Abstract
The north–south (N–S) asymmetry of solar activity is a known statistical phenomenon, but its significance is difficult to prove or to explain theoretically. Here we consider each solar hemisphere as a separate dynamical system connected with the other hemisphere via an unknown coupling parameter. We use a nonlinear dynamics approach to calculate the scale-dependent conditional dispersion (CD) of sunspots between hemispheres. Using daily Greenwich sunspot areas, we calculate the Neumann and Pearson chi-squared distances between CDs as indices showing the direction of coupling. We introduce an additional index of synchronization that shows the strength of coupling and allows us to distinguish between complete synchronization and independency of hemispheres. All indices are evaluated in a four-year moving window showing the evolution of coupling between hemispheres. We find that the driver-response interrelation changes between hemispheres have a few pulses during 130 years of Greenwich data with an at least 40-year-long period of unidirectional coupling. These sharp nearly simultaneous pulses of all causality indices are found at the decay of some 11-year cycles. The pulse rate of this new phenomenon of dynamic coupling is irregular: although the first two pulses repeat after the 22-year Hale cycles, the last two pulses repeat after three and four 11-year cycles, respectively. The last pulse occurs at the decay phase of Cycle 23, which means that the next pulse will likely appear during the decay of the future Cycle 25 or later. This new phenomenon of dynamic coupling reveals additional constraints for understanding and modeling the long-term behavior of solar activity cycles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andrzejak, R.G., Kraskov, A., Stögbauer, H., Mormann, F., Kreuz, T.: 2003, Bivariate surrogate techniques: Necessity, strengths, and caveats. Phys. Rev. E 68(6), 066202. DOI .
Bushby, P.J., Tobias, S.M.: 2007, On predicting the solar cycle using mean-field models. Astrophys. J. 661(2), 1289.
Carbonell, M., Oliver, R., Ballester, J.L.: 1993, On the asymmetry of solar activity. Astron. Astrophys. 274, 497. ADS .
Carbonell, M., Terradas, J., Oliver, R., Ballester, J.L.: 2007, The statistical significance of the north–south asymmetry of solar activity revisited. Astron. Astrophys. 476(2), 951. DOI .
Čenys, A., Lasiene, G., Pyragas, K.: 1991, Estimation of interrelation between chaotic observables. Physica D 52(2), 332. DOI .
Chatterjee, P., Choudhuri, A.R.: 2006, On magnetic coupling between the two hemispheres in solar dynamo models. Solar Phys. 239(1 – 2), 29. DOI .
Chatterjee, P., Nandy, D., Choudhuri, A.R.: 2004, Full-sphere simulations of a circulation-dominated solar dynamo: Exploring the parity issue. Astron. Astrophys. 427(3), 1019. DOI .
Chicharro, D., Andrzejak, R.G.: 2009, Reliable detection of directional couplings using rank statistics. Phys. Rev. E 80(2), 026217. DOI .
Deza, M.M., Deza, E.: 2006, Dictionary of Distances, Elsevier, Amsterdam.
dos Santos, A.M., Lopes, S.R., Viana, R.R.L.: 2004, Rhythm synchronization and chaotic modulation of coupled Van der Pol oscillators in a model for the heartbeat. Physica A 338(3), 335. DOI .
Goel, A., Choudhuri, A.R.: 2009, The hemispheric asymmetry of solar activity during the last century and the solar dynamo. Res. Astron. Astrophys. 9(1), 115. DOI .
Granger, C.W.: 1988, Some recent development in a concept of causality. J. Econom. 39(1), 199. DOI .
Hazra, G., Karak, B.B., Banerjee, D., Choudhuri, A.R.: 2015, Correlation between decay rate and amplitude of solar cycles as revealed from observations and dynamo theory. Solar Phys. 290(6), 1851. DOI .
Hotta, H., Yokoyama, T.: 2010, Solar parity issue with flux-transport dynamo. Astrophys. J. Lett. 714(2), L308. DOI .
Javaraiah, J.: 2015, Long-term variations in the north–south asymmetry of solar activity and solar cycle prediction, III: Prediction for the amplitude of solar cycle 25. New Astron. 34, 54. DOI .
Jiang, J., Chatterjee, P., Choudhuri, A.R.: 2007, Solar activity forecast with a dynamo model. Mon. Not. Roy. Astron. Soc. 381(4), 1527. DOI .
Karak, B.B., Choudhuri, A.R.: 2011, The Waldmeier effect and the flux transport solar dynamo. Mon. Not. Roy. Astron. Soc. 410(3), 1503. DOI .
Ma, H., Aihara, K., Chen, L.: 2014, Detecting causality from nonlinear dynamics with short-term time series. Sci. Rep. 4, 7464. DOI .
Mandal, S., Hegde, M., Samanta, T., Hazra, G., Banerjee, D., Ravindra, B.: 2017, Kodaikanal digitized white-light data archive (1921 – 2011). Analysis of various solar cycle features. Astron. Astrophys. DOI .
McCracken, J.M., Weigel, R.S.: 2014, Convergent cross-mapping and pairwise asymmetric inference. Phys. Rev. E 90(6), 062903. DOI .
McIntosh, S.W., Leamon, R.J., Krista, L.D., Title, A.M., Hudson, H.S., Riley, P., Harder, J.W., Kopp, G., Snow, M., Woods, T.N., Kasper, J.C., Stevens, M.L., Ulrich, R.K.: 2015, The solar magnetic activity band interaction and instabilities that shape quasi-periodic variability. Nat. Commun. 6, 6491. DOI .
Mininni, P.D., Gomez, D.O., Mindlin, G.B.: 2001, Simple model of a stochastically excited solar dynamo. Solar Phys. 201(2), 203. DOI .
Nagovitsyn, Yu.A., Kuleshova, A.I.: 2015, North–South asymmetry of solar activity on a long timescale. Geomagn. Aeron. 55(7), 887. DOI .
Olemskoy, S.V., Kitchatinov, L.L.: 2013, Grand minima and north–south asymmetry of solar activity. Astrophys. J. 777(1), 71. DOI .
Passos, D., Lopes, I.: 2008, A low-order solar dynamo model: Inferred meridional circulation variations since 1750. Astrophys. J. 686(2), 1420. http://iopscience.iop.org/article/10.1086/591511/meta .
Sauer, T., Yorke, J.A., Casdagli, M.: 1991, Embedology. J. Stat. Phys. 65(3 – 4), 579. DOI .
Shetye, J., Tripathi, D., Dikpati, M.: 2015, Observations and modeling of north–south asymmetries using a flux transport dynamo. Astrophys. J. 799(2), 220. DOI .
Sokoloff, D., Nesme-Ribes, E.: 1994, The Maunder minimum: A mixed-parity dynamo mode? Astron. Astrophys. 288, 293. ADS .
Sugihara, G., May, R., Ye, H., Hsieh, C.H., Deyle, E., Fogarty, M., Munch, S.: 2012, Detecting causality in complex ecosystems. Science 338(6106), 496. DOI .
Temmer, M., Rybák, J., Bendík, P., Veronig, A., Vogler, F., Otruba, W., Pötzi, W., Hanslmeier, A.: 2006, Hemispheric sunspot numbers Rn and Rs from 1945 – 2004: Catalogue and N–S asymmetry analysis for solar cycles 18 – 23. Astron. Astrophys. 447(2), 735. DOI .
Van der Pol, B., Van der Mark, J.: 1928, LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. Phil. Mag. 6(38), 763.
van Nes, E.H., Scheffer, M., Brovkin, V., Lenton, T.M., Ye, H., Deyle, E., Sugihara, G.: 2015, Causal feedbacks in climate change. Nat. Clim. Chang. DOI .
Volobuev, D.: 2006, “TOY” dynamo to describe the long-term solar activity cycles. Solar Phys. 238(2), 421. DOI .
Volobuev, D.M., Makarenko, N.G.: 2008, Forecast of the decadal average sunspot number. Solar Phys. 249(1), 121. DOI .
Volobuev, D.M., Makarenko, N.G.: 2016, The dynamic relation between activities in the northern and southern solar hemispheres. Geomagn. Aeron. 56(7), 880. DOI .
Acknowledgements
We thank the anonymous referee for useful discussions and suggestions that greatly improved the manuscript. The work was supported by the Russian Foundation for Basic Research, Project No. 15-01-09156.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Disclosure of Potential Conflicts of Interest
The authors declare that they have no conflicts of interest.
Rights and permissions
About this article
Cite this article
Volobuev, D.M., Makarenko, N.G. Long-Term Pulses of Dynamic Coupling Between Solar Hemispheres. Sol Phys 292, 68 (2017). https://doi.org/10.1007/s11207-017-1092-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11207-017-1092-5