Astron. Astrophys. 322, 1007-1017 (1997)

The solar cycle: parity interactions and amplitude modulation

S.M. Tobias

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, UK

Received 12 November 1996 / Accepted 6 December 1996

Abstract

Two mechanisms for producing modulation of the basic eleven year solar cycle are included in a nonlinear 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 of modulation in different parameter regimes. For a suitable choice of parameters solutions display behaviour similar to that observed on the Sun. The magnetic 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.

Key words: MHD Sun: magnetic fields; activity

Present address: Joint Institute for Laboratory Astrophysics, Boulder, Colorado, CO 80309-0440 USA

Contents

• 1. Introduction
• 2. Derivation of the model
• 3. Results for fixed
• 4. Dependence of solutions on
• 5. Discussion
• Acknowledgements
• Appendix A
• References

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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