Preprint from ``Multi-Wavelength Observations of Coronal Structure and Dynamics --- Yohkoh 10th Anniversary Meeting'', COSPAR Colloquia Series, P.C.H. Martens and D. Cauffman (eds.)



Comparative Analysis of Solar Neutrino Data and SXT X-Ray Data



Peter A. Sturrock and Mark A. Weber

Center for Space Science and Astrophysics, Stanford University, Stanford, CA 94305, USA



ABSTRACT

We compare power spectra derived from the Homestake and GALLEX-GNO solar neutrino experiments with power spectra derived from equatorial SXT data and from high-latitude SXT data, and find a remarkable agreement. In the range 10-16 y-1, the principal peak in the Homestake spectrum is at 12.88 y-1, whereas the principal peak in the high-latitude SXT spectrum is at 12.86 y-1; the principal peak in the GALLEX-GNO spectrum is at 13.59 y-1, whereas the principal peak in the equatorial SXT spectrum is at 13.55 y-1. We estimate the correspondence to be significant at the 0.04% level. We speculate on the implications of this result.


INTRODUCTION

When solar neutrino data were first obtained by the Homestake experiment, there was great interest in the possibility that the flux may be variable. Sakurai (1981) suggested that the flux varies with a 2 y period. There were also claims that the flux varies with the solar cycle---usually based on claimed correlations between the neutrino flux and some solar activity index such as the sunspot number (see, for instance, Massetti & Storini, 1996). Walther (1997) has reviewed these claims and found reasons to discount them. Although there is no convincing evidence that the solar neutrino flux varies with the solar cycle, evidence is now accumulating that the flux varies on a much shorter time scale. Power spectrum analysis of the Homestake data (Cleveland et al., 1998) yields a significant peak at 12.88 y-1 (period 28.4 days, corresponding to rotation near the tachocline; Sturrock, Walther, & Wheatland, 1997). Similar analysis of the GALLEX-GNO data (Hampel et al., 1997; Altmann et al., 2000) yields a significant periodicity at 13.59 y-1 (26.9 days, corresponding to the deep convection zone; Sturrock & Weber, 2002). We find additional evidence for variability in the fact that the variance of the Homestake data is larger than expected (Sturrock, Walther, & Wheatland, 1997), and the histogram of GALLEX-GNO data is bimodal (Sturrock & Scargle 2001). We here compare these results with the power spectrum of SXT data.


POWER SPECTRUM ANALYSIS

We have analyzed Homestake and GALLEX-GNO data by the method developed by Lomb (1976) and Scargle (1982) for the analysis of irregular time series. The spectrum obtained from Homestake data, over the frequency range 10-16 y-1, is shown as Figure 1a; the biggest peak occurs at 12.88 +/- 0.02 y-1 (period 28.36 days). The spectrum obtained from GALLEX-GNO data is shown in Figure 1b; the biggest peak occurs at 13.59 +/- 0.03 y-1 (period 26.88 days). We have carried out a similar spectrum analysis of SXT X-ray data compiled over the six years 1992 through 1997, divided into nine latitude ranges centered on 60N, 45N, 30N, 15N, Equator, 15S, 30S, 45S, and 60S (Weber & Sturrock, 2002). We formed the logarithm of the flux measurements, in order to de-emphasize singular events such as flares, and de-trended the data. Figure 2a shows the mean of the spectra formed from 60N and 60S data; the principal peak is at 12.86 +/- 0.02 y-1. Figure 2b shows the spectrum of the SXT equatorial flux; the principal peak occurs at 13.55 +/- 0.02 y-1.

Figure 1. Power spectra for Homestake (left) and GALLEX-GNO (right).


Figure 2. Power spectra for SXT Latitudes N60 and S60 (left) and Equator (right).


To simplify the comparison of the spectra, we show in Figure 3 the corresponding probability distribution functions (pdf's; see Bretthorst, 1988), where each is related to the power S by
(Eq. 1)

There is excellent agreement between the principal Homestake peak and the equatorial SXT peak, and between the principal GALLEX-GNO peak and the high-latitude SXT peak.


Figure 3. Comparison of normalized probability distribution functions formed from spectra of data from SXT Equator (red), SXT N60--S60 (blue), Homestake (black), and GALLEX-GNO (blue).



DISCUSSION

If B is the width of the search band (6 y-1) in Figures 1 and 2, the separation (0.02 y-1) between the Homestake peak and high-latitude SXT peak, and the separation (0.04 y-1) between the GALLEX-GNO peak and equatorial SXT peak, the probability of obtaining both correspondences by chance is the product of the probability of finding the Homestake peak within of one of the two SXT peaks times the probability of finding the GALLEX-GNO peak within of one of the two SXT peaks. This is given by

(Eq. 2)


We find that p = 0.0004, so that the correspondence is significant at the 0.04% level.

The most likely interpretation of the variation of the solar neutrino flux is that neutrinos have nonzero mass and nonzero magnetic moment, so that they are subject to Resonant Spin-Flavor Precession, whereby neutrinos change both flavor and spin as they travel through matter permeated by a magnetic field (Akhmedov, 1997). According to this scenario, the neutrino flux is probably influenced by two distinct magnetic structures within the Sun: one located where the rotation rate is 13.57 +/- 0.04 y-1, influencing primarily the equatorial SXT flux and the GALLEX-GNO neutrino flux; and the other located where the rotation rate is 12.87 +/- 0.02 y-1, influencing primarily the high latitude X-ray flux and the Homestake neutrino flux. In order to locate these two regions, we have examined the "rotational modulation index" (Sturrock & Weber, 2002),

(Eq. 3)


where is the pdf of the power spectrum, and is the pdf of the rotation rate at each radius and latitude, as determined by the MDI instrument on the SOHO spacecraft (Schou et al., 1998). We map this statistic on a meridional section of the Sun. Since the SXT spectra are simpler than those derived from neutrino data, we adopt the former for display purposes. The rotational-modulation map of the equatorial SXT data (and GALLEX-GNO data) is shown in Figure 4a. That of the high-latitude SXT data (and Homestake data) is shown in Figure 4b. Since the neutrino flux is produced in the core of the Sun, modulation must occur at or close to the equator. Hence we see that the region responsible for modulation of the GALLEX-GNO flux and of the equatorial SXT flux appears to be located in the convection zone at normalized radius 0.8. The region responsible for modulation of the Homestake neutrino flux and the high-latitude X-ray flux is probably located near the tachocline, but possibly in the radiative zone at normalized radius 0.6.

Figure 4. Rotational modulation statistic formed from the spectrum of (a) the equatorial SXT flux, and (b) the N60 and S60 SXT flux.


Since the above spectra were formed from many-year data sets, it appears that the structures responsible for the above rotational modulation have lifetimes of at least several years and perhaps many years. The above results are, therefore, a challenge to the conventional model of the solar dynamo, in which the magnetic structure changes completely every eleven years.


ACKNOWLEDGEMENTS

This article is based on work supported in part by NASA grant NAS 8-37334 and NSF grant AST-0097128.


REFERENCES

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Sturrock, P.A., & M.A. Weber, Comparative Analysis of GALLEX-GNO Solar Neutrino Data and SOHO/MDI Helioseismology Data: Further Evidence for Rotational Modulation of the Solar Neutrino Flux, Ap.J., 565, 1366 (2002).

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Weber, M.A., & P.A. Sturrock, Differential Rotation of the Soft X-Ray Corona over a Solar Cycle, these proceedings (2002).




Maintained by Mark Weber.

Last modified: 2002 April 25.