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Double maxima of 11-year solar cycles

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Abstract

We propose a scenario to explain the observed phenomenon of double maxima of sunspot cycles, including the generation of a magnetic field near the bottom of the solar convection zone (SCZ) and the subsequent rise of the field from the deep layers to the surface in the royal zone. Five processes are involved in the restructuring of the magnetic field: the Ω-effect, magnetic buoyancy, macroscopic turbulent diamagnetism, rotary ∇ρ-effect, and meridional circulation. It is found that the restructuring of magnetism develops differently in high-latitude and equatorial domains of the SCZ. A key role in the proposed mechanism of the double maxima is played by two waves of toroidal fields from the lower base of the SCZ to the solar surface in the equatorial domain. The deep toroidal fields are excited by the Ω-effect near the tachocline at the beginning of the cycle. Then these fields are transported to the surface due to the combined effect of magnetic buoyancy, macroscopic turbulent diamagnetism, and the rotary magnetic ∇ρ-flux in the equatorial domain. After a while, these magnetic fragments can be observed as bipolar sunspot groups at the middle latitudes in the royal zone. This first, upward-directed wave of toroidal fields produces the main maximum of sunspot activity. However, the underlying toroidal fields in the high-latitude polar domains are blocked at the beginning of the cycle near the SCZ bottom by two antibuoyancy effects — the downward turbulent diamagnetic transfer and the magnetic ∇ρ-pumping. In approximately 1 or 2 years, a deep equatorward meridional flow transfers these fields to low-latitude parts of the equatorial domain (where there are favorable conditions for magnetic buoyancy), and the belated magnetic fields (the second wave of toroidal fields) rise to the surface. When this second batch of toroidal fields comes to the solar surface at low latitudes, it leads to the second sunspot maximum.

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References

  1. S. I. Vainshtein, Ya. B. Zel’dovich, and A. A. Ruzmaikin, The Turbulent Dynamo in Astrophysics (Nauka, Moscow, 1980) [in Russian].

    Google Scholar 

  2. S. I. Vainshtein, Magnetic Fields in Space (Nauka, Moscow, 1983) [in Russian].

    Google Scholar 

  3. Yu. I. Vitinskii, M. Konetskii, and G. V. Kuklin, Statistics of the Spot-Forming Activity of the Sun (Nauka, Moscow, 1986) [in Russian].

    Google Scholar 

  4. A. G. Zagorodnii and O. K. Cheremnykh, Introduction to Plasma Physics (Nauk. Dumka, Kyiv, 2014) [in Russian].

    Google Scholar 

  5. Ya. B. Zel’dovich, “The magnetic field in the two-dimensional motion of a conducting turbulent liquid,” J. Exp. Theor. Phys. 31, 460–462 (1957).

    MATH  Google Scholar 

  6. L. L. Kichatinov, “On magnetohydrodynamics of mean fields in inhomogeneous turbulent medium,” Magn. Gidrodin., No. 3, 67–73 (1982).

    Google Scholar 

  7. L. V. Kozak, R. I. Kostyk, and O. K. Cheremnykh, “Two spectra of turbulence of the Sun,” Kinematics Phys. Celestial Bodies 29, 66–70 (2013).

    Article  ADS  Google Scholar 

  8. A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk SSSR 30, 299–303 (1941).

    ADS  MathSciNet  Google Scholar 

  9. V. N. Krivodubskii, “On turbulent conductivity and magnetic permeability of the solar plasma,” Soln. Dannye, No. 7, 99–109 (1982).

    ADS  Google Scholar 

  10. V. K. Krivodubskii, “Intensity of sources of magnetic fields of the solar alpha-omega dynamo,” Astron. Zh. 61, 540–548 (1984).

    ADS  Google Scholar 

  11. Yu. P. Ladikov-Roev and O. K. Cheremnykh, Mathematical Models of Continuous Media (Nauk. Dumka, Kyiv, 2010) [in Russian].

    Google Scholar 

  12. V. N. Obridko, “Magnetic fields and indexes of activity,” in Plama Helio-Geophysics, Ed. by L. M. Zelenyi and I. S. Veselovskii (Fizmatlit, Moscow, 2008), Vol. 1, pp. 41–60 [in Russian].

    Google Scholar 

  13. A. A. Solov’ev and E. A. Kiritchek, The Diffusion Theory of Solar Magnetic Cycle (Kalmytskii Gos. Univ., Elista, 2004) [in Russian].

    Google Scholar 

  14. A. Antalova and M. N. Gnevyshev, “Principal characteristics of the 11-year solar activity cycle,” Sov. Astron. 9, 198–201 (1965).

    ADS  Google Scholar 

  15. B. Belucz, M. Dikpati, and E. Forgács-Dajka, “A Babcock–Leighton solar dynamo model with multi-cellular meridional circulation in advection-and diffusion-dominated regimes,” Astrophys. J. 806, 169 (2015).

    Article  ADS  Google Scholar 

  16. E. E. Benevolenskaya, “A model of the double magnetic cycle of the Sun,” Astrophys. J. Lett. 509, L49–L52 (2003).

    Article  ADS  Google Scholar 

  17. A. Brandenburg, D. Sokoloff, and K. Subramanian, “Current status of turbulent dynamo theory. From largescale to small-scale dynamos,” Space Sci. Rev. 169, 123–157 (2012).

    Article  ADS  Google Scholar 

  18. D. Braun and A. Birc, “Prospects for the detection of the deep solar meridional circulation,” Astrophys. J. Lett. 689, L161–L165 (2008).

    Article  ADS  Google Scholar 

  19. A. S. Brun, M. K. Browning, M. Dikpati, et al., “Recent advances on solar global magnetism and variability,” Space Sci. Rev. 196, 101–136 (2015).

    Article  ADS  Google Scholar 

  20. R. Cameron, M. Dikpati, and A. Brandenburg, “The global solar dynamo” (2016). https://arxiv.org/abs/1602.01754.

    Google Scholar 

  21. R. Cameron and M. Schüssler, “The crucial role of surface magnetic fields for the solar dynamo,” Science 347, 1333–1335 (2015).

    Article  ADS  Google Scholar 

  22. P. Charbonneau, “Dynamo models of the solar cycle,” Living Rev. Sol. Phys. 7 (3), 1–91 (2010).

    ADS  Google Scholar 

  23. A. R. Choudhuri, P. Chatterjee, and J. Jiang, “Predicting solar cycle 24 with a solar dynamo model,” Phys. Rev. Lett. 98, 131103 (2007).

    Article  ADS  Google Scholar 

  24. A. R. Choudhuri, M. Schüssler, and M. Dikpati, “The solar dynamo with meridional circulation,” Astron. Astrophys. 303, L29 (1995).

    ADS  Google Scholar 

  25. M. Dikpati and P. A. Gilman, “Simulating and predicting solar cycles using a flux-transport dynamo,” Astrophys. J. 649, 498–514 (2006).

    Article  ADS  Google Scholar 

  26. E. M. Drobyshevski, “Magnetic field transfer by two-dimensional convection and solar ‘semi-dynamo’,” Astrophys. Space Sci. 46, 41–49 (1977).

    Article  ADS  MATH  Google Scholar 

  27. A. E. Dudorov, V. N. Krivodubskii, T. V. Ruzmaikina, and A. A. Ruzmaikin, “The internal large-scale magnetic field of the Sun,” Sov. Astron. 33, 420–426 (1989).

    ADS  Google Scholar 

  28. K. Georgieva, “Why the sunspot cycle is doubly peaked,” ISRN Astron. Astrophys., 437838 (2011).

  29. K. Georgieva and B. Kirov, “Solar dynamo and geomagnetic activity,” J. Atmos. Sol.-Terr. Phys. 73, 207–222 (2011).

    Article  ADS  Google Scholar 

  30. P. M. Giles, T. L. Duval, P. K. Scherrer, and R. S. Bogart, “A subsurface flow of material from the Sun’s equator to its poles,” Nature 390, 52–54 (1997).

    Article  ADS  Google Scholar 

  31. L. Gizon and A. C. Birch, “Local helioseismology,” Living Rev. Sol. Phys. 2 (6), 1–75 (2005).

    ADS  Google Scholar 

  32. M. N. Gnevyshev, “The corona and the 11-year cycle of solar activity,” Sov. Astron. 7, 311–318 (1963).

    ADS  Google Scholar 

  33. M. N. Gnevyshev, “On the 11-years cycle of solar activity,” Sol. Phys. 1, 107–120 (1967).

    Article  ADS  Google Scholar 

  34. M. N. Gnevyshev, “Essential features of the 11-year solar cycle,” Sol. Phys. 51, 175–183 (1977).

    Article  ADS  Google Scholar 

  35. D. H. Hathaway, “Doppler measurements of the Sun’s meridional flow,” Astrophys. J. 460, 1027–1033 (1996).

    Article  ADS  Google Scholar 

  36. D. H. Hathaway, “Supergranules as probes of the Sun’s meridional circulation,” Astrophys. J. 760, 84 (2012).

    Article  ADS  Google Scholar 

  37. D. H. Hathaway, “The solar cycle,” Living Rev. Sol. Phys. 12 (4), 1–87 (2015).

    ADS  Google Scholar 

  38. D. H. Hathaway, D. Nandy, R. M. Wilson, and E. J. Reichmann, “Evidence that a deep meridional flow sets the sunspot cycle,” Astrophys. J. 589, 665–670 (2003).

    Article  ADS  Google Scholar 

  39. G. Hazra, B. B. Karak, and A. R. Choudhuri, “Is a deep one-cell meridional circulation essential for the flux transport solar dynamo?,” Astrophys. J. 782, 93 (2014).

    Article  ADS  Google Scholar 

  40. R. Howe, “Solar interior rotation and its variation,” Living Rev. Sol. Phys. 6 (1), 1–75 (2009).

    ADS  Google Scholar 

  41. R. Howe, J. Christensen-Dalsgaard, F. Hill, et al., “Dynamic variations at the base of the solar convection zone,” Science 287, 2456–2460 (2000).

    Article  ADS  Google Scholar 

  42. T. S. Ivanova and A. A. Ruzmaikin, “A magnetohydrodynamic dynamo model of the solar cycle,” Sov. Astron. 20, 227–233 (1976).

    ADS  Google Scholar 

  43. J. Jackiewicz, A. Serebryanskiy, and S. Kholikov, “Meridional flow in the solar convection zone. II. Helioseismic inversions of GONG DATA,” Astrophys. J. 805, 133 (2015).

    Article  ADS  Google Scholar 

  44. E. Jensen, “On tubes of magnetic force embedded in stellar material,” Ann. d’Astrophys. 18, 127–140 (1955).

    ADS  Google Scholar 

  45. J. Jiang, R. H. Cameron, and M. Schiissler, “The case of the weak solar cycle 24,” Astrophys. J. Lett. 808, L28 (2015).

    Article  ADS  Google Scholar 

  46. J. Jiang, P. Chatterjee, and A. R. Choudhuri, “Solar activity forecast with a dynamo model,” Mon. Not. R. Astron. Soc. 381, 1527–1542 (2007).

    Article  ADS  Google Scholar 

  47. L. L. Kitchatinov, “Turbulent transport of magnetic fields in a highly conducting rotating fluid and the solar cycle,” Astron. Astrophys. 243, 483–491 (1991).

    ADS  Google Scholar 

  48. L. L. Kitchatinov, “The solar dynamo: Inferences from observations and modeling,” Geomagn. Aeron. (Engl. Transl.) 54, 867–876 (2014).

    Article  ADS  Google Scholar 

  49. L. L. Kitchatinov and G. Rudiger, “Magnetic-field advection in inhomogeneous turbulence,” Astron. Astrophys. 260, 494–498 (1992).

    ADS  Google Scholar 

  50. I. Kitiashvili and A. G. Kosovichev, “Application of data assimilation method for predicting solar cycles,” Astrophys. J. Lett. 688, L49–L52 (2008).

    Article  ADS  Google Scholar 

  51. R. W. Komm, R. F. Howard, and J. Harvey, “Meridional flow of small photospheric magnetic features,” Sol. Phys. 147, 207–223 (1993).

    Article  ADS  Google Scholar 

  52. M. Kopecký and G. V. Kuklin, “A few notes on the sunspot activity in dependence on the phase of the 11-year cycle and on the heliographic latitude,” Bull. Astron. Inst. Czech. 20, 22–29 (1969).

    ADS  Google Scholar 

  53. A. G. Kosovichev, “Probing solar and stellar interior dynamics and dynamo,” Adv. Space Res. 41, 830–837 (2008).

    Article  ADS  Google Scholar 

  54. R. H. Kraichnan, “Inertial-range spectrum of hydromagnetic turbulence,” Phys. Fluids 8, 1385–1387 (1965).

    Article  ADS  Google Scholar 

  55. F. Krause and K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, 1980).

    MATH  Google Scholar 

  56. V. N. Krivodubskii, “Magnetic field transfer in the turbulent solar envelope,” Sov. Astron. 28, 205–211 (1984).

    ADS  Google Scholar 

  57. V. N. Krivodubskii, “Transfer of the large-scale solar magnetic field by inhomogeneity of the material density in the convective zone,” Sov. Astron. Lett. 13, 338–341 (1987).

    ADS  Google Scholar 

  58. V. N. Krivodubskii, “Rotational anisotropy and magnetic quenching of gyrotropic turbulence in the solar convective zone,” Astron. Rep. 42, 122–126 (1998).

    ADS  Google Scholar 

  59. V. N. Krivodubskii, “The structure of the global solar magnetic field excited by the turbulent dynamo mechanism,” Astron. Rep. 45, 738–745 (2001).

    Article  ADS  Google Scholar 

  60. V. N. Krivodubskij, “Turbulent dynamo near tachocline and reconstruction of azimuthal magnetic field in the solar convection zone,” Astron. Nachr. 326, 61–74 (2005).

    Article  ADS  Google Scholar 

  61. V. N. Krivodubskii, “Turbulent effects of sunspot magnetic field reconstruction,” Kinematics Phys. Celestial Bodies 28, 232–238 (2012).

    Article  ADS  Google Scholar 

  62. V. N. Krivodubskij, “On the extended 23rd solar cycle,” in Solar and Astrophysical Dynamos and Magnetic Activity: Proc. 294th IAU Symp., Ed. by A. G. Kosovichev; Proc. Int. Astron. Union S294, 69–70 (2013).

    ADS  Google Scholar 

  63. V. N. Krivodubskij and N. I. Lozitska, “Dependence of solar cycles duration on the magnitude of the annual module of the sunspots magnetic field,” Proc. Int. Astron. Union S294, 71–72 (2013).

    Google Scholar 

  64. V. N. Krivodubskij, “Small scale alpha-squared effect in the solar convection zone,” Kinematics Phys. Celestial Bodies 31, 55–64 (2015).

    Article  ADS  Google Scholar 

  65. V. D. Kuznetsov and S. I. Syrovatskii, “The floating up of magnetic fields and the 11-year cyclicity of solar activity,” Sov. Astron. 23, 715–719 (1979).

    ADS  Google Scholar 

  66. V. I. Makarov, A. G. Tlatov, D. K. Callebaut, et al., “Large-scale magnetic field and sunspot cycles,” Sol. Phys. 198, 409–421 (2001).

    Article  ADS  Google Scholar 

  67. M. S. Miesch and M. Dikpati, “A three-dimensional Babcock–Leighton solar dynamo model,” Astrophys. J. Lett. 785, L8 (2014).

    Article  ADS  Google Scholar 

  68. F. Moreno-Insertis, “Rise times of horizontal magnetic flux tubes in the convection zone of the sun,” Astron. Astrophys. 122, 241–250 (1983).

    ADS  Google Scholar 

  69. A. Muñoz-Jamarillo, M. Dasi-Espuig, L. A. Balmaceda, and E. E. DeLuca, “Solar cycle propagation, memory, and prediction: Insights from a century of magnetic proxies,” Astrophys. J. Lett. 767, L25 (2013).

    Article  ADS  Google Scholar 

  70. D. Nandy and A. R. Choudhuri, “Explaining the latitudinal distribution of sunspots with deep meridional flow,” Science 296, 1671–1673 (2002).

    Article  ADS  Google Scholar 

  71. D. Nandy, A. Muñoz-Jaramillo, and P. Martens, “The unusual minimum of sunspot cycle 23 caused by meridional plasma flow variations,” Nature 471, 80–82 (2011).

    Article  ADS  Google Scholar 

  72. N. J. Nelson, B. P. Brown, A. Sacha Brun, et al., “Buoyant magnetic loops generated by global convective dynamo action,” Sol. Phys. 289, 441–458 (2014).

    Article  ADS  Google Scholar 

  73. E. Nesme-Ribes, N. Meunier, and I. Vince, “Solar dynamics over cycle 19 using sunspots as tracers,” Astron. Astrophys. 321, 323–329 (1997).

    ADS  Google Scholar 

  74. M. Ossendrijver, “The solar dynamo,” Astron. Astrophys. Rev. 11, 287–367 (2003).

    Article  ADS  Google Scholar 

  75. E. N. Parker, “The formation of sunspots from the solar toroidal field,” Astrophys. J. 121, 491–507 (1955).

    Article  ADS  Google Scholar 

  76. V. V. Pipin and A. G. Kosovichev, “The mean-field solar dynamo with double cell meridional circulation pattern,” Astrophys. J. 776, 36 (2013).

    Article  ADS  Google Scholar 

  77. E. P. Popova, K. A. Potemina, and N. A. Yukhina, “Double cycle of solar activity in a two-layer medium,” Geomagn. Aeron. (Engl. Transl.) 54, 877–881 (2015).

    Article  ADS  Google Scholar 

  78. E. Popova, V. Zharkova, and S. Zharkov, “Probing latitudinal variations of the solar magnetic field in cycles 21–23 by Parker’s two-layer dynamo model with meridional circulation,” Ann. Geophys. 31, 2023–2028 (2013).

    Article  ADS  Google Scholar 

  79. K.-H. Rädler, “Zur Elektrodynamik turbulent bewegter leitender Mediem._I. Grundzüge der Elektrodynamik der mittleren Felder,” Z. Naturforsch., A: Phys. Sci. 23, 1841–1851 (1968)

    Article  ADS  Google Scholar 

  80. K.-H. Radler, “Zur Elektrodynamik turbulent bewegter leitender Mediem. II. Turbulenzbedingte Leitfähigkeits-und Permeabilitätsänderungen,” Z. Naturforsch., A: Phys. Sci. 23, 1851–1860 (1968).

    Article  ADS  Google Scholar 

  81. G. Rüdiger and R. Arlt, “Physics of the solar cycle,” in Advances in Nonlinear Dynamos, Ed. by A. Ferriz-Mas and M. Núñes (Taylor & Francis, London, 2004), in Ser. The Fluid Mechanics of Astrophysics and Geophysics, pp. 147–194.

    Google Scholar 

  82. A. Schad, J. Timmer, and M. Roth, “Global helioseismic evidence for a deeply penetrating solar meridional flow consisting of multiple flow cells,” Astrophys. J. Lett. 778, L38 (2013).

    Article  ADS  Google Scholar 

  83. K. H. Schatten, P. H. Scherrer, L. Svalgaard, and J. M. Wilcox, “Using dynamo theory to predict the sunspot number during solar cycle 21,” Geophys. Rev. Lett. 5, 411–414 (1978).

    Article  ADS  Google Scholar 

  84. J. Schou, H. M. Antia, S. Basu, et al., “Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the Michelson Doppler Imager,” Astrophys. J. 505, 390–417 (1998).

    Article  ADS  Google Scholar 

  85. M. Schüssler, “On buoyant magnetic flux tubes in the solar convection zone,” Astron. Astrophys. 56, 439–442 (1977).

    ADS  Google Scholar 

  86. H. Schwabe, “Sonnenbeobachtungen im Jahre 1843. Von Herrn Hofrath Schwabe in Dessau,” Astron. Nachr. 21, 233–236 (1844).

    Article  ADS  Google Scholar 

  87. S. J. Shepherd, S. I. Zharkov, and V. V. Zharkova, “Prediction of solar activity from solar background magnetic field variations in cycles 21–23,” Astrophys. J. 795, 46 (2014).

    Article  ADS  Google Scholar 

  88. H. B. Snodgrass and S. B. Dailey, “Meridional motions of magnetic features in the solar photosphere,” Sol. Phys. 163, 21–42 (1996).

    Article  ADS  Google Scholar 

  89. M. Stix, The Sun: An Introduction, 2nd ed. (Springer-Verlag, Berlin, 2002).

    Book  MATH  Google Scholar 

  90. L. Svalgaard, E. W. Cliver, and Y. Kamide, “Sunspot cycle 24: Smallest cycle in 100 years?,” Geophys. Res. Lett. 32, L01104 (2005).

    Article  ADS  Google Scholar 

  91. A. Tlatov, E. Illarionov, D. Sokoloff, and V. Pipin, “A new dynamo pattern revealed by the tilt angle of bipolar sunspot groups,” Mon. Not._R. Astron. Soc. 432, 2975–2984 (2013).

    Article  ADS  Google Scholar 

  92. W. Unno and E. Ribes, “On magnetic buoyancy in the convection zone,” Astrophys. J. 208, 222–223 (1976).

    Article  ADS  Google Scholar 

  93. Y.-M. Wang, N. R. Sheeley, Jr., and A. G. Nash, “A new solar cycle model including meridional circulation,” Astrophys. J. 383, 431–442 (1991).

    Article  ADS  Google Scholar 

  94. Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, Magnetic Fields in Astrophysics (Gordon and Breach, New York, 1983).

    Google Scholar 

  95. J. Zhao, R. S. Bogart, A. G. Kosovichev, T. L. Duvall, T. Hartlep, “Detection of equatorward meridional flow and evidence of double-cell meridional circulation inside the Sun,” Astrophys. J. Lett. 774, L29 (2013).

    Article  ADS  Google Scholar 

  96. J. Zhao and A. G. Kosovichev, “Torsional oscillation, meridional flows, and vorticity inferred in the upper convection zone of the Sun by time-distance helioseismology,” Astrophys. J. 603, 776–784 (2004).

    Article  ADS  Google Scholar 

  97. V. V. Zharkova, S. J. Shepherd, and S. I. Zharkov, “Principal component analysis of background and sunspot magnetic field variations during solar cycles 21–23,” Mon. Not. R. Astron. Soc. 424, 2943–2953 (2012).

    Article  ADS  Google Scholar 

  98. S. Zharkov, E. Gavryuseva, and V. Zharkova, “The observed long-and short-term phase relation between the toroidal and poloidal magnetic fields in cycle 23,” Sol. Phys. 248, 339–358 (2008).

    Article  ADS  Google Scholar 

  99. N. V. Zolotova and D. I. Ponyavin, “Impulse-like behavior of the sunspot activity,” Astron. Rep. 56, 250–255 (2012).

    Article  ADS  Google Scholar 

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Original Russian Text © V.N. Krivodubskij, 2017, published in Kinematika i Fizika Nebesnykh Tel, 2017, Vol. 33, No. 1, pp. 55–80.

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Krivodubskij, V.N. Double maxima of 11-year solar cycles. Kinemat. Phys. Celest. Bodies 33, 24–38 (2017). https://doi.org/10.3103/S0884591317010044

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