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Solar Physics

, 294:60 | Cite as

A Model of a Tidally Synchronized Solar Dynamo

  • F. StefaniEmail author
  • A. Giesecke
  • T. Weier
Article

Abstract

We discuss a solar dynamo model of Tayler–Spruit type whose \(\Omega \)-effect is conventionally produced by a solar-like differential rotation but whose \(\alpha \)-effect is assumed to be periodically modulated by planetary tidal forcing. This resonance-like effect has its rationale in the tendency of the current-driven Tayler instability to undergo intrinsic helicity oscillations which, in turn, can be synchronized by periodic tidal perturbations. Specifically, we focus on the 11.07-years alignment periodicity of the tidally dominant planets Venus, Earth, and Jupiter, whose persistent synchronization with the solar dynamo is briefly touched upon. The typically emerging dynamo modes are dipolar fields, oscillating with a 22.14-years period or pulsating with a 11.07-years period, but also quadrupolar fields with corresponding periodicities. In the absence of any constant part of \(\alpha \), we prove the sub-critical nature of this Tayler–Spruit type dynamo. The resulting amplitude of the \(\alpha \) oscillation that is required for dynamo action turns out to lie in the order of \(1~\mbox{m}\,\mbox{s}^{-1}\), which seems not implausible for the Sun. When starting with a more classical, non-periodic part of \(\alpha \), even less of the oscillatory \(\alpha \) part is needed to synchronize the entire dynamo. Typically, the dipole solutions show butterfly diagrams, although their shapes are not convincing yet. Phase coherent transitions between dipoles and quadrupoles, which are reminiscent of the observed behavior during the Maunder minimum, can easily be triggered by long-term variations of dynamo parameters, but may also occur spontaneously even for fixed parameters. Further interesting features of the model are the typical second intensity peak and the intermittent appearance of reversed helicities in both hemispheres.

Keywords

Solar cycle Models helicity Theory 

Notes

Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programm (grant agreement No 787544). The work was also supported in frame of the Helmholtz – RSF Joint Research Group “Magnetohydrodynamic instabilities: Crucial relevance for large scale liquid metal batteries and the sun–climate connection”, contract No HRSF-0044. We would like to thank Norbert Weber for his numerical work on the tidal synchronization of helicity oscillations. Inspiring discussions with Jürg Beer, Antonio Ferriz Mas, Peter Frick, Laurène Jouve, Günther Rüdiger, Dmitry Sokoloff, Rodion Stepanov and Teimuraz Zaqarashvili on various aspects of the solar dynamo are gratefully acknowledged. We thank Willie Soon for pointing out the importance of mid-term fluctuations, and for valuable comments on the Sun–star connection problem. We highly appreciate the constructive criticism of the anonymous reviewer which prompted us to significantly revise the paper.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Authors and Affiliations

  1. 1.Helmholtz-Zentrum Dresden-RossendorfDresdenGermany

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