Joseph Lazio <jlazio@patriot.net>

A middle-aged main-sequence star like the Sun is in a slowly-evolving
equilibrium, in which pressure exerted by the hot gas balances the
self-gravity of the gas mass. Slow evolution results from the star
radiating energy away in the form of light, fusion reactions occurring
in the core heating the gas and replacing the energy lost by
radiation, and slow structural adjustment to compensate the changes in
entropy and composition.

We cannot directly observe the center, because the mean-free path of a
photon against absorption or scattering is very short, so short that
the radiation-diffusion time scale is of order 10 million years.  In
other words, the energy produced in the Sun's center and carried by
photons takes about 10 million years to make its way to the Sun's
surface.  But the main proton-proton reaction (PP1) in the Sun
involves emission of a neutrino:

       PP1:     p + p --> D + positron + neutrino(0.26 MeV),

which is directly observable since the cross-section for interaction
with ordinary matter is so small (0.26 MeV is the average energy
carried away by the neutrino).  Essentially all the neutrinos escape
the Sun. Of course, this property also makes it difficult to detect
the neutrinos. The first experiments by Davis and collaborators,
involving large tanks of chloride fluid placed underground, could only
detect higher-energy neutrinos from small side-chains in the solar
fusion:

        PP2:    Be(7) + electron --> Li(7) + neutrino(0.80 MeV),
        PP3:    B(8) --> Be(8) + positron + neutrino(7.2 MeV).

Recently, however, the GALLEX experiment, using a gallium-solution
detector system, has observed the PP1 neutrinos to provide the first
unambiguous confirmation of proton-proton fusion in the Sun.

There are some discrepancies, however.  

1. The first, and most well-known, "solar neutrino problem" is that
every experiment has measured a shortfall of neutrinos. About one- to
two-thirds of the neutrinos expected are observed, depending on
experimental error. In the case of GALLEX, the data read 80 units
where 120 are expected, and the discrepancy is about two standard
deviations.

2. The second solar neutrino problem arises when one compares the
number of neutrinos detected at various detectors.  The Kamiokande
experiment detects neutrinos by their interaction with water while the
experiment by Davis uses chlorine.  One can use the Kamiokande
experiment to predict how many neutrinos can be detected in Davis'
experiment.  The observed number is only 80% that of the predicted
number.

3. The third problem arises when one compares how many neutrinos are
expected from the various processes shown above.  The observed number
of neutrinos in the gallium experiments can be compared with the
number expected from the PP1 process and from the PP3 process, after
accounting for the fact that the gallium experiments only see a
fraction of the PP3 process neutrinos.  The observed number agrees
with the expected number.  But that means that the PP2 process cannot
contribute any neutrinos.

To explain these various shortfall, one of two things must be the
case: (1) the temperature in the Sun's core is slightly less than we
think it is, or (2) something happens to the neutrinos during their
flight over the 150-million-km journey to Earth. A third possibility
is that the Sun undergoes relaxation oscillations in central
temperature on a time scale shorter than 10 Myr, but since no one has
a credible mechanism this alternative is not seriously entertained.

(1) The fusion reaction rate is a very strong function of the
temperature, because particles much faster than the thermal average
account for most of it. Reducing the temperature of the standard solar
model by 6 per cent would entirely explain GALLEX; indeed, Bahcall has
ublished an article arguing that there may be no solar
neutrino problem at all. However, the community of solar
seismologists, who observe small oscillations in spectral line
strengths due to pressure waves traversing through the Sun, argue that
such a change is not permitted by their results.

(2) A mechanism (called MSW, after its authors) has been proposed, by
which the neutrinos self-interact to periodically change flavor
between electron, muon, and tau neutrino types. Here, we would only
expect to observe a fraction of the total, since only electron
neutrinos are detected in the experiments. (The fraction is not
exactly 1/3 due to the details of the theory.) Efforts continue to
verify this theory in the laboratory. The MSW phenomenon, also called
"neutrino oscillation", requires that the three neutrinos have finite
and differing mass, which is also still unverified.

To use explanation (1) with the Sun in thermal equilibrium generally
requires stretching several independent observations to the limits of
their errors, and in particular the earlier chloride results must be
explained away as unreliable (there was significant scatter in the
earliest ones, casting doubt in some minds on the reliability of the
others).  Further data over longer times will yield better statistics
so that we will better know to what extent there is a
problem. Explanation (2) depends of course on a proposal whose
veracity has not been determined. Until the MSW phenomenon is observed
or ruled out in the laboratory, the matter will remain open.

In summary, fusion reactions in the Sun can only be observed through
their neutrino emission. Fewer neutrinos are observed than expected,
by two standard deviations in the best result to date. This can be
explained either by a slightly cooler center than expected or by a
particle-physics mechanism by which neutrinos oscillate between
flavors. The problem is not as severe as the earliest experiments
indicated, and further data with better statistics are needed to
settle the matter.

References:

[0] The main-sequence Sun: D. D. Clayton, Principles of Stellar Evolution
    and Nucleosynthesis, McGraw-Hill, 1968. Still the best text.
[0] Solar neutrino reviews: J. N. Bahcall and M. Pinsonneault, Reviews of
    Modern Physics, vol 64, p 885, 1992; S. Turck-Chieze and I. Lopes,
    Astrophysical Journal, vol 408, p 347, 1993. See also J. N. Bahcall,
    Neutrino Astrophysics (Cambridge, 1989); J. N. Bahcall, "Solar
    Neutrinos: Where We Are, Where We Are Going," 1996, Astrophysical
    Journal, vol. 467, p. 475.
[1] Experiments by R. Davis et al: See October 1990 Physics Today, p 17.
[2] The GALLEX team: two articles in Physics Letters B, vol 285, p 376
    and p 390. See August 1992 Physics Today, p 17. Note that 80 "units" 
    correspond to the production of 9 atoms of Ge(71) in a solution 
    containing 12 tons Ga(71), after three weeks of run time!
[3] Bahcall arguing for new physics: J. N. Bahcall and H. A. Bethe,
    Physical Review D, vol 47, p 1298, 1993; against new physics: J. N. 
    Bahcall et al, "Has a Standard Model Solution to the Solar Neutrino 
    Problem Been Found?", preprint IASSNS-94/13 received at the National
    Radio Astronomy Observatory, 1994.    
[4] The MSW mechanism, after Mikheyev, Smirnov, and Wolfenstein: See the
    second GALLEX paper.
[5] Solar seismology and standard solar models: J. Christensen-Dalsgaard 
    and W. Dappen, Astronomy and Astrophysics Reviews, vol 4, p 267, 1992;
    K. G. Librecht and M. F. Woodard, Science, vol 253, p 152, 1992. See
    also the second GALLEX paper.