  Although sunspots have been systematically observed on the Sun's surface over
the last four centuries, their magnetic properties have been revealed and
documented only since the early 1900s. Sunspots typically appear in pairs of
opposite magnetic polarities which have a systematic orientation. This polarity
orientation is opposite across the equator -- a trend that has persisted over
the last century over which magnetic field observations exist. Taken together
with the configuration of the global poloidal field of the Sun -- that governs
the heliospheric open flux and cosmic ray flux at Earth -- this phenomenon is
consistent with the dipolar parity state of an underlying magnetohydrodynamic
dynamo. Although hemispheric asymmetry in the emergence of sunspots is observed
in the Sun, a parity shift has never been observed. We simulate hemispheric
asymmetry through the introduction of random fluctuations in a computational
dynamo model of the solar cycle and demonstrate that changes in parity are
indeed possible in long-term simulations covering thousands of years.
Quadrupolar modes are found to exist over a significant fraction of the
simulated time. In particular, we find that a parity shift in the underlying
nature of the sunspot cycle is more likely to occur when sunspot activity
dominates in any one hemisphere for a time which is significantly longer than
the cycle period. We establish causal pathways connecting hemispheric asymmetry
and cross-equatorial phase-shifts to parity flips in the underlying dynamo
mechanism. Our findings indicate that the solar cycle may have resided in
quadrupolar parity states in the distant past, and provides a possible pathway
for predicting parity flips in the future.
