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Waves of Solar Activity

Published online by Cambridge University Press:  12 April 2016

M.R.E. Proctor  and
E.A. Spiegel
M.R.E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, U.K.
E.A. Spiegel
Affiliation:
Department of Astronomy, Columbia University, New York, NY 10027, U.S.A.

Abstract

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We develop a theory of the sunspot cycle predicated on the assumption that the observed bands of activity are packets of dynamo waves. An approximate equation is proposed to describe the dynamics of these packets, using standard ideas from bifurcation theory. We show that in a certain limit the system can be described in terms of a slowly-evolving solitary wave, and that periodic behavior, like that of the observed butterfly diagram, can easily be found. Generalizations of the theory are discussed.

Type
Part II Current stellar dynamo theory
Information
International Astronomical Union Colloquium , Volume 130: The Sun and Cool Stars: activity, magnetism, dynamos , 1991 , pp. 117 - 128
Copyright
Copyright © Springer-Verlag 1991

References

Bibliographical notes

In this informal sketch of our ideas on the mathematics of the solar cycle, we have not given any explicit references since we have assumed that our readers have in mind the basic ideas that we are using. We shall of course make a careful accounting of the provenance of the basic ideas in a more detailed treatment that we shall prepare in the relatively near future. What we shall simply do here is to give some references to basic topics that we have drawn on in this discussion, dynamo theory and nonlinear instability theory.

The main physical assumption of this work is that there is lurking somewhere inside the sun, but accessible to convective upwelling, a thin-layer dynamo. The theory of such dynamos has been elaborated in terms of the ‘α-effect’ or two-scale model by

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