Stars as Laboratories for Fundamental Physics - MPP Theory Group

Solar Neutrinos 351
a certain range of neutrino masses and mixing angles (Sect. 10.3.4).
Of course, the Superkamiokande detector with its much improved sensitivity
and lower threshold could still detect a deviation; this would
be a clear indication for neutrino oscillations or other neutrino-related
novel phenomena.
For the neutrino lines from e − + 7 Be → 7 Li + ν e (861.8 keV) and
e − + 7 Be → 7 Li ∗ + ν e (384.3 keV) thermal broadening effects are of some
interest because they dominate the line shape. A detailed discussion
is found in Bahcall (1994) who calculated the observable spectra at
Earth shown in Fig. 10.4 where E 0 is the energy of the transition in
the laboratory. The peak of the lines is shifted to higher energies by
0.43 and 0.19 keV, respectively, while the average energy is shifted by
an even larger amount because of the asymmetric form. Perhaps in
some next-century detector this line shape could be used to measure
the central temperature of the Sun.
10.2.2 Standard Solar Models
In order to calculate the expected solar neutrino flux at Earth one
needs to construct a model of the Sun. A “standard solar model” is
obtained by solving the stellar structure equations discussed in Sect. 1.2
in several time steps to evolve it to the solar age of 4.5×10 9 yr. At this
point it must produce the observed present-day luminosity of the Sun
of 1 L ⊙ = 3.85×10 33 erg s −1 (it is about 30% brighter than a zero-age
model). This agreement is enforced by tuning the unknown presolar
helium abundance Y initial to the required value which is usually found
to be about 27%.
Another present-day boundary condition is the measured solar radius
of 1 R ⊙ = 6.96×10 10 cm which is adjusted by the mixing-length
parameter which enters the standard treatment of convection. In the
Sun, the outer layers (depth about 0.3 R ⊙ ) are found to be convective;
in lower-mass main-sequence stars convection reaches deeper, in highermass
ones it disappears entirely near the surface while the central region
becomes convective. The Sun calibrates the mixing-length parameter
which is then used in evolutionary calculations of other stars.
In order to calculate a standard solar model one needs a variety of
calculated or measured input information, notably the photon opacities,
the equation of state, nuclear cross sections with an appropriate
screening prescription, diffusion coefficients, a prescription to treat convection,
the abundances of metals (elements heavier than helium), and
the solar age, luminosity, and radius. Because of the large number