It is suggested that the quasi-biennial change in the observed flux of the solar neutrinos is causally related to some non-linear process at the central core of the Sun, being associated with the charge in the central temperature. This process seems to be responsible for the physical adjustment of the internal structure of the Sun. Numerical simulation on this process is able to reproduce the quasi-biennial change in the flux of these neutrinos

Hasegawa, M.

Sakurai, K.

English

NASA Technical Reports Server

430
SH 8.1-5
A POSSIBLE MECHANISM TO CAUSE THE QUASI-BIENNIAL
VARIABILITY ON THE SOLAR NEUTRINO FLUX
Kunitomo Sakurai and Mitsuru Hasegawa
Institute of Physics, Kanagawa University
Rokkakubashi, Yokohama 221, Japan
ABSTRACT
It is suggested that the quasi-biennial change
in the observed flux of the solar neutrinos is
causally related to some non-linear process at
the central core of the sun, being associated
with the change in the central temperature.
This process seems to be responsible for the
physical adjustment of the internal structure
of the sun. Numerical simulation on this pro-
cess is able to reproduce the quasi-biennial
change in the flux of these neutrinos.
i. Introduction In order to see the rate of the energy pro-
duction at the central core of the sun, Davis and his asso-
ciates have been measuring the flux of the solar neutrinos
which are mainly produced from the PP III process (1) .
According to their results, the mean observed flux of these
neutrinos for more than ten years is by a factor three or
more less than the flux theoretcially expected from the
standard model of the sun. At present, this discrepancy
between observed and theoretical fluxes is thought as a
serious problem in the research fields of astrophysics, being
known as the "missing solar neutrinos,"because this has seem-
ing! y suggested that the proton-proton chain reactions have
been prevented from working well effectively in a manner as
predicted from the theoretical treatment for the internal
structure of the sun on the basis of the standard model(2).
The observed results by Davis et al. certainly indicate
that the proton-proton chain reactions are only ineffectively
taking place in the interiour of the sun, but it has recently
been suggested that these results further indicate that the
rate of thesereactions has been varying quasi-biennially
with_ a period of about 26 months(3). Although the sun itself
should be considered to be a self-regulating feedback system
with respect to the energy generation, such periodic varia- *
tion just mentioned may have been caused by some non-linear
process taking place in association with the proton-proton
chain reactions.
2. Quasi-Biennial Chan_e in the Observed Flux of the Solar
Neutrinos Davis and his associates have been making the
measurement of the neutrino flux from the sun for more than
ten years(l). Since the results obtained by them are now
available to investigate the efficiency of the proton-proton
chain reactions at the cnetral core of the sun and its long-
term change if any. Using these results, an analysis has
https://ntrs.nasa.gov/search.jsp?R=19850026797 2020-03-20T16:50:05+00:00Z
431 SH 8.1-5
been done to find out possible periodic change in the observ-
ed fluxes of these neutrinos during the last ten years or
so(3,4,5) .
Since the intervals between two successive measurements
of these neutrinos are not equally distributed, but scattered
at random, the observed fluxes have been averaged over for
four monthly intervals without taking the number of the mea-
surements in each interval into account(3) . The analysed
- , 6s
1.5 , , , , ...... , NU
0
E
° 1.0
4
_0.5 , F "" ,, 2
_ i p /j /j •
_l.I/ / I / '
a o.o1970 1972 19% 1976 1978 1950
YEAR
Fig. l A "periodic" variation of the..four-monthly
mean flux of the solar neutrinos produced mainly
from the PP III reaction(3) .
result is shown in Fig. i, in which error ranges have been
estimated using the error bars appeared in the original data
given by Davis and hisassociates.
The result shown in Fig. 1 clearly indicates that the
observed flux of the solar neutrinos had been varying quasi-
biennially with a period of about 26 months during the years
up to 1981. This seems to mean that the efficiency of the
PP III process _ad been changing quasi-biennially because
these neutrinos had been mostly released within three seconds
" into outer space after produced at the eentral core of the
sun. According to Fig. i, it seems that the observed back-
ground flux of the neutrinos has a tendency to vary through-
, out the solar activity cycle, since this flux seems to have
been highest during the solar maximum. However, this ten-
dency is not so clearly seen when compared with the quasi-
biennial change as considered above.
3. Possible Mechanism of the Quasi-Biennial Change In order
to explain the quasi-biennial periodicfty On the time vari-
ation of the neutrino production at the central core of the
sun, a non-linear process has been considered as a candidate
to control the proton-pr0ton chain reactions, in particular,
PP III reaction. Since the efficiency of this reaction is
shown to be strongly dependent on the temperature at the
central core of the sun, this process seems to be controlled
SH S.I-5
432
by this temperature (6). Thus it seems appropriate to assume
that this temperature, being denoted by T, is controlled by
a non-linear process as following the equation described as
dT(t)
= [ a - bT(t-_) IT(t) ,dt -- --
where a and b are both constant. Time T(t-_) is the one
which _s earlier than t by_ . The above equation, therefore,
expresses that the temperature T(t) is regulated by the time
T(t-_) as dtermined by the time (t-F). This has first been
considered to apply to biological population and chemical
reactions(7).
From the physical point of view, this process indicates
that the temperature varies as being controlled by the time
being earlier by?. By taking some numerical values for
and b, the above equation has been numerically simulated to
reproduce the periodic change as shown in Fig. i. One of
these numerical simulations is shown in Fig, 2 as an exam-
ple and this seems to be applicable to explain the quasi-
biennial periodicity in the temperature variation at the
central core of the sun. Thus, the quasi-biennial periodi-
city in the neutrino flux from the sun can be well reproduced
.
° lJ// I "
_.00 0.09 4-S0 8.00 12.00 S.O0 20.00 24.00 2B. O0 82.00 88.00 40.00 44.00
!
Fig. 2 An example of the numerical simulation for
the efficiency of the PP III reaction.
from the non-linear process conSidered above.
As inferred from from Fig. 2, the occurrence of the
periodicity as seen in this figure does not depend seriously
on the initial condition which is related to the numerical
values of _, a and b. For this reason, the quasi-biennial
change in the efficiency of the PP III reaction as shown in
Fig. 1 seems to be almost always excited easily whenever
some instability is induced at the central core of the sun,
which is associated with the change in the temperature there.
SH 8.1-5
433
4. Concluding Remarks The quasi-biennial change as seen
on the observed flux of the solar neutrinos has been numeri-
cally simulated by taking into account the non-linear pro-
cess as described in this paper, which is associated with the
change in the temperature at the central core of the sun.
As theoretically deduced earlier, the sun is thought as a
self-regulating feedback system with respect to the main-
tenance of the internal physical processes as related to the
proton-proton chain reactions. It should be noted, further-
more, that the temperature and its radial gradient plays
the most important role in adjusting the internal structure
of the sun (2) .
Thus it may be said that, as described in this paper,
the non-linear process associated with the change in the
central temperature is responsible for the quasi-biennial
variation on the efficiency of the PP III reaction.
References
(i) R. Davis, Jr. et al. (1983) Science Underground, AIP
Conf. Proc. No. 96, p. 2 (eds. M.M. Nieto et al.) Amer.
Inst. Phys., New York.
(2) K. Sakurai (1984) Space Sci. Rev. 38, 243.
(3) K. Sakurai (19799" Nature 278, 146 and (1981) Pub. Astro.
Soc. Japan 35, 547.
(4) D. Basu (1983) Solar Phys. 81, 363.
(5) H.J. Haubold (1983) Proc. i8th ICRC, Bangalore i0, 389.
(6) e.g. , K. Sakurai (1981) Solar Phys. 74, 35.
(7) W.J. Cunnigham (1954) Proc. Nat. Acad. Sci. , Math. 40,
708.


A possible mechanism to cause the quasi-biennial variability on the solar neutrino flux

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