  A search for any particular feature in any single solar neutrino dataset is
unlikely to establish variability of the solar neutrino flux since the count
rates are very low. It helps to combine datasets, and in this article we
examine data from both the Homestake and GALLEX experiments. These show
evidence of modulation with a frequency of 11.85 yr-1, which could be
indicative of rotational modulation originating in the solar core. We find that
precisely the same frequency is prominent in power spectrum analyses of the
ACRIM irradiance data for both the Homestake and GALLEX time intervals. These
results suggest that the solar core is inhomogeneous and rotates with sidereal
frequency 12.85 yr-1. We find, by Monte Carlo calculations, that the
probability that the neutrino data would by chance match the irradiance data in
this way is only 2 parts in 10,000. This rotation rate is significantly lower
than that of the inner radiative zone (13.97 yr-1) as recently inferred from
analysis of Super-Kamiokande data, suggesting that there may be a second, inner
tachocline separating the core from the radiative zone. This opens up the
possibility that there may be an inner dynamo that could produce a strong
internal magnetic field and a second solar cycle.
