Preprint from ``MultiWavelength 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 XRay 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 GALLEXGNO
solar neutrino experiments with power spectra derived from equatorial
SXT data and from highlatitude SXT data, and find a remarkable
agreement. In the range 1016 y^{1}, the principal peak in the
Homestake spectrum is at 12.88 y^{1}, whereas the principal peak in the
highlatitude SXT spectrum is at 12.86 y^{1}; the principal peak in the
GALLEXGNO 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 cycleusually
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 GALLEXGNO 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 GALLEXGNO 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 GALLEXGNO 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 GALLEXGNO 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 Xray 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 deemphasize singular events such as flares, and detrended
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 GALLEXGNO (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 GALLEXGNO peak
and the highlatitude SXT peak.
Figure 3. Comparison of normalized probability distribution functions
formed from spectra of data from SXT Equator (red), SXT N60S60
(blue), Homestake (black), and GALLEXGNO (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 highlatitude SXT
peak, and the separation
(0.04 y^{1}) between the GALLEXGNO 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 GALLEXGNO 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 SpinFlavor 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 GALLEXGNO neutrino
flux; and the other located where the rotation rate is 12.87 +/ 0.02
y^{1}, influencing primarily the high latitude Xray 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 rotationalmodulation map of the equatorial SXT data (and GALLEXGNO
data) is shown in Figure 4a. That of the highlatitude 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 GALLEXGNO 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 highlatitude
Xray 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 manyyear 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
837334 and NSF grant AST0097128.
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