Proc. Neutrino Astrophysics - MPP Theory Group

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as follows: (1) All the detectors measure a significant neutrino flux, and so confirm that
nuclear energy generation actually takes place in the Sun. (2) The results of the two gallium
experiments agree with each other, and the results of the two water experiments agree with
each other. (3) All experiments measure a flux that lies significantly below the prediction of
the standard solar model. (4) The deficit depends on neutrino energy. This last point is of
particular interest for the solar model builder, because it is for this reason that it appears to
be impossible to repair all the deficits simultaneously by modifications of the solar model.
The significance of the neutrino deficit and its energy dependence has been illustrated by
a calculation of 1000 standard models [3] based on input parameters having normal distributions
with appropriate means and standard deviations. For the diverse neutrino experiments
these 1000 models predict results that have a certain spread but are clearly in conflict with
the actual measurements. If the predicted flux of energetic neutrinos originating from the
beta decay of 8 B is replaced by the value obtained in the water experiments (≈ 42% of the
predicted), then the predictions for the chlorine and gallium experiments become smaller
but are still significantly above the measurements. In other words, the existing experiments
cannot simultaneously be reconciled with the standard solar model.
In two recent calculations [13, 14] all the input parameters have been pushed to the extreme
in order to minimize the neutrino flux; nevertheless the prediction is still significantly too high.
Non-Standard Models
The aim of most non-standard solar models is to lower the temperature in the energygenerating
central region and thereby change the branching ratios of the three pp chains,
in particular in order to suppress a part of the high-energy 8 B neutrino flux. Castellani
et al. [9] discuss in detail the influence of the diverse input parameters on the central temperature
of the Sun. For example, a 45% increase of S11, or a 50% decrease of Z/X, or a 29%
decrease of the opacity would result in a 4% smaller central temperature. For the neutrino
fluxes resulting from 7 Be and 8 B the temperature dependence is [2]
Φν( 7 Be) ∝ T 8 c , Φν( 8 B) ∝ T 18
c .
Hence, a 4% cooler solar core reduces the predicted 8 B neutrino flux to 0.48 of the standard
value, and the flux of 7 Be neutrinos to 0.72. This may help to remove the discrepancy for the
water experiments, and to reduce the discrepancy for the chlorine experiment, but it provides
almost no help for the gallium experiments. Of the 137 snu (above table, last line) there
are only 16 from the decay of 8 B, but 38 from the electron capture of 7 Be. Thus a large
discrepancy remains; more specifically, the gallium experiments appear to leave no room for
the predicted 7 Be neutrinos. This is the major difficulty of the non-standard solar models.
Perhaps the neutrino discrepancy will finally be resolved by a combination of various
effects. A slight decrease of the central solar temperature Tc may be one of these effects,
although it is entirely unclear at present how such a decrease of Tc could be achieved. Heavy
element diffusion increases Tc, as we have seen. Mixing of the solar core apparently helps,
but the mixed-core model seems to fail the seismological test [28]. Other handles, such as
the opacity or the equation of state, permit only variations of Tc that are too small for a
substantial effect.
The conclusion is that most of the discrepancy should rather be resolved by non-standard
neutrinos. The energy-dependent conversion of electron neutrinos into other neutrino flavours
by the Mikeyev-Smirnov-Wolfenstein effect is a possibility; for a recent review see [17].