Effect of Coulomb collisions on time variations of the solar neutrino flux

We consider the processes that might suppress the time variations in the solar neutrino flux produced by the radial motion of the Earth through the neutrino interference pattern. We calculate these time variations and the extent to which they are suppressed by Coulomb collisions of the neutrino-emitting nuclei. This is done for both the 0.862-MeV ⁷Be neutrino line and the continuous neutrino spectrum, assuming a Gaussian energy response function of the neutrino detector. We find that the collisional decoherence averages out the time variations for neutrino masses A simple and clear physical picture of the time-dependent solar neutrino problem is presented and qualitative coherence criteria are discussed.     

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.     

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.     

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.     

Solar neutrino data and the 11-year solar activity cycle

Recent data on solar neutrino flux have been analysed and it is shown that there is a statistically significant variation of solar neutrino flux data with the solar activity cycle. Thus the observation suggests that the solar activity cycle is due to the pulsating characters of the nuclear energy generation in the interior of the Sun.     

A model independent approach to future solar neutrino experiments

We discuss here what model independent information about properties of neutrinos and of the sun can be obtained from future solar neutrino experiments (SNO, Super-Kamiokande). It is shown that in the general case of transitions of solar ν_e's into νμ and/or ντ the initial ⁸B neutrino flux can be measured by the observation of NC events. From the CC measurements the ν_e survival probability can be determined as a function of neutrino energy. The general case of transitions of solar ν_e's into active as well as sterile neutrinos is considered. A number of relations between measurable quantities the test of which will allow to answer the question whether there are sterile neutrinos in the solar neutrino flux on the earth are derived. Transitions of solar ν_e's into active and sterile states due to neutrino mixing and Dirac magnetic moments or into active left-handed neutrinos and active right-handed antineutrinos due to neutrino mixing and Majorana transition magnetic moments are also considered. It is shown that future solar neutrino experiments will allow to distinguish between the cases of Dirac and Majorana magnetic moments.     

New results on standard solar models

We describe the current status of solar modeling and focus on the problems originating with the introduction of solar abundance determinations with low CNO abundance values. We use models computed with solar abundance compilations obtained during the last decade, including the newest published abundances by Asplund and collaborators. The results presented here focus on both helioseismic properties and models as well as neutrino flux predictions. We also discuss changes in radiative opacities to restore agreement between helioseismology, solar models, and solar abundances and show the effect of such modifications on solar neutrino fluxes.     

Evidence for solar neutrino flux variability and its implications

Although KamLAND apparently rules out resonant-spin-flavor-precession (RSFP) as an explanation of the solar neutrino deficit, the solar neutrino fluxes in the Cl and Ga experiments appear to vary with solar rotation. Added to this evidence, summarized here, a power spectrum analysis of the Super-Kamiokande data reveals significant variation in the flux matching a dominant rotation rate observed in the solar magnetic field in the same time period. Three frequency peaks, all related to this rotation rate, can be explained quantitatively. A Super-Kamiokande paper reported no time variation of the flux, but showed the same peaks, there interpreted as statistically insignificant, due to an inappropriate analysis. This modulation is small (7%) in the Super-Kamiokande energy region (and below the sensitivity of the Super-Kamiokande analysis) and is consistent with RSFP as a subdominant neutrino process in the convection zone. The data display effects that correspond to solar-cycle changes in the magnetic field, typical of the convection zone. This subdominant process requires new physics: a large neutrino transition magnetic moment and a light sterile neutrino, since an effect of this amplitude occurring in the convection zone cannot be achieved with the three known neutrinos. It does, however, resolve current problems in providing fits to all experimental estimates of the mean neutrino flux, and is compatible with the extensive evidence for solar neutrino flux variability.     

太阳中微子"亏缺"与非标准太阳模型

系统阐述了太阳中微子“亏缺”问题出现的背景,包括介绍标准太阳模型,太阳内部的相聚变反应,太阳中微子能谱和流量的理论估算,以及太阳中微子探测实验和结果。讨论了为解释太阳中微子“亏缺”而提出的各种非标准太阳模型以及近年来愈益受到重视的中微子振动问题。     

Evidence for solar neutrino flux variability and its implications

Although KamLAND apparently rules out resonant-spin-flavor-precession (RSFP) as an explanation of the solar neutrino deficit, the solar neutrino fluxes in the Cl and Ga experiments appear to vary with solar rotation. Added to this evidence, summarized here, a power spectrum analysis of the Super-Kamiokande data reveals significant variation in the flux matching a dominant rotation rate observed in the solar magnetic field in the same time period. Three frequency peaks, all related to this rotation rate, can be explained quantitatively. A Super-Kamiokande paper reported no time variation of the flux, but showed the same peaks, there interpreted as statistically insignificant, due to an inappropriate analysis. This modulation is small (7%) in the Super-Kamiokande energy region (and below the sensitivity of the Super-Kamiokande analysis) and is consistent with RSFP as a subdominant neutrino process in the convection zone. The data display effects that correspond to solar-cycle changes in the magnetic field, typical of the convection zone. This subdominant process requires new physics: a large neutrino transition magnetic moment and a light sterile neutrino, since an effect of this amplitude occurring in the convection zone cannot be achieved with the three known neutrinos. It does, however, resolve current problems in providing fits to all experimental estimates of the mean neutrino flux, and is compatible with the extensive evidence for solar neutrino flux variability.     

Solar neutrino in relation to solar wind particles

A relationship was found earlier (Basu, 1982, 1992) between the solar neutrino flux and the flux of solar wind particles received on the Earth. However, the data used in these analyses have recently been revised and extended. This prompted us to re-examine the relationship using the new updated solar neutrino data base. The present analysis confirms the earlier findings and establishes that the two quantities are related at statistically significant levels. This suggests that the two may have a common cause of origin in the interior of the solar atmosphere and needs further investigation.     

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.     

On the homestake neutrino data

³⁷ Ar production rates from the Homestake experiment suggest a possible anticorrelation between solar neutrino flux and solar activity. In this paper we present results from linear correlation analyses between Homestake data and several solar activity parameters in the period 1970–1990. Our results support the hypothesis that Homestake neutrino fluxes exhibit a (positive or negative) correlation with those parameters, but they also suggest that the heliomagnetic field in the subphotosphere could be responsible for the observed flux modulation.     

The search for possible time variations in Davis' measurements of the argon production rate in the solar neutrino experiment

With the gradual accumulation of experimental data in the solar neutrino experiment of DAVIS and collaborators (runs 18–74 for 1970–1982), the question, whether there are time variations of the solar neutrino flux, is of renewed interest. We discuss the mathematical-numerical methods applied to the statistical analysis of DAVIS ' argon-37 production rate up till now known in the literature. These methods are characterized by the arbitrary arrangement of the DAVIS data in a time series. We perform a certain Fourier transformation for unequally-spaced time series of the measuring data of the argon-37 production rate, discuss the discovered periods and give significance criteria with respect to each period. We find that all periods discussed in the literature are contained in our series of periods. Pointing out the more mathematical character of the time series analysis we emphasize the predominant significance of the detected periods.     

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.     

On the fourier spectrum analysis of the solar neutrino capture rate

Periodic variations in Davis' experimental data concerning the solar neutrino capture rate are derived on the basis of a Fourier spectrum analysis. Variations in the ³⁷Ar production rate are obtained for a series of randomly spaced observations in the period 1970–1985 (runs 18–89). The harmonic analysis of runs 18–89 has determined solar neutrino capture rate variations with periods of 8.33, 5.00, 2.13, 1.61, 0.83, 0.61, 0.54, and 0.51 yr, thereby confirming earlier calculations performed for the set of runs 18–69 (1983), 18–74 (1985a), and 18–80 (1985b). The results also confirm those of Sakurai (1979) who showed that there is strong evidence that the observed solar neutrino flux has a tendency to vary with quasi-biennial periodicity. We show that the results of the Fourier spectrum analysis do not depend upon certain high or low values in Davis' experimental data.     

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.     

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.     

An analytic approach to the connection between stellar structure parameters and the neutrino emission rate in a simple stellar model

In order to obtain the internal structure of a main-sequence star such as the Sun usually one has to solve the detailed structure equations numerically. This paper is an attempt to construct analytic models for the stellar nuclear energy generation. We give closed-form analytic results for the stellar luminosity and stellar neutrino emission rate when the radial matter density of the spherical star under consideration is linear. For the numerical estimation of the neutrino flux of a specified stellar nuclear reaction we take into account parameters of the standard solar model. The present paper gives for the first time the connection between stellar structure parameters and neutrino fluxes in an analytic stellar model.     

Searching for neutrinos from WIMP annihilations in the Galactic stellar disc

Weakly interacting massive particles (WIMPs) are a viable candidate for the relic abundance of dark matter (DM) produced in the early universe. So far, WIMPs have eluded direct detection through interactions with baryonic matter. Neutrino emission from accumulated WIMP annihilations in the solar core has been proposed as a signature of DM, but has not yet been detected. These null results may be due to small-scale DM density fluctuations in the halo with the density of our local region being lower than the average  (∼0.3 GeV cm⁻³)  . However, the accumulated neutrino signal from WIMP annihilations in the Galactic stellar disc would be insensitive to local density variations. Inside the disc, DM can be captured by stars causing an enhanced annihilation rate and therefore a potentially higher neutrino flux than what would be observed from elsewhere in the halo. We estimate a neutrino flux from the WIMP annihilations in the stellar disc to be enhanced by more than an order of magnitude compared to the neutrino fluxes from the halo. We offer a conservative estimate for this enhanced flux, based on the WIMP–nucleon cross-sections obtained from direct-detection experiments by assuming a density of  ∼0.3 GeV cm⁻³  for the local DM. We also compare the detectability of these fluxes with a signal of diffuse high-energy neutrinos produced in the Milky Way by the interaction of cosmic rays with the interstellar medium. These comparative signals should be observable by large neutrino detectors.