We decided some time ago to analyze the data in as model independent a
context as possible [9,51]. Though most explicitly-constructed
nonstandard models involve either the temperature or the cross sections
[9,12] there is always the possibility of very nonstandard
physical inputs which cannot be described in this way. The idea in a model
independent analysis is that all that really matters for the neutrinos are
the magnitudes 
, 
, 
and 
of the
various flux components. We can then analyze the data making only three
minimal assumptions. One is that the solar luminosity is quasi-static and
generated by the normal nuclear fusion reactions. This leads
to the constraints (6) and (7). The second
assumption is that astrophysical mechanisms cannot distort the shape of the
spectrum significantly from what is given by normal weak interactions.
Nobody has found any astrophysical mechanism that can significantly distort
the shape, and all explicitly studied mechanisms are negligibly small
[35]. It is this assumption which differentiates
astrophysical mechanisms from MSW, which can distort the shape
significantly. Our third assumption is that the experiments are correct, as
are the detector cross section calculations.
In this (almost) most general possible solar model all one has to play with
are the four neutrino flux components subject to the luminosity
constraint. The strategy is to fit the data to the 
and 
fluxes.
For each set of fluxes, one varies 
and 
so as to
get the best fit. The CNO and other minor fluxes play little role because
they are bounded below by zero, and larger values make the fits worse. The
constraints from the individual classes of experiments are shown in
Figure 3.
Figure: 
and 
fluxes relative to the standard
solar model prediction as constrained by different classes of experiments.
The SSM corresponds to the point (1,1) while the uncertainties in the SSM
are shown as an ellipse. From [50].
Figure 4 displays the allowed region from all data. The best fit
would occur in the unphysical region of negative 
fluxes.
Constraining the flux to be positive, the best fit requires 
and 
of the SSM [9,10]. This, however, has a
poor 
. One finds 
for 1 d.f., which is
excluded at 93% CL, i.e., it is only marginally
allowed statistically.
More important, the best fit it is in a region that is hard to account
for by astrophysical mechanisms. Figure 4 also
displays predictions of the BP and TCL standard solar models, the 1,000
Monte Carlos SSMs of Bahcall and Ulrich (dots) [46], other explicitly
constructed nonstandard models [52], and the general predictions of
cool sun and low 
models.
Most of the nonstandard models are approximately parameterized by the cool
sun models [9,12], but none come close to what is required by
the data. As can be seen in the figure, the low 
models are
especially far from the observation. The problem is that the data is
requiring an almost total suppression of 
neutrinos compared to the
neutrinos [8]--[14].
That is hard to understand astrophysically,
because boron is produced from the beryllium by proton capture. If one
gets rid of all of the beryllium there is no plausible explanation of why
so much 
is still produced.
People have occasionally questioned the validity of the Homestake results,
although there is no clear reason to doubt them. In fact, the data is now
sufficiently good that one can draw the same conclusion about the complete
suppression of 
neutrinos from any two types of experiments, as can be
seen in Table 4. For example, Figure 5 shows the
constraint if the chlorine data is omitted. In this case the overall
is acceptable, but the allowed region is still not consistent with
any explicit solar model.
One concludes that it is unlikely that any NSSM will explain the data
unless at least two of the experiments are wrong [10,11,13].
One can reach much the same conclusion in another way. In Figure 6 the predictions for gallium are shown for various explicitly constructed nonstandard models which agree with Kamiokande but ignore the Homestake rate. All of the explicit models predict rates in excess of 100 SNU, well above the combined observations.
Figure: 90% CL combined fit for the 
and 
fluxes. The best fit,
which occurs at 
% and 
relative to the SSM, has a poor 
of 3.3 for 1 d.f. Also shown are
the predictions of the BP and TCL SSM's, 1000 Monte Carlo SSM's
[46], various nonstandard solar models, and the models
characterized by a low 
or low 
. From
[9,10,50].
Figure: Constraints on the 
and 
fluxes without the Homestake
data.
Table: Predicted fluxes compared to the 
standard solar model for
various combinations of experiments. From [10].
Figure: Predictions for the gallium rate
of explicit nonstandard models which agree with
Kamiokande, compared with the experimental
observations. From [49,50].