The solar cycle: parity interactions and amplitude modulation

Two mechanisms for producing modulation of the basic eleven year solar cycle are included in a nonlinear αω dynamo model. In the first, the modulation of the toroidal magnetic field energy is associated with large changes in the parity (symmetry) of solutions. The second mechanism introduces modulation of the magnetic field by including the action of the Lorentz force in driving macrodynamic velocity perturbations (the Malkus-Proctor mechanism) in the limit of small magnetic Prandtl numbers. The nonlinear model shows that solutions can display both types ofmodulation in different parameter regimes. For a suitable choice of parameters solutions display behaviour similar to that observed on the Sun. Themagnetic field is significantly modulated whilst staying largely dipolar. However when the field is weak, during Grand Minima, the field is no longer symmetric and magnetic activity is confined to one hemisphere.