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\IBVShead{4160}{15 February 1995}

\title{SOLAR MAGNETIC FIELD MODULATION\\ OF THE NEUTRINO FLUX}

\begintext

  Soon after the first neutrino observations had been published it
became clear that the solar neutrino flux was not only  much  smaller
than expected from the  solar  standard  model  (the  first  neutrino
problem). It also proved to be variable in time (the second  neutrino
problem), which implied that the Sun was a  variable  neutrino  star.
(For more detail  see  Bahcall (1993),  Rivin (1993)  and  references
therein).

     Time  fluctuations  of  the  solar  neutrino   are   not   quite
understood. Some authors believe them associated with solar  activity
whose growth results in a decreased neutrino  flux  $\nu$  ($^{37}Ar$
measurements at South Dakota), i.e. a negative correlation  with  the
solar activity indices is supposed (Voloshin  {\it et  al.},  1986,  Rivin,
1993)  According  to  this  hypothesis,  the  neutrino  flux  passing
through a  strong  magnetic  field  is  modulated,  as  part  of  the
left--hand neutrino are transformed into  the  right--hand  neutrino.
The modulation mainly depends on two factors: the magnetic moment  of
the neutrino and the absolute value of the transverse magnetic field
component. This modulation is  difficult  to  obtain  in  laboratory.
However there is evidence indicating that it occurs in  the  Sun,  as
the high--energy neutrino flux  from  the  core  passes  through  the
magnetic field in the solar convection zone.

     To verify this hypothesis, it is essential to  choose  an  index
that would characterize most adequately the  magnetic  field  in  the
solar interior along the neutrino propagation line. Such indices used
in early work are the Wolf number or  the  mean  photospheric  field.
However both of them are dissatisfactory, as they are global  indices.
We have used magnetic field measured every day from the Zeeman effect
at  intersection  of  the  ``solar  center -- Earth''  line   with   the
photosphere. The data were obtained at the John Wilcox Observatory of
the Stanford University (WSO). These observations started in May 1976
(Carrington rotation 1641) and the data  are  available  up  to  1992
inclusive (Hoeksema and Scherrer, 1986; Hoeksema, 1991). The  earlier
period since 1970 is covered by the data obtained at the Mount Wilson
Observatory (MWO) by Robert Howard's group and kindly placed  at
our disposal by J. Stenflo. Both data series are used in our  analysis
in spite of some nonuniformity.

     These measurements based on potential approximation can be  used
to calculate the daily and, then, the annual mean values of the three
magnetic field  components  ($B_r$,  $B_{\theta}$, and  $B_{\varphi}$
--- the radial, meridional and  azimuthal  components,  respectively).
The error is shown to be no more than $\sim10\%$. Since the neutrino flux
propagates radially  from  the  solar  interior  to  the  Earth,  the
absolute values of the two latter components  must  play  a  decisive
role in its modulation.

     The high--energy boron neutrino flux ($E\simeq0.1$  MeV)  from
the solar core has been measured at South Dakota  (USA)  since  1970.
The data of several observation runs with their errors are  given  in
(Bahcall, 1993). As the runs are different in length,  the  scale  of
data is nonuniform. We have applied linear interpolation to obtain  a
uniform scale as a\break
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\centerline{2}
\vskip 1mm
\noindent
series of monthly mean values covering  the  whole
observation interval. These have been  used  in  turn  to  yield  the
annual mean values, as well as the mean square root error.

     The data from individual runs have  been  analyzed  to  give  an
average signal--to--noise ratio equal to $\simeq0.5$.  This  ratio
however grows to $\simeq2-2.5$ when  the  annual  mean  values  are
considered.

These facts allow us to compare the neutrino flux variations
and the absolute values of the magnetic field  components  along  the
flux  propagation  line  over  a  time  interval  of  22  years.  The
correlation  coefficient  between  the  neutrino  flux   and   $<\mid
B_{\theta}\mid>$, $<\mid B_{\varphi}\mid>$,  and  $<\mid  R_r\mid>$  was
found  to  be  $-0.66$,  $-059$,  and  $-0.62$,  respectively.  Note   that
correlation coefficient with the Wolf number is as small as $-0.37$. On
the other hand, the correlation coefficient reaches $-0.84$ if only the
uniform data series from Stanford is used.

     The  high  correlation  coefficient  indicates  a   possible
relationship between both phenomena. As should  be  expected,  it  is
most  pronounced  when  direct  physical parameters of magnetic  fields  are  considered.
Relationship  between  the  neutrino  flux  and  the  average   field
components ($<B_{\theta}>$,  $<B_{\varphi}>$,  $<B_r>$)  is  practically
absent (correlation coefficient from $-0.35$ to $-0.15$).

     Besides South Dakota, neutrino measurements (though much shorter
series) were  also  obtained  with  the  Japanese  neutrino  detector
Kamiokande--II. The annual mean values of the neutrino flux from  both
detectors show a good agreement over the time interval of  1988--1991.
It should be noted that neutrino flux variations over  this  interval
are relatively small compared to the Wolf numbers, so that dependence
on the solar cycle may not exist. This inconsistency can be avoided
by using direct physical parameters. In  fact,  the  heights  of  the
solar maxima in Wolf numbers in 1979 and 1989 are practically  equal,
whereas the amplitude of magnetic field components in 1989  are  much  lower
than in 1979.

     Besides the  11--year  cycle,  the  $^{37}Ar$  curve  displays  a
significant  quasi--biennial  fluctuation  (Sakurai, 1979; Rivin,  1993).   In   time
variations of the absolute magnetic field values, this fluctuation is
absent.  Therefore  it  should  be  suppressed  to  obtain   adequate
correlation coefficients.

     Suppression has been realized  by  smoothing  the  original  data
series over 3--year intervals. For the smoothed data, the  correlation
coefficients of  the  neutrino  flux  with  $<\mid  B_{\theta}\mid>$,
$<\mid
B_{\varphi}\mid>$, and $<\mid B_r\mid>$ increases to make $-0.79$, $-0.79$, and
$-0.85$, respectively. The correlation coefficient with the Wolf number
also increases ($-0.60$), but it still remains lower  than  correlation
between $^{37}Ar$ and the field components. And  finally,  comparison
of the smoothed neutrino data with a uniform series of magnetic field
data from WSO yields a correlation coefficient as high as $-0.90$.

\medskip
Our conclusions are as follows:
\medskip

     1. The fact that linear correlation between  the  neutrino  flux
and the solar magnetic field increases  significantly  when  absolute
values of the magnetic field components along the ``solar  center ---
Earth'' line are considered, as well as high correlation coefficients
themselves suggest that solar magnetic  fields  are  responsible  for
variations of the high--energy neutrino flux from the  solar  interior
detected at South Dakota.

     2. As the absolute  values  of  the  magnetic  field  components
display mainly an 11--year variation, the neutrino flux  is  modulated
by the fields in the convection (or maybe even  radiative)  zones  in
the Sun. These are the fields that determine the basic solar activity
cycle with a period of $\simeq22$ years.
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\centerline{3}
\vskip 1mm

     3.  The  fact  that  magnetic  field  curves  do   not   display
significant quasi--biennial fluctuation that is present in the  curve
of  the  neutrino  flux  shows  that  generation  of   quasi--biennial
fluctuations has nothing to do with the fields  of  the  basic  solar
cycle, but is rather due to the thermal processes in the solar  core,
as suggested by Sakurai (1979).


Acknowlegment. The authors are grateful to  J.T. Hoeksema  and  J.O. Stenflo  for
observation data that were  kindly  placed  at  our  disposal prior to
publication. The work was sponsored by  the  Russian  Foundation  for
Fundamental Research (grant N 93--02--02886).


\vskip 1cm

\beginauthors
\authorsrightcol
V.N. OBRIDKO

Yu.R. RIVIN

Institute of Terrestrial Magnetism,

Ionosphere and Radio Wave

Propagation

of Russian Academy of Sciences

Troitsk

Moscow Region 142092

Russia

\endauthors

\references

Bahcall, J.N., 1993, {\it Neutrino Astrophysics}, M., Mir, 623 p.

Hoeksema, J.T., 1991, {\it Report CSSA-ASTRO-91-01}, USA

Hoeksema, J.T., Scherrer, P.H., 1986, {\it WDCA,  UAG  Report 94},
    Boulder, USA

Rivin, Yu.R., 1993, {\it AZh.}, {\bf 70}, 392

Sakurai, K., 1979, {\it Nature}, {\bf 278}, 146

Voloshin, M.B., Vysotsky, M.I., Okun, L.B., 1986, {\it ZhETF}, {\bf 91}, 754

\end{document}

