Geomagnetism and Aeronomy

, Volume 58, Issue 7, pp 930–936 | Cite as

Shape of the 11-Year Cycle of Solar Activity and the Evolution of Latitude Characteristics of the Sunspot Distribution

  • V. G. IvanovEmail author


The solar activity index and parameters of the spatial distribution of sunspots are known to be related. Using these relationships, we propose interrelated approximations for the sunspot number (SN) and the two key latitude characteristics of their distribution in the cycle: the mean latitude of sunspots and the standard deviation of their latitudes. The two parameters of these approximations are the cycle amplitude SNmax and the drift of its downward branch relative to the cycle beginning t0. These approximations specifically take into account the relationship between amplitudinal and spatial properties of the 11-year solar cycle, as well as the universality of the behavior of the activity and mean latitude of sunspots in the declining phase of the cycle. We demonstrate that the pair of parameters SNmax and t0 allows approximation of both the shape of the cyclic curve and the latitude–time diagram for sunspots of this cycle (“Maunder’s butterfly”).



This study was supported by the Russian Foundation for Basic Research, project no. 16-02-00090 and by the Presidium of the Russian Academy of Sciences, program nos. 21 and 22.


  1. 1.
    Cameron, R.H. and Schüssler, M., The turbulent diffusion of toroidal magnetic flux as inferred from properties of the sunspot butterfly diagram, Astron. Astrophys., 2016, vol. 591, p. A46. doi 10.1051/0004-6361/201527284CrossRefGoogle Scholar
  2. 2.
    Eigenson, M.S., Gnevyshev, M.N., Ol’, A.I., and Rubashev, B.M., Solnechnaya aktivnost' i ee zemnye poyavleniya (Solar Activity and Its Terrestrial Manifestations), Moscow–Leningrad: OGIZ, 1948.Google Scholar
  3. 3.
    Gnevyshev, M.N. and Gnevysheva, R.S., Relationship between the Schwabe–Wolf and Sporer laws, Byull. Kom. Issled. Solntsa, 1949, no, 1, pp. 1–8.Google Scholar
  4. 4.
    Hathaway, D.H., A standard law for the equatorward drift of the sunspot zones, Sol. Phys., 2011, vol. 273, pp. 221–230. doi 10.1007/s11207-011-9837-zCrossRefGoogle Scholar
  5. 5.
    Hathaway, D.H., Wilson, R.M., and Reichmann, R.J., The shape of the sunspot cycle, Sol. Phys., 1994, vol. 151, pp. 177–190. doi 10.1007/BF00654090CrossRefGoogle Scholar
  6. 6.
    Ivanov, V.G. and Miletsky, E.V., Sporer’s law and relationship between the latitude and amplitude parameters of solar activity, Geomagn. Aeron. (Engl. Transl.), 2014, vol. 54, pp. 907–914.Google Scholar
  7. 7.
    Ivanov, V.G., Miletsky, E.V., and Nagovitsyn, Yu.A., Form of the latitude distribution of sunspot activity, Astron. Rep., 2011, vol. 55, no. 10, pp. 911–917. doi 10.1134/S1063772911100040CrossRefGoogle Scholar
  8. 8.
    Roshchina, E.M. and Sarychev, A.P., Sporer’s law and the rhythm of sunspot cycles, Sol. Syst. Res., 2011, vol. 45, no. 4, pp. 365–371. doi 10.1134/S003809461104006XCrossRefGoogle Scholar
  9. 9.
    Steward, J.Q. and Panofsky, H.A.A., The mathematical characteristics of sunspot variations, Astrophys. J., 1938, vol. 88, pp. 385–407. doi 10.1086/143994CrossRefGoogle Scholar
  10. 10.
    Vitinsky, Yu.I., Kopecký, M., and Kuklin, G.V., Statistika pyatnoobrazovatel’noi deyatel’nosti Solntsa (Statistics of Sunspot Formation Activity), Moscow: Nauka, 1986.Google Scholar
  11. 11.
    Waldmeier, M., Neue Eigenschaften der Sonnenfleckenkurve, Astron. Mitt. Eidgenossischen Sternwarte Zurich, 1935, vol. 14, pp. 105–136.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.The Central Astronomical Observatory of the Russian Academy of Sciences at PulkovoSt. PetersburgRussia

Personalised recommendations