁻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.     

On the proposed associations of solar neutrino flux with solar particles,cosmic rays,and the solar activity cycle

It has been proposed that the observed solar neutrino flux exhibits important correlations with solar particles, galactic cosmic rays, and the sunspot cycle, with the latter correlation being opposite in phase and lagging behind the sunspot cycle by about one year. Re-examination of the data-available interval 1971–1981, employing various tests of statistical significance, however, suggests that such a claim is, at present, unwarrantable. For example, on the associations of solar neutrino flux and cosmic-ray flux with the Ap geomagnetic index, neither were found to be statistically significant (at the 95% level of confidence), regardless of the choice of lag (-1, 0, or +1 yr). Presuming linear fits, all correlations with Ap had coefficients of determination (r ², where r is the linear correlation coefficient) less than 16%, meaning that 16% of the variation in the selected test parameters could be explained by the variation in Ap. Similarly, on the associations of solar neutrino flux and cosmic ray flux with sunspot number, only the latter association proved to be of statistical importance. Using the best linear fits, the correlation between yearly averages of solar neutrino flux and sunspot number had r ² 19%, the correlation between weighted moving averages (of order 5) of solar neutrino flux and sunspot number had r ² 45%, and the correlation between cosmic-ray flux and sunspot number had r ² 76%, all correlations being inverse associations. Solar neutrino flux was found not to correlate strongly with cosmic-ray flux, and the Ap geomagnetic index was found not to correlate strongly with sunspot number.     

Vacuum oscillations and excess of high energy solar neutrino events observed in Superkamiokande

The excess of solar-neutrino events above 13 MeV that has been recently observed by Superkamiokande can be explained by the vacuum oscillation solution to the Solar Neutrino Problem (SNP). If the boron neutrino flux is 20% smaller than the standard solar model (SSM) prediction and the chlorine signal is assumed 30% (or 3.4σ) higher than the measured one, there exists a vacuum oscillation solution to SNP that reproduces both the observed spectrum of the recoil electrons, including the high energy distortion, and the other measured neutrino rates. The most distinct signature of this solution is a semi-annual seasonal variation of the ⁷Be neutrino flux with maximal amplitude. While the temporal series of the GALLEX and Homestake signals suggest that such a seasonal variation could be present, future detectors (BOREXINO, LENS and probably GNO) will be able to test it.     

On the long-period variations and magnitude of the solar neutrino flux

We analyze the solar neutrino flux fluctuations using data from the Homestake, GALLEX, GNO, SAGE, and Super Kamiokande experiments. Spectral analysis and direct quantitative estimations show that the quasi-five-year periodicity is the most stable neutrino flux variation. Revised mean solar neutrino fluxes are presented. These are used to estimate the observed pp flux of the solar electron neutrinos near the Earth. We consider two alternative explanations for the origin of the variable component of the solar neutrino deficit.     

Solar neutrino flux,cosmic rays,and the solar activity cycle

It is suggested that the experimental data on the solar neutrino flux as measured by Davis and his collaborators from 1970 to 1982 vary with the solar activity cycle to a very high level of statistical significance for all the available tests of the hypothesis (e.g., (t-test, ²-test, run test, Wilcoxon-Mann-Whitney test) when the solar neutrino flux data are computed from the weighted moving averages of order 5. The above tests have also been applied to the data that have been generated by the Monte Carlo simulation with production rate and background rate parameters that are typical of those in the actual experiment. It is shown that the Monte Carlo simulated data do not indicate a variation within the solar cycle. Thus the moving average data strongly favours the variation within the solar activity cycle.     

How is the sun working?

I assume that at the solar core finite amplitude flows are generated by some process for which a candidate can be the planetary tides. I assume also that there are some local magnetic flux bundles at the solar core with a strength larger than 10³ G. The aim of this paper is to show that these assumptions involve an electric field generation which then produces local thermonuclear runaways which shoot up convective cells to the outer layers. Within certain conditions these primal convective cells erupt in the subphotospheric layers which phenomenon can produce high-energy particle beams which when injected into magnetic flux tubes appear as flares. I suggest these processes for solving the neutrino problem, and also to interpret the spiky character of the solar neutrino flux and the correlation of the energy production of the Sun with its atmospheric activity.     

Standard and Non-Standard Solar Models

We summarize the physical input and assumptions commonly adopted in modern standard solar models that also produce good agreement with solar oscillation frequencies. We discuss two motivations for considering non-standard models: the solar neutrino problem and surface lithium abundance problem. We begin to explore the potential for mixed core models to solve the neutrino problem, and compare the structure, neutrino flux, and oscillation frequency predictions for several models in which the inner 25% of the radius is homogenized, taking into account the effects of non-local equilibrium abundances of ³He. The results for the neutrino flux and helioseismic predictions are far from satisfactory, but such models have the potential to reduce the predicted ⁷Be/⁸B neutrino flux ratio, and further studies are warranted. Finally, we discuss how much the neutrino problem can be alleviated in the framework of the standard solar model by using reaction rates, abundances and neutrino capture cross-sections at the limits of their uncertainties, while still satisfying the constraints of helioseismology.     

Seasonal Variations in Solar High-Energy Neutrino Flux and Their Probable Source

Cyclic variations of the solar neutrino flux (Homestake detector data) have been analyzed both from season to season and within different seasons and were compared with the corresponding variations of the large-scale deep-layer solar magnetic field. The analysis revealed a seasonal variation of the flux in the last twenty years with extremes at equinox epochs. The mechanism of this variation can be due to the asymmetry in magnitudes or to the twisting of the large-scale magnetic fields in the southern and northern hemispheres of the Sun in the flux modulation region.     

On the origin of transient effects in the solar neutrino experiment

Correlation studies of the pattern of time variation of the recorded solar neutrino flux monitored through the reaction Cl³⁷ → Ar³⁷ with various parameters of solar activity is suggestive of possible emission of a penetrating neutral particle from the sun influencing directly or indirectly the transformation Cl³⁷ → Ar³⁷ deep underground at the required rates. This possibility has to be invoked in view of the difficulties in generating the observed pattern of variations through a large modulatory mechanism involving the electron neutrino. The prediction that follows is the possible existence of a time varying component (diurnal) in the rate of some nuclear transmutations deep underground caused by an unknown neutral radiation having an interaction cross section with matter probably much larger than the canonical value of 10^-36 cm² per nucleon speculated upon by some authors in the WIMP scenario for the sun.     

Similar periodicities in the range 12 to 150 days in solar,ionospheric and atmospheric time series

Data series for the same time interval of characteristic solar parameters (sunspot number R; flux at 2.8 GHz), ionospheric parameters (critical frequency of the E-region) and atmospheric parameters (stratospheric and tropospheric temperatures T) have been analysed by the maximum-entropy method, in order to study the occurrence of periodicities in those parameters in the range from 12 to 150 days. Digital filtering of the most pronounced of the detected periods (mainly in the range between 19 to 33 days) shows a similar but not identical feature in the time interval 1974–1978. It is demonstrated that sunspot number and solar radio flux at 2.8 GHz behave in a similar way on the average, and at periods greater than 20 days. Although a number of similar periods occurred in solar, ionospheric and atmospheric parameters, cross-correlation estimations only show a relationship between periods in solar and ionospheric data, but none between solar data and stratospheric and tropospheric temperatures; exception: T (35 km) correlates with R at 12.3 days. The most obvious correlation was found between the critical frequency of the E layer and the solar flux at 2.8 GHz at a frequency of approximately 1/23 days^–1.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

An investigation on the relationship between solar irradiance signal from ERBS and 8B solar neutrino flux signals from SNO

In the present work an attempt has been made to investigate statistical association between solar neutrino flux data (both D₂O and Salt data) collected from Sudbury Neutrino Observatory and solar irradiance data detected by Earth Radiation Budget Satellite. To serve the present purpose we have used the Multifractal Detrended Cross Correlation Analysis (MF-DCCA) based on Detrended Fluctuation Analysis (MF-X-DFA) method and the Detrending Moving Average Analysis (MF-X-DMA) which explores the long term power-law cross correlations between above two pairs of data sets. Investigation also has been made to find the frequency and time dependent local phase relationship in each pair of data sets using continuous wavelet transform (CWT) based Semblance Analysis. The Semblance Analysis reveals that there exists positive phase correlation as well as negative phase correlation between solar irradiance and D₂O data at different time sub-intervals. This type of mixed phase correlation is also experienced between solar irradiance and Salt data at different time sub-intervals. The causal relationship between the D₂O and the solar irradiance time series and that between Salt and solar irradiance time series have been revealed using Singular Spectral Analysis (SSA). Calculations indicate that possibly the present solar neutrino flux data (both D₂O and Salt data) is supportive to predict the solar irradiance data but may not the vice versa which in turn suggests that the variability of nuclear energy generation process inside the Sun may influence the solar activity.     

Detection of Solar Neutrinos

The present status of solar neutrino detection is reviewed. Results from the Homestake, Kamiokande, Super-Kamiokande, GALLEX and SAGE detectors all show a deficit when compared to recent standard solar model calculations. Two of these detectors, GALLEX and SAGE, have recently been checked with artificial 51Cr neutrino sources. It is shown that astrophysical scenarios to solve the solar neutrino problems are not favoured by the data. There is hope that the results of Super-Kamiokande and the forthcoming solar neutrino experiments can provide the answers to the open questions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Comparative Analyses of Brookhaven National Laboratory Nuclear Decay Measurements and Super-Kamiokande Solar Neutrino Measurements: Neutrinos and Neutrino-Induced Beta-Decays as Probes of the Deep Solar Interior

An experiment carried out at the Brookhaven National Laboratory over a period of almost 8 years acquired 364 measurements of the beta-decay rates of a sample of \({}^{32}\mbox{Si}\) and, for comparison, of a sample of \({}^{36}\mbox{Cl}\). The experimenters reported finding “small periodic annual deviations of the data points from an exponential decay?…?of uncertain origin”. We find that power-spectrum and spectrogram analyses of these datasets show evidence not only of the annual oscillations, but also of transient oscillations with frequencies near 11 year^?1 and 12.5 year^?1. Similar analyses of 358 measurements of the solar neutrino flux acquired by the Super-Kamiokande neutrino observatory over a period of about 5 years yield evidence of an oscillation near 12.5 year^?1 and another near 9.5 year^?1. An oscillation near 12.5 year^?1 is compatible with the influence of rotation of the radiative zone. We suggest that an oscillation near 9.5 year^?1 may be indicative of rotation of the solar core, and that an oscillation near 11 year^?1 may have its origin in a tachocline between the core and the radiative zone. Modulation of the solar neutrino flux may be attributed to an influence of the Sun’s internal magnetic field by the Resonant Spin Flavor Precession (RSFP) mechanism, suggesting that neutrinos and neutrino-induced beta decays can provide information about the deep solar interior.     

Zeitlich periodische Variationen des solaren Neutrinoflusses und das Standardmodell der Sonne

The FOURIER analysis of the measured ³⁷Ar production rate for DAVIS well known solar neutrino experiment shows time variations of the solar neutrino flux with periods of 100.0, 58.8, 35.7, 25.6, 19.6, 15.2, 8.8, and 6.3 months, respectively. We discuss physical assumptions of the standard solar model which are not generally confirmed by observations and trace back the time variations of the neutrino flux with the time scale of the order of years to gravity oscillations of the solar centre.     

History of neutrino telescope/astronomy

Neutrinos represent a new window to the Universe. In this paper we discuss the attempts to detect neutrinos, starting with the Homestake experiment, which showed the deficit of solar neutrinos. The detection of neutrinos from SN 1987A gave a new impetus to neutrino research. By using successive generations of neutrino detectors it was possible to show that the solar neutrino deficit could be explained by a flavor change of massive neutrinos. With the latest detector, kamLAND, it is possible to investigate the interior of the Earth through the detection of geoneutrinos.     

Wavelet Analysis of the New Solar Neutrino Capture Rate Data for the Homestake Experiment

Wavelet analysis offers an alternative to Fourier based time- series analysis and is particularly useful when spectral features are time dependent. We analyze the solar neutrino capture rate of the radiochemical Homestake chlorine experiment with abbreviated Morlet wavelets, using Foster's (AJ, 111,1709(1996)) rescaled wavelet technique. We emphasize the complementarity of wavelet analysis to Fourier analysis. Wavelet analysis confirms the results of previously undertaken Fourier analysis. The Homestake data seem to contain a harmonic content with periodicities of 4.76 yr, 1.89 yr, 0.85 yr, and 0.51 yr. Wavelet analysis reveals that the 4.76 yr and 1.89 yr periods show an almost constant behavior over the 25 yr Homestake data record, while the 0.85 yr and 0.51 yr periods exhibit a transient phenomenon. The analysis does not show strong evidence for a period of the solar 11 yr cycle. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis and Packaging of Radiochemical Solar Neutrino Data: A Bayesian Approach

According to current practice, the results of each run of a radiochemical solar neutrino experiment comprise an estimate of the flux and upper and lower error estimates. These estimates are derived by a maximum-likelihood procedure from the times of decay events in the analysis chamber. This procedure has the following shortcomings: (a) published results sometimes include negative flux estimates; (b) even if the flux estimate is non-negative, the probability distribution function implied by the flux and error estimates will extend into negative territory; and (c) the overall flux estimate derived from the results of a sequence of runs may differ substantially from an estimate made by a “global” analysis of all of the timing data taken together. These defects indicate that the usual “packaging” of data in radiochemical solar neutrino experiments provides an inadequate summary of the data, which implies a loss of information. This article reviews this problem from a Bayesian perspective, and we suggest an alternative scheme for the packaging of radiochemical solar neutrino data, which we believe is free from these shortcomings.     

The future of solar physics

The future of solar physics is founded on the existing fundamental unsolved problems in stellar physics. Thus, for instance, the physics of stellar interiors has been called into serious question by the very low-measured neutrino flux. The ⁷¹Ga neutrino detection experiment is the next step in unravelling this mystery. If that experiment should find the expected neutrino flux from the basic p-p reaction in the Sun, then astrophysics is in a difficult situation, because the most likely explanation for the low neutrino flux found in the ³⁷Cl experiment would be an error in our calculation of the opacity or an error in our understanding of the elemental abundances in stellar interiors, with serious implications for present ideas on stellar structure and the age of the galaxy.The new methods of helioseismology, for probing the interior of the Sun, have already found the primordial rapid rotation of the central core. The forthcoming world-wide helioseismology observing network will permit fuller exploitation of the method, promising to provide the first direct sounding of the interior of a star, hitherto known to us only through theoretical inference and the discrepant neutrino emission.The activity of all stars involves much the same phenomena as make up the activity of the Sun. The effects are too complex, and too foreign to the familiar dynamics in the terrestrial laboratory, to be deciphered by theoretical effort alone. It has become clear through the observational and theoretical work of the past decade or two that much of the essential dynamics of the activity of the atmosphere takes place on scales of the order of 10² km. Thus, an essential step in developing the physics of stellar activity will be the Solar Optical Telescope (presently planned by NASA to be launched early in the next decade) to permit a microscopic examination of the surface of the Sun to study the source of the action. The activity and X-ray emission of other stars depend on much the same effects, so that the study is essential to determining the significance of the X-ray emission from other stars.This work was supported in part by the National Aeronautics and Space Administration under grant NGL-14-001-001.     

An analysis of apparent r-mode oscillations in solar activity,the solar diameter,the solar neutrino flux,and nuclear decay rates,with implications concerning the Sun’s internal structure and rotation,and neutrino processes

This article presents a comparative analysis of solar activity data, Mt Wilson diameter data, Super-Kamiokande solar neutrino data, and nuclear decay data acquired at the Lomonosov Moscow State University (LMSU). We propose that salient periodicities in all of these datasets may be attributed to r-mode oscillations. Periodicities in the solar activity data and in Super-Kamiokande solar neutrino data may be attributed to r-mode oscillations in the known tachocline, with normalized radius in the range 0.66–0.74, where the sidereal rotation rate is in the range 13.7–14.6 year⁻¹. We propose that periodicities in the Mt Wilson and LMSU data may be attributed to similar r-mode oscillations where the sidereal rotation rate is approximately 12.0 year⁻¹, which we attribute to a hypothetical “inner” tachocline separating a slowly rotating core from the radiative zone. We also discuss the possible role of the Resonant Spin Flavor Precession (RSFP) process, which leads to estimates of the neutrino magnetic moment and of the magnetic field strength in or near the solar core.