Abstract
We consider to what extent the long-term dynamics of cyclic solar activity in the form of Grand Minima can be associated with random fluctuations of the parameters governing the solar dynamo. We consider fluctuations of the alpha coefficient in the conventional Parker migratory dynamo, and also in slightly more sophisticated dynamo models, and demonstrate that they can mimic the gross features of the phenomenon of the occurrence of Grand Minima over suitable parameter ranges. The temporal distribution of these Grand Minima appears chaotic, with a more or less exponential waiting time distribution, typical of Poisson processes. In contrast, however, the available reconstruction of Grand Minima statistics based on cosmogenic isotope data demonstrates substantial deviations from this exponential law. We were unable to reproduce the non-Poissonic tail of the waiting time distribution either in the framework of a simple alpha-quenched Parker model or in its straightforward generalization, nor in simple models with feedback on the differential rotation. We suggest that the disagreement may only be apparent and is plausibly related to the limited observational data, and that the observations and results of numerical modeling can be consistent and represent physically similar dynamo regimes.
Similar content being viewed by others
References
Abarbanel, H.D., Brown, R., Sidorowich, J.J., Tsimring, L.Sh.: 1993, Rev. Mod. Phys. 65, 1331.
Baliunas, S., Frick, P., Moss, D., Popova, E., Sokoloff, D., Soon, W.: 2006, Mon. Not. Roy. Astron. Soc. 365, 181.
Brandenburg, A., Sokoloff, D.: 2002, Geophys. Astrophs. Fluid Dyn. 96, 319.
Brandenburg, A., Spiegel, E.: 2008, Astron. Nachr. 329, 351.
Brandenburg, A., Krause, F., Meinel, R., Tuominen, I., Moss, D.: 1989, Astron. Astrophys. 213, 411.
Brooke, J., Moss, D., Phillips, A.: 2002, Astron. Astrophys. 395, 1013.
Charbonneau, P.: 2005, Living Rev. Solar Phys. 2(2). http://solarphysics.livingreviews.org/Articles/lrsp-2005-2/.
Covas, E., Tavakol, R., Tworkowski, A., Brandenburg, A.: 1998, Astron. Astrophys. 329, 350.
Gleissberg, W.: 1944, Terr. Magn. Atmos. Electr. 49, 243.
Gruzinov, A.V., Diamond, P.H.: 1994, Phys. Rev. Lett. 72, 1651.
Jennings, R.L.: 1991, Geophys. Astrophys. Fluid Dyn. 57, 147.
Jennings, R.L., Weiss, N.O.: 1991, Mon. Not. Roy. Astron. Soc. 252, 249.
Hoyng, P.: 1993, Astron. Astrophys. 272, 321.
Hoyng, P., Schmitt, D., Teuben, L.J.W.: 1994, Astron. Astrophys. 289, 265.
Kuzanyan, K.M., Sokoloff, D.D.: 1996, Astron. Rep. 40, 425.
Moss, D., Brandenburg, A., Tavakol, R.K., Tuominen, I.: 1992, Astron. Astrophys. 265, 843.
Moss, D., Brooke, J.: 2000, Mon. Not. Roy. Astron. Soc. 315, 521.
Otmianowska-Mazur, K., Kowal, G., Hanasz, M.: 2006, Astron. Astrophys. 445, 915.
Ossendrijver, A.J.H., Hoyng, P.: 1996, Astron. Astrophys. 313, 959.
Parker, E.: 1955, Astrophys. J. 122, 293.
Petrovay, K.: 2000, In: Wilson, A. (ed.) The Solar Cycle and Terrestrial Climate, Solar and Space Weather 463, ESA, Noordwijk, 3.
Petrovay, K.: 2007, Astron. Nachr. 328, 777.
Ruzmaikin, A.: 2001, Space Sci. Rev. 95, 43.
Sokoloff, D.D., Fioc, M., Nesme-Ribes, E.: 1996, Magnetohydrodynamics 31, 18.
Soon, W.H., Posmentier, E.S., Baliunas, S.L.: 1996, Astrophys. J. 472, 891.
Stefani, F., Xu, M., Sorriso-Valvo, L., Gerbeth, G., Günther, U.: 2007, Geophys. Astrophys. Fluid Dyn. 101, 227.
Tobias, S.M., Weiss, N.O., Kirk, V.: 1995, Mon. Not. Roy. Astron. Soc. 273, 1150.
Tworkowski, A., Tavakol, R., Brandenburg, A., Brooke, J.M., Moss, D., Tuominen, I.: 1998, Mon. Not. Roy. Astron. Soc. 296, 287.
Usoskin, I.G., Solanki, S.K., Kovaltsov, G.A.: 2007, Astron. Astrophys. 471, 301.
Zeldovich, Ya.B., Ruzmaikin, A.A., Sokoloff, D.D.: 1991, The Almighty Chance, World Science, Singapore.
Zhang, H., Sokoloff, D., Rogachevskii, I., Moss, D., Lamburt, V., Kuzanyan, K., Kleeorin, N.: 2006, Mon. Not. Roy. Astron. Soc. 365, 276.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Moss, D., Sokoloff, D., Usoskin, I. et al. Solar Grand Minima and Random Fluctuations in Dynamo Parameters. Sol Phys 250, 221–234 (2008). https://doi.org/10.1007/s11207-008-9202-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11207-008-9202-z