  We investigate the energy dependence of the astrophysical $S$ factor for the
reaction $^7$Be$(p,\gamma)^8$B, the primary source of high-energy solar
neutrinos in the solar $pp$ chain. Using simple models we explore the model
dependence in the extrapolation of the experimental data to the region of
astrophysical interest near 20 keV. We find that below approximately 400 keV
the energy dependence is very well understood and constrained by the data for
the elastic scattering of low energy neutrons from $^7$Li. Above 400 keV
nuclear distortion of the wave function of the incident proton introduces a
significant model dependence. This is particularly important for the s-wave
contribution to the $S$ factor. The extracted value of S(0) is $19.0 \pm 1.0
\pm 0.2$~eVb. The first error is experimental while the second is an estimate
of the theoretical error in the extrapolation.
