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The Shape of Solar Cycle Described by a Modified Gaussian Function

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Abstract

The shape of each sunspot cycle is found to be well described by a modified Gaussian function with four parameters: peak size A, peak timing t m, width B, and asymmetry α. The four-parameter function can be further reduced to a two-parameter function by assuming that B and α are quadratic functions of t m, computed from the starting time (T 0). It is found that the shape can be better fitted by the four-parameter function, while the remaining behavior of the cycle can be better predicted by the two-parameter function when using the data from a few (about two) months after the starting time defined by the smoothed monthly mean sunspot numbers. As a new solar cycle is ongoing, its remaining behavior can be constructed by the above four- or two-parameter function. A running test shows that the maximum amplitude of the cycle can be predicted to within 15% at about 25 months into the cycle based on the two-parameter function. A preliminary modeling to the first 24 months of data available for the current cycle indicates that the peak of cycle 24 may probably occur around June 2013±7 months with a size of 72±11. The above results are compared to those by quasi-Planck functions.

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References

  1. Cameron, R., Schüssler, M.: 2007, Astrophys. J. 659, 801.

  2. Choudhuri, A.R., Chatterjee, P., Jiang, J.: 2007, Phys. Rev. Lett. 98, 131103.

  3. Cohen, T.J., Lintz, P.R.: 1974, Nature 250, 398.

  4. Cole, T.W.: 1973, Solar Phys. 30, 103.

  5. Dikpati, M., de Toma, G., Gilman, P.A.: 2006, Geophys. Res. Lett. 33, L05102.

  6. Du, Z.L.: 2006, Astron. Astrophys. 457, 309.

  7. Du, Z.L.: 2011, Solar Phys. 270, 407.

  8. Du, Z., Du, S.: 2006, Solar Phys. 238, 431.

  9. Du, Z.L., Wang, H.N., He, X.T.: 2006, Chin. J. Astron. Astrophys. 6, 338.

  10. Du, Z.L., Wang, H.N., Zhang, L.Y.: 2009, Solar Phys. 255, 179.

  11. Elling, W., Schwentek, H.: 1992, Solar Phys. 137, 155.

  12. Gnevyshev, M.N., Ohl, A.I.: 1948, Astron. Zh. 25, 18.

  13. Hathaway, D.H.: 2010, Living Rev. Solar Phys. 7(1).

  14. Hathaway, D.H., Wilson, R.M., Reichmann, E.J.: 1994, Solar Phys. 151, 177.

  15. Hiremath, K.M.: 2008, Astrophys. Space Sci. 314, 45.

  16. Javaraiah, J.: 2005, Mon. Not. Roy. Astron. Soc. 362, 1311.

  17. Kane, R.P.: 2007, Solar Phys. 246, 487.

  18. Kane, R.P.: 2008, Ann. Geophys. 26, 3329.

  19. Kimura, H.: 1913, Mon. Not. Roy. Astron. Soc. 73, 543.

  20. Li, K.J.: 1999, Astron. Astrophys. 345, 1006.

  21. Nordemann, D.J.R.: 1992, Solar Phys. 141, 199.

  22. Nordemann, D.J.R., Trivedi, N.B.: 1992, Solar Phys. 142, 411.

  23. Obridko, V.N., Shelting, B.D.: 2008, Solar Phys. 248, 191.

  24. Ohl, A.I.: 1976, Soln. Dannye 9, 73.

  25. Pesnell, W.D.: 2008, Solar Phys. 252, 209.

  26. Petrovay, K.: 2010, Living Rev. Solar Phys. 7(6).

  27. Sabarinath, A., Anilkumar, A.K.: 2008, Solar Phys. 250, 183.

  28. Schwabe, H.: 1844, Astron. Nachr. 21, 233.

  29. Schatten, K.H., Scherrer, P.H., Svalgaard, L., Wilcox, J.M.: 1978, Geophys. Res. Lett. 5, 411.

  30. Stewart, J.Q., Panofsky, H.A.A.: 1938, Astrophys. J. 88, 385.

  31. Svalgaard, L., Cliver, E.W., Kamide, Y.: 2005, Geophys. Res. Lett. 32, L01104.

  32. Thompson, R.J.: 1993, Solar Phys. 148, 383.

  33. Turner, H.H.: 1913, Mon. Not. Roy. Astron. Soc. 73, 714.

  34. Vitinskii, Yu.I.: 1965, Solar-Activity Forecasting, Israel Program for Scientific Translations Jerusalem, NASA-TT-F-289.

  35. Vitinskij, Yu.I., Kopetskij, M., Kuklin, G.V.: 1986, Statistics of Sunspot Activity, Nauka, Moscow, 296 (in Russian).

  36. Volobuev, D.M.: 2009, Solar Phys. 258, 319.

  37. Waldmeier, M.: 1935, Astron. Mitt. Zürich 14, 133.

  38. Waldmeier, M.: 1939, Astron. Mitt. Zürich 14, 439.

  39. Wang, J.L., Miao, J., Liu, S.Q., Gong, J.C., Zhu, C.L.: 2008, Sci. China Ser. G 51, 1938.

  40. Wilson, R.M., Hathaway, D.H., Reichmann, E.J.: 1998, J. Geophys. Res. 103, 6595.

  41. Wolf, R.: 1852, C. R. Acad. Sci. 35, 704.

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Correspondence to Zhanle Du.

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Du, Z. The Shape of Solar Cycle Described by a Modified Gaussian Function. Sol Phys 273, 231–253 (2011). https://doi.org/10.1007/s11207-011-9849-8

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Keywords

  • Models
  • Solar cycle
  • Sunspots