Double maxima 11-year solar cycles

Heading: 
1Krivodubskij, VN
1Astronomical Observatory of Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Kinemat. fiz. nebesnyh tel (Online) 2017, 33(1):55-80
https://doi.org/10.15407/kfnt2017.01.055
Start Page: Solar Physics
Language: Russian
Abstract: 

We propose a scenario to explain the observed phenomenon of double maxima of sunspot cycles, including the generation of the magnetic field near the bottom of the solar convection zone (SCZ) and its subsequent removal from the deep layers to the surface in the “royal zone”. Five processes are involved for reconstructing of the magnetic field: the Ω-effect, magnetic buoyancy, macroscopic turbulent diamagnetism, rotary ∇ρ-effect and meridional circulation. It was found that the reconstruction of magnetism in the high-latitude and equatorial domains of the SCZ occurs in different modes. A key role in the developed mechanism of double maxima play two waves of toroidal fields from the lower base of the SCZ bottom to the solar surface in the equatorial domain. Deep toroidal fields are excited due to the Ω-effect near tachocline at the beginning of the cycle. Then these fields are transported to the surface due to combined acting of magnetic buoyancy, macroscopic turbulent diamagnetism and rotary magnetic ∇ρ-flow in the equatorial domain. Over time these magnetic fragments can be seen as bipolar sunspot groups in the middle latitudes in the “royal zone”. This first wave of toroidal fields, which is directed up, gives the main maximum of sunspot activity. However, the underlying toroidal fields in the high-latitude polar domains at the beginning of the cycle are blocked near bottom of the SCZ by two antibuoyancy effects, directed downward turbulent diamagnetic transfer and magnetic ∇ρ-pumping. Deep meridional flow toward the equator transfers these fields to the low latitudes of the equatorial domain (where there are favourable conditions for magnetic floating) during about 1-2 years. Then “belated” magnetic fields float up /rise up to surface (second wave of toroidal field). This second portion of toroidal fields, coming to the solar surface at low latitudes, leads to second (repeated) sunspot maximum.

Keywords: 11-year solar cycles, magnetic fields, maximum of sunspot activity, toroidal fields
References: 

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

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

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

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

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).zbMATH

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

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).
https://doi.org/10.3103/S0884591313020050

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).MathSciNet

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

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

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

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].

13.A. A. Solov’ev and E. A. Kiritchek, The Diffusion Theory of Solar Magnetic Cycle (Kalmytskii Gos. Univ., Elista, 2004) [in Russian].
https://doi.org/10.1017/S1743921304005459

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

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).
https://doi.org/10.1088/0004-637X/806/2/169

16.E. E. Benevolenskaya, “A model of the double magnetic cycle of the Sun,” Astrophys. J. Lett. 509, L49–L52 (2003).
https://doi.org/10.1086/311755

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).
https://doi.org/10.1007/s11214-012-9909-x

18.D. Braun and A. Birc, “Prospects for the detection of the deep solar meridional circulation,” Astrophys. J. Lett. 689, L161–L165 (2008).
https://doi.org/10.1086/595884

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).
https://doi.org/10.1007/s11214-013-0028-0

20.R. Cameron, M. Dikpati, and A. Brandenburg, “The global solar dynamo” (2016).
https://arxiv.org/abs/1602.01754.
https://doi.org/10.1007/978-94-024-1521-6_13

21.R. Cameron and M. Schüssler, “The crucial role of surface magnetic fields for the solar dynamo,” Science 347, 1333–1335 (2015).
https://doi.org/10.1126/science.1261470

22.P. Charbonneau, “Dynamo models of the solar cycle,” Living Rev. Sol. Phys. 7 (3), 1–91 (2010).
https://doi.org/10.12942/lrsp-2010-3

23.A. R. Choudhuri, P. Chatterjee, and J. Jiang, “Predicting solar cycle 24 with a solar dynamo model,” Phys. Rev. Lett. 98, 131103 (2007).
https://doi.org/10.1103/PhysRevLett.98.131103

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

25.M. Dikpati and P. A. Gilman, “Simulating and predicting solar cycles using a flux-transport dynamo,” Astrophys. J. 649, 498–514 (2006).
https://doi.org/10.1086/506314

26.E. M. Drobyshevski, “Magnetic field transfer by two-dimensional convection and solar ‘semi-dynamo’,” Astrophys. Space Sci. 46, 41–49 (1977).
https://doi.org/10.1007/BF00643752

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).

28.K. Georgieva, “Why the sunspot cycle is doubly peaked,” ISRN Astron. Astrophys., 437838 (2011).
https://doi.org/10.5402/2011/437838

29.K. Georgieva and B. Kirov, “Solar dynamo and geomagnetic activity,” J. Atmos. Sol.-Terr. Phys. 73, 207–222 (2011).
https://doi.org/10.1016/j.jastp.2010.03.003

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).
https://doi.org/10.1038/36294

31.L. Gizon and A. C. Birch, “Local helioseismology,” Living Rev. Sol. Phys. 2 (6), 1–75 (2005).
https://doi.org/10.12942/lrsp-2005-6

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

33.M. N. Gnevyshev, “On the 11-years cycle of solar activity,” Sol. Phys. 1, 107–120 (1967).
https://doi.org/10.1007/BF00150306

34.M. N. Gnevyshev, “Essential features of the 11-year solar cycle,” Sol. Phys. 51, 175–183 (1977).
https://doi.org/10.1007/BF00240455

35.D. H. Hathaway, “Doppler measurements of the Sun’s meridional flow,” Astrophys. J. 460, 1027–1033 (1996).
https://doi.org/10.1086/177029

36.D. H. Hathaway, “Supergranules as probes of the Sun’s meridional circulation,” Astrophys. J. 760, 84 (2012).
https://doi.org/10.1088/0004-637X/760/1/84

37.D. H. Hathaway, “The solar cycle,” Living Rev. Sol. Phys. 12 (4), 1–87 (2015).
https://doi.org/10.1007/lrsp-2015-4

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).
https://doi.org/10.1086/374393

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).
https://doi.org/10.1088/0004-637X/782/2/93

40.R. Howe, “Solar interior rotation and its variation,” Living Rev. Sol. Phys. 6 (1), 1–75 (2009).
https://doi.org/10.12942/lrsp-2009-1

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).
https://doi.org/10.1126/science.287.5462.2456

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

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).
https://doi.org/10.1088/0004-637X/805/2/133

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

45.J. Jiang, R. H. Cameron, and M. Schiissler, “The case of the weak solar cycle 24,” Astrophys. J. Lett. 808, L28 (2015).
https://doi.org/10.1088/2041-8205/808/1/L28

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).
https://doi.org/10.1111/j.1365-2966.2007.12267.x

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).

48.L. L. Kitchatinov, “The solar dynamo: Inferences from observations and modeling,” Geomagn. Aeron. (Engl. Transl.) 54, 867–876 (2014).
https://doi.org/10.1134/S0016793214070056

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

50.I. Kitiashvili and A. G. Kosovichev, “Application of data assimilation method for predicting solar cycles,” Astrophys. J. Lett. 688, L49–L52 (2008).
https://doi.org/10.1086/594999

51.R. W. Komm, R. F. Howard, and J. Harvey, “Meridional flow of small photospheric magnetic features,” Sol. Phys. 147, 207–223 (1993).
https://doi.org/10.1007/BF00690713

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).

53.A. G. Kosovichev, “Probing solar and stellar interior dynamics and dynamo,” Adv. Space Res. 41, 830–837 (2008).
https://doi.org/10.1016/j.asr.2007.05.023

54.R. H. Kraichnan, “Inertial-range spectrum of hydromagnetic turbulence,” Phys. Fluids 8, 1385–1387 (1965).
https://doi.org/10.1063/1.1761412

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

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

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).

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

59.V. N. Krivodubskii, “The structure of the global solar magnetic field excited by the turbulent dynamo mechanism,” Astron. Rep. 45, 738–745 (2001).
https://doi.org/10.1134/1.1398923

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).
https://doi.org/10.1002/asna.200310340

61.V. N. Krivodubskii, “Turbulent effects of sunspot magnetic field reconstruction,” Kinematics Phys. Celestial Bodies 28, 232–238 (2012).
https://doi.org/10.3103/S0884591312050054

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).
https://doi.org/10.1017/S174392131300224X

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).
https://doi.org/10.1017/S1743921313002251

64.V. N. Krivodubskij, “Small scale alpha-squared effect in the solar convection zone,” Kinematics Phys. Celestial Bodies 31, 55–64 (2015).
https://doi.org/10.3103/S0884591315020038

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).

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).
https://doi.org/10.1023/A:1005249531228

67.M. S. Miesch and M. Dikpati, “A three-dimensional Babcock–Leighton solar dynamo model,” Astrophys. J. Lett. 785, L8 (2014).
https://doi.org/10.1088/2041-8205/785/1/L8

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

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).
https://doi.org/10.1088/2041-8205/767/2/L25

70.D. Nandy and A. R. Choudhuri, “Explaining the latitudinal distribution of sunspots with deep meridional flow,” Science 296, 1671–1673 (2002).
https://doi.org/10.1126/science.1070955

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).
https://doi.org/10.1038/nature09786

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).
https://doi.org/10.1007/s11207-012-0221-4

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

74.M. Ossendrijver, “The solar dynamo,” Astron. Astrophys. Rev. 11, 287–367 (2003).
https://doi.org/10.1007/s00159-003-0019-3

75.E. N. Parker, “The formation of sunspots from the solar toroidal field,” Astrophys. J. 121, 491–507 (1955).
https://doi.org/10.1086/146010

76.V. V. Pipin and A. G. Kosovichev, “The mean-field solar dynamo with double cell meridional circulation pattern,” Astrophys. J. 776, 36 (2013).
https://doi.org/10.1088/0004-637X/776/1/36

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).
https://doi.org/10.1134/S0016793214070111

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).
https://doi.org/10.5194/angeo-31-2023-2013

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)
https://doi.org/10.1515/zna-1968-1124

79a.K.-H. Radler, “Zur Elektrodynamik turbulent bewegter leitender Mediem. II. Turbulenzbedingte Leitfähigkeits-und Permeabilitätsänderungen,” Z. Naturforsch., A: Phys. Sci. 23, 1851–1860 (1968).
https://doi.org/10.1515/zna-1968-1124

80.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.
https://doi.org/10.1201/9780203493137-6

81.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).
https://doi.org/10.1088/2041-8205/778/2/L38

82.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).
https://doi.org/10.1029/GL005i005p00411

83.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).
https://doi.org/10.1086/306146

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

85.H. Schwabe, “Sonnenbeobachtungen im Jahre 1843. Von Herrn Hofrath Schwabe in Dessau,” Astron. Nachr. 21, 233–236 (1844).
https://doi.org/10.1002/asna.18440211505

86.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).
https://doi.org/10.1088/0004-637X/795/1/46

87.H. B. Snodgrass and S. B. Dailey, “Meridional motions of magnetic features in the solar photosphere,” Sol. Phys. 163, 21–42 (1996).
https://doi.org/10.1007/BF00165454

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

89.L. Svalgaard, E. W. Cliver, and Y. Kamide, “Sunspot cycle 24: Smallest cycle in 100 years?,” Geophys. Res. Lett. 32, L01104 (2005).
https://doi.org/10.1029/2004GL021664

90.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).
https://doi.org/10.1093/mnras/stt659

91.W. Unno and E. Ribes, “On magnetic buoyancy in the convection zone,” Astrophys. J. 208, 222–223 (1976).
https://doi.org/10.1086/154597

92.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).
https://doi.org/10.1086/170800

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

94.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).
https://doi.org/10.1088/2041-8205/774/2/L29

95.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).
https://doi.org/10.1086/381489

96.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).
https://doi.org/10.1111/j.1365-2966.2012.21436.x

97.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).
https://doi.org/10.1007/s11207-007-9109-0

98.N. V. Zolotova and D. I. Ponyavin, “Impulse-like behavior of the sunspot activity,” Astron. Rep. 56, 250–255 (2012).
https://doi.org/10.1134/S1063772912030080