  We show that there is a previously unreported quad-annual variation in the
~13.5 day component of the aa index of geomagnetic activity. We derive a model
based on the planetary tidal effect at the solar surface due to Mercury and
Jupiter that, when combined with an equinoctial response of the magnetosphere,
predicts the times of occurrence of predominantly quad-annual variation or
predominantly semi-annual variation in the ~13.5 day component of the aa index.
In support of the model we show that, during years when the quad-annual
variation in the ~13.5 day component of aa index is predominant there is a
large component at the 88 day periodicity of Mercury in the ~13.5 day component
of solar wind speed. As further support for the model we establish that
significant peaks in the aa index spectrum are due to an 88 day modulation of
27 day period solar activity. The model also predicts the occurrence of
planetary tidal effect maximum in anti-phase with solar cycle maximums around
1970 and we show this is consistent with prior observations of higher solar
emissions during the 1975 solar cycle minimum than in the following solar cycle
maximum. This effect offers a possible explanation of the reduced solar cycle
maximums around 1970 and during the Dalton Minimum.
