arXiv subjects

P. A. Sturrock

Publications and source records attributed to P. A. Sturrock.

At least 37 records · Page 2Linked to original sources

arXiv2008

Time-Frequency Analysis of GALLEX and GNO Solar Neutrino Data: Evidence Suggestive of Asymmetric and Variable Nuclear Burning

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. We normalize data for each of the four experiments in the GALLEX series, concatenate the resulting normalized data, and then form time-frequency displays. We also form time-frequency displays of the two principal modulations found in the data, at 11.87 yr-1 and at 13.63 yr-1, and of the datasets formed by subtracting these modulations from the actual (normalized) data. The results suggest that the true modulation is that at 11.87 yr-1, consistent with the results of our earlier analysis of Homestake solar neutrino data. Comparison with helioseismology data indicates that modulation is occurring either in the radiative zone just below the tachocline, presumably by the RSFP (resonant spin-flavor precession) process, or in the core, presumably due to inhomogeneities and fluctuations in the nuclear-burning process.

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arXiv2008

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, not far from the value 13.88 year-1 found some time ago in Homestake data, or 13.87 year-1 found recently in GALLEX data. These estimates are incompatible with the rotation rate in the convection zone, but fully compatible with current estimates of the rotation rate in the radiative zone, including the solar core. These results are suggestive of variability originating in the core from fluctuating and asymmetric nuclear burning.

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arXiv2007

Analysis of bimodality in histograms formed from GALLEX and GNO solar neutrino data

A histogram display of the solar neutrino capture-rate measurements made by the GALLEX experiment appears to be bimodal, but that of the follow-on GNO experiment does not. To assess the significance of these results, we introduce a "bimodality index" based on the probability-transform procedure. This confirms that the GALLEX measurements are indeed bimodal (at the 99.98 percent confidence level), and that the GNO measurements are not. Tracking the bimodality index as a function of time shows that the strongest contribution to bimodality comes from runs 42 to 62, i.e. from the time interval 1995.1 to 1996.9. The bimodality index for the first half (runs 1 through 33) is 2.56, whereas that for the second half (runs 33 through 65) is 7.05. Power-spectrum analysis shows a similar distinction: the peaks in the power spectrum formed from the second half are stronger than those in the power spectrum formed from the first half, suggesting that bimodality and rotational modulation are related.

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arXiv2007

Analysis and packaging of radiochemical solar neutrino data. 1. 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 suggests an alternative scheme for the packaging of radiochemical solar neutrino data, which is we believe free from the above objections.

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arXiv2006

Comparative Analysis of Super-Kamiokande and SNO Solar-Neutrino Data and the Photospheric Magnetic Field

We analyze Super-Kamiokande, SNO, and photospheric magnetic-field data for the common time interval, namely the SNO D2O phase. Concerning rotational modulation, the magnetic-field power spectrum shows the strongest peaks at the second and sixth harmonics of the solar synodic rotation frequency [3 nu(rot) and 7 nu(rot)]. The restricted Super-Kamiokande dataset shows strong modulation at the second harmonic. The SNO D2O dataset shows weak modulation at that frequency, but strong modulation in the sixth-harmonic frequency band. We estimate the significance level of the correspondence of the Super-Kamiokande second-harmonic peak with the corresponding magnetic-field peak to be 0.0004, and the significance level of the correspondence of the SNO D2O sixth-harmonic peak with the corresponding magnetic-field peak to be 0.009. By estimating the amplitude of the modulation of the solar neutrino flux at the second harmonic from the restricted Super-Kamiokande dataset, we find that the weak power at that frequency in the SNO D2O power spectrum is not particularly surprising. Concerning 9.43 yr-1, we find no peak at this frequency in the power spectrum formed from the restricted Super-Kamiokande dataset, so it is no surprise that this peak does not show up in the SNO D2O dataset, either.

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arXiv2006

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 (based on likelihood methods) of the Super-Kamiokande 5-day dataset that takes account of the asymmetry in the error estimates. Whereas the likelihood analysis involves a linear optimization procedure for symmetrical error estimates, it involves a nonlinear optimization procedure for asymmetrical error estimates. We find that for most frequencies there is little difference between the power spectra derived from analyses of symmetrized error estimates and from asymmetrical error estimates. However, this proves not to be the case for the principal peak in the power spectra, which is found at 9.43 yr-1. A likelihood analysis which allows for a "floating offset" and takes account of the start time and end time of each bin and of the flux estimate and the symmetrized error estimate leads to a power of 11.24 for this peak. A Monte Carlo analysis shows that there is a chance of only 1% of finding a peak this big or bigger in the frequency band 1 - 36 yr-1 (the widest band that avoids artificial peaks). On the other hand, an analysis that takes account of the error asymmetry leads to a peak with power 13.24 at that frequency. A Monte Carlo analysis shows that there is a chance of only 0.1% of finding a peak this big or bigger in that frequency 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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arXiv2006

Comparative analysis of Gallex and GNO solar neutrino data

Since the GALLEX and GNO datasets were derived from closely related experiments, there is a natural tendency to merge them. This is perhaps appropriate for any analysis based on the hypothesis that the solar neutrino flux is constant, but it is not necessarily appropriate for an analysis that allows for possible variability, since the GALLEX and GNO experiments belong to different solar cycles. Moreover, we find significant differences between the GALLEX and GNO datasets. It appears, from inspection of the time series and histograms, that GNO measurements are compatible with the assumption that the solar neutrino flux is constant, but GALLEX measurements are not. Furthermore, power-spectrum analysis yields evidence of rotational modulation in GALLEX data but not in GNO data. We compare our results with those of Pandola, who claims that GALLEX-GNO data show no evidence for variability.

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arXiv2005

Power-Spectrum Analyses of Super-Kamiokande Solar Neutrino Data: Variability and its Implications for Solar Physics and Neutrino Physics

There have been conflicting claims as to whether or not power-spectrum analysis of the Super-Kamiokande solar neutrino data yields evidence of variability. Comparison of these claims is complicated by the fact that the relevant articles may use different datasets, different methods of analysis, and different procedures for significance estimation. The purpose of this article is to clarify the role of power spectrum analysis. To this end, we analyze only the Super-Kamiokande 5-day dataset, and we use a standard procedure for significance estimation proposed by the Super-Kamiokande collaboration. We then analyze this dataset, with this method of significance estimation, using six methods of power spectrum analysis. We find that the significance of the principal peak in the power spectrum (that at 9.43 yr-1with a depth of modulation of 7%) shows a clear correlation with the amount and relevance of the information being processed, as would be expected if there were a real signal in the data. The significance level reaches 99.3% for one method of analysis. We discuss, in terms of sub-dominant processes, possible neutrino-physics interpretations of the apparent variability of the Super-Kamiokande measurements, and we suggest steps that could be taken to resolve the question of variability of the solar neutrino flux.

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arXiv2005

Evidence for Solar Neutrino Flux Variability and its Implications

Althogh 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.

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arXiv2005

Combined and Comparative Analysis of Power Spectra

In solar physics, especially in exploratory stages of research, it is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might have been, or one may wish to estimate the significance of a particular peak that shows up in two or more power spectra. One may also on occasion need to search for a complex of peaks in a single power spectrum, such as a fundamental and one or more harmonics, or a fundamental plus sidebands, etc. Visual inspection can be revealing, but it can also be misleading. This leads one to look for one or more ways of forming statistics, which readily lend themselves to significance estimation, from two or more power spectra. We derive formulas for statistics formed from the sum, the minimum, and the product of two or more power spectra. A distinguishing feature of our formulae is that, if each power spectrum has an exponential distribution, each statistic also has an exponential distribution.

astro-ph↗

arXiv2004

Comment on "Search for periodic modulations of the solar neutrino flux in Super-Kamiokande" by J. Yoo et al

We comment on a recent article by Yoo et al. that presents an analysis of Super-Kamiokande 10-day and 5-day data, correcting certain errors in that article. We also point out that, in using the Lomb-Scargle method of power spectrum analysis, Yoo et al. ignore much of the relevant data. A likelihood analysis, that can take account of all of the relevant data, yields evidence indicative of modulation by solar processes.

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arXiv2004

Review of Methods of Power-Spectrum Analysis as Applied to Super-Kamiokande Solar Neutrino Data

To help understand why different published analyses of the Super-Kamiokande solar neutrino data arrive at different conclusions, we have applied six different methods to a standardized problem. The key difference between the various methods rests in the amount of information that each processes. A Lomb-Scargle analysis that uses the mid times of the time bins and ignores experimental error estimates uses the least information. A likelihood analysis that uses the start times, end times, and mean live times, and takes account of the experimental error estimates, makes the greatest use of the available information. We carry out power-spectrum analyses of the Super-Kamiokande 5-day solar neutrino data, using each method in turn, for a standard search band (0 to 50 yr-1). For each method, we also carry out a fixed number (10,000) of Monte-Carlo simulations for the purpose of estimating the significance of the leading peak in each power spectrum. We find that, with one exception, the results of these calculations are compatible with those of previously published analyses. (We are unable to replicate Koshio's recent results.) We find that the significance of the peaks at 9.43 yr-1 and at 43.72 yr-1 increases progressively as one incorporates more information into the analysis procedure.

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arXiv2003

Analysis of Super-Kamiokande 5-day Measurements of the Solar Neutrino Flux

Data in 5-day bins, recently released by the Super-Kamiodande Consortium, has been analyzed by a likelihood procedure that has certain advantages over the Lomb-Scargle procedure used by the consortium. The two most prominent peaks in the power spectrum of the 10-day data were at 9.42 y-1 and 26.57 y-1, and it was clear that one was an alias of the other caused by the regularity of the binning. There were reasons to believe that the 9.42 y-1 peak was an alias of the 26.57 y-1 peak, but analysis of the 5-day data makes it clear that the reverse is the case. In addition to a strong peak near 9.42 y-1, we find peaks at 43.72 y-1and at 39.28 y-1. After comparing this analysis with a power-spectrum analysis of magnetic-field data, we suggest that these three peaks may be attributed to a harmonic of the solar rotation rate and to an r-mode oscillation with spherical harmonic indices l = 2, m = 2.

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arXiv2003

Statistics of the Chi-Square Type, with Application to the Analysis of Multiple Time-Series Power Spectra

It is often necessary to compare the power spectra of two or more time series: one may, for instance, wish to estimate what the power spectrum of the combined data sets might have been, or one may wish to estimate the significance of a particular peak that shows up in two or more power spectra. Also, one may occasionally need to search for a complex of peaks in a single power spectrum, such as a fundamental and one or more harmonics, or a fundamental plus sidebands, etc. Visual inspection can be revealing, but it can also be misleading. This leads one to look for one or more ways of forming statistics, which readily lend themselves to significance estimation, from two or more power spectra. The familiar chi-square statistic provides a convenient mechanism for combining variables drawn from normal distributions, and one may generalize the chi-square statistic to be any function of any number of variables with arbitrary distributions. In dealing with power spectra, we are interested mainly in exponential distributions. One well-known statistic, formed from the sum of two or more variables with exponential distributions, satisfies the gamma distribution. We show that a transformation of this statistic has the convenient property that it has an exponential distribution. We introduce two additional statistics formed from two or more variables with exponential distributions. For certain investigations, we may wish to study the minimum power (as a function of frequency) drawn from two or more power spectra. In other investigations, it may be helpful to study the product of the powers. We give numerical examples and an example drawn from our solar-neutrino research.

astro-ph↗

arXiv2003

Further Evidence for Neutrino Flux Variability from Super-Kamiokande Data

While 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 vary with solar rotation rates. Added to this evidence, summarized here, a power spectrum analysis of the Super-Kamiokande data reveals (99.9% CL) an oscillation in the band of twice the equatorial rotation frequencies of the solar interior. An m=2 magnetic structure and RSFP, perhaps as a subdominant process, would give this effect. Solar cycle data changes are seen, as expected for convection zone modulations.

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arXiv2003

Joint Time-Series Analysis of Homestake and GALLEX-GNO Solar Neutrino Data: Evidence for Rieger-Type Periodicities and their Interpretation as R-Mode Oscillations

Previous power-spectrum analyses of the Homestake and GALLEX-GNO radiochemical solar neutrino data have shown evidence of the effects of solar rotation and also indications of oscillations with two periods that are well known in solar physics: one at about 154 days period (the Rieger periodicity) and another at about 52 days period. We here analyze both data sets, taken together, to test the hypothesis that the above periodicities, and a related periodicity with a period of about 77 days, are due to r-mode oscillations with spherical harmonic indices l = 3 and m = 1, 2, and 3. These would have frequencies nuR/6, nuR/3, and nuR/2, where nuR is the sidereal rotation rate where the waves are excited. We first form a statistic that combines information from power spectra formed from Homestake and GALLEX-GNO data. From this statistic, we form another statistic to search for a sidereal rotation frequency that leads simultaneously to four peaks in the Homestake-GALLEX-GNO spectrum: one corresponding to the synodic rotation frequency nuR - 1, and the other three corresponding to the l = 3 r-modes. We find that, in the range 0 to 20 cycles per year, there is one notable peak at 13.88 cycles per year; This falls in the rotation frequency range of the radiative zone. The corresponding synodic rotation period is 28.4 days, and the corresponding r-mode periods are 157, 78, and 52 days. By applying the shuffle test to the data, we find that the probability of obtaining by chance a peak this big or bigger in the rotation-frequency band of the radiative-zone is less than 0.1%. The modulation of the neutrino flux is attributed to the poloidal motion of a magnetic structure that moves in and out of the narrow beam of neutrinos that originate in the solar core and are detected on Earth.

hep-ph↗

arXiv2003

Combined and Comparative Time-Series Spectrum Analysis

It is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might have been. One might also wish to estimate the significance of a particular peak that shows up in two or more power spectra. Visual comparison can be revealing, but it can also be misleading. This leads one to look for one or more ways of forming statistics, which lend themselves to significance estimation, from two or more power spectra. We here propose two such statistics, one that is most useful for the combined study of two or more similar time series, and another that is more useful for the study of dissimilar time series.

astro-ph↗

arXiv2003

Time-Series Analysis of Super-Kamiokande Measurements of the Solar Neutrino Flux

The Super-Kamiokande Consortium has recently released data suitable for time-series analysis. The binning is highly regular: the power spectrum of the acquisition times has a huge peak (power S > 120) at the frequency (in cycles per year) 35.98 (period 10.15 days), where power measurements are such that the probability of obtaining a peak of strength S or more by chance at a specified frequency is exp(-S). This inevitably leads to severe aliasing of the power spectrum. The strongest peak in the range 0 - 100 in a power spectrum formed by a likelihood procedure is at 26.57 (period 13.75 days) with S = 11.26. For the range 0 - 40, the second-strongest peak is at 9.42 (period 38.82 days) with S = 7.3. Since 26.57 + 9.42 = 35.99, we conclude that the weaker peak at 9.42 is an alias of the stronger peak at 26.57. We note that 26.57 falls in the band 26.36 - 27.66, formed from twice the range of synodic rotation frequencies of an equatorial section of the Sun for normalized radius larger than 0.1. Oscillations at twice the rotation frequency, attributable to "m = 2" structures, are not uncommon in solar data. We find from the shuffle test that the probability of obtaining a peak of S = 11.26 or more by chance in this band is 0.1 %. This new result therefore supports at the 99.9% confidence level previous evidence, found in Homestake and GALLEX-GNO data, for rotational modulation of the solar neutrino flux. The frequency 25.57 points to a source of modulation at or near the tachocline.

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