Astron. Astrophys. 360, 319-330 (2000)

Nonlinear analysis of solar cycles

T. Serre ¹ and E. Nesme-Ribes <sup>2

1</sup> 14, rue Jean Giono, 13 580 La Fare-les-Oliviers, France
² Observatoire de Paris, 5 Place Jules Janssen, 92 195 Meudon, France

Received 27 October 1998 / Accepted 11 May 2000

Abstract

In this paper, the recent improvement of the Wolf sunspot time-series by Hoyt and co-workers has been analysed with the Global Flow Reconstruction (GFR) method (Serre et al. 1996a and b). A nonlinear 4-dimensional chaotic model has been extracted from the data which captures the principal characteristic features of the sunspot group time-series. The hypothesis of interactions between magnetic modes is implicitly tested; presumably, this is the cause of the irregular variations of solar cycle amplitudes recorded since the year 1610. The present results indicate that interactions are occurring between few global magnetic modes.

Key words: chaos methods: data analysis Sun: sunspots

Send offprint requests to: T. Serre (Thierry.Serre@Wanadoo.fr)

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Contents

• 1. Introduction
• 2. The mechanism driving solar cycles: an alpha-omega dynamo
• 3. Sunspot group number (SGN) time series
• 4. Characteristics of solar cycles
• 5. The reconstruction of the dynamics from data
  • 5.1. Geometric reconstruction of the solar attractor
  • 5.2. Principles of dynamics reconstruction
• 6. Application to solar cycles
  • 6.1. The GFR method
  • 6.2. A fitting of the SGN time-series
  • 6.3. The construction of synthetic solutions
  • 6.4. Results
  • 6.5. Additional tests
    • 6.5.1. Principle of the Lyapunov exponent estimations
    • 6.5.2. Results
    • 6.5.3. Occurrence of the Maunder minima
• 7. Comparisons with other methods of signal analysis
• 8. Discussion and conclusion
• Acknowledgements
• References

© European Southern Observatory (ESO) 2000

Online publication: July 27, 2000
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