Space Science Reviews

, Volume 152, Issue 1–4, pp 591–616 | Cite as

The Solar Dynamo

  • Chris A. JonesEmail author
  • Michael J. Thompson
  • Steven M. Tobias


Observations relevant to current models of the solar dynamo are presented, with emphasis on the history of solar magnetic activity and on the location and nature of the solar tachocline. The problems encountered when direct numerical simulation is used to analyse the solar cycle are discussed, and recent progress is reviewed. Mean field dynamo theory is still the basis of most theories of the solar dynamo, so a discussion of its fundamental principles and its underlying assumptions is given. The role of magnetic helicity is discussed. Some of the most popular models based on mean field theory are reviewed briefly. Dynamo models based on severe truncations of the full MHD equations are discussed.

Solar magnetism Solar dynamo Sunspots Solar cycles Solar interior Helioseismology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. J.A. Abreu, J. Beer, F. Steinhilber, S.M. Tobias, N.O. Weiss, For how long will the current grand maximum of solar activity persist? Geophys. Res. Lett. 35, L20109 (2008). doi: 10.1029/2008GL035442 ADSCrossRefGoogle Scholar
  2. P. Ashwin, E. Covas, R. Tavakol, Transverse instability for non-normal parameters. Nonlinearity 12, 563–577 (1999) zbMATHADSCrossRefMathSciNetGoogle Scholar
  3. H.W. Babcock, The topology of the Sun’s magnetic field and the 22-year cycle. Astrophys. J. 133, 572–587 (1961) ADSCrossRefGoogle Scholar
  4. C.S. Baldner, S. Basu, Solar cycle related changes at the base of the convection zone. Astrophys. J. 686, 1349–1361 (2008) ADSCrossRefGoogle Scholar
  5. S. Basu, Effects of errors in the solar radius on helioseismic inferences. Mon. Not. R. Astron. Soc. 298, 719–728 (1998) ADSCrossRefGoogle Scholar
  6. S. Basu, H.M. Antia, Effects of diffusion on the extent of overshoot below the solar convection zone. Mon. Not. R. Astron. Soc. 269, 1137–1144 (1994) ADSGoogle Scholar
  7. S. Basu, H.M. Antia, A study of possible temporal and latitudinal variations in the properties of the solar tachocline. Mon. Not. R. Astron. Soc. 324, 498–508 (2001) ADSCrossRefGoogle Scholar
  8. S. Basu, H.M. Antia, Changes in solar dynamics from 1995 to 2002. Astrophys. J. 585, 553–565 (2003) ADSCrossRefGoogle Scholar
  9. J.G. Beck, A comparison of differential rotation measurements. Solar Phys. 191, 47–70 (1999) ADSCrossRefGoogle Scholar
  10. J. Beer, S.M. Tobias, N.O. Weiss, An active Sun throughout the Maunder minimum. Solar Phys. 181, 237–249 (1998) ADSCrossRefGoogle Scholar
  11. S. Boldyrev, F. Cattaneo, Magnetic-field generation in Kolmogorov turbulence. Phys. Rev. Lett. 92, 144501 (2004) ADSCrossRefGoogle Scholar
  12. S.I. Braginsky, Nearly axisymmetric model of the hydromagnetic dynamo of the Earth. Geomagn. Aeron. 15, 122–128 (1975) Google Scholar
  13. A. Brandenburg, The case for a distributed solar dynamo shaped by near-surface shear. Astrophys. J. 625, 539–547 (2005) ADSCrossRefGoogle Scholar
  14. A. Brandenburg, D. Schmitt, Simulations of an alpha-effect due to magnetic buoyancy. Astron. Astrophys. 338, L55–L58 (1998) ADSGoogle Scholar
  15. A. Brandenburg, D. Subramanian, Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209 (2005) ADSCrossRefMathSciNetGoogle Scholar
  16. A. Brandenburg, K.-H. Rädler, M. Rheinhardt, P.J. Kapyla, Magnetic diffusivity tensor and dynamo. Astrophys. J. 676, 740–751 (2008) ADSCrossRefGoogle Scholar
  17. M.K. Browning, M.S. Miesch, A.S. Brun, J. Toomre, Dynamo action in the solar convection zone and tachocline: pumping and organization of toroidal fields. Astrophys. J. 648, L157–L160 (2006) ADSCrossRefGoogle Scholar
  18. A.S. Brun, M.S. Miesch, J. Toomre, Global-scale turbulent convection and magnetic dynamo action in the solar envelope. Astrophys. J. 614, 1073–1098 (2004) ADSCrossRefGoogle Scholar
  19. A.S. Brun, M. Rempel, Large scale flows in the solar convection zone. Space Sci. Rev. 144, 151–173 (2009) ADSCrossRefGoogle Scholar
  20. F. Cattaneo, On the origin of magnetic fields in the quiet photosphere. Astrophys. J. 515, L39–L42 (1999) ADSCrossRefGoogle Scholar
  21. F. Cattaneo, D.W. Hughes, Dynamo action in a rotating convective layer. J. Fluid Mech. 553, 401–418 (2006) zbMATHADSCrossRefMathSciNetGoogle Scholar
  22. K.H. Chan, X. Liao, K. Zhang, A three-dimensional multilayered spherical dynamic interface dynamo using the Malkus-Proctor formulation. Astrophys. J. 682, 1392–1403 (2008) ADSCrossRefGoogle Scholar
  23. P. Charbonneau, K.B. MacGregor, Solar interface dynamos II. Linear, kinematic models in spherical geometry. Astrophys. J. 486, 502 (1997) ADSCrossRefGoogle Scholar
  24. J. Christensen-Dalsgaard, M.J. Thompson, Observational results and issues concerning the tachocline, in The Solar Tachocline, ed. by D.W. Hughes, R. Rosner, N.O. Weiss (Cambridge University Press, Cambridge, 2007), pp. 53–85 CrossRefGoogle Scholar
  25. J. Christensen-Dalsgaard, D.O. Gough, M.J. Thompson, The depth of the solar convection zone. Astrophys. J. 378, 413–437 (1991) ADSCrossRefGoogle Scholar
  26. J. Christensen-Dalsgaard, M.J.P.F.G. Monteiro, M.J. Thompson, Helioseismic estimation of the convective overshoot in the Sun. Mon. Not. R. Astron. Soc. 276, 283–292 (1995) ADSGoogle Scholar
  27. K.S. Cline, N.H. Brummell, F. Cattaneo, Dynamo action driven by shear and magnetic buoyancy. Astrophys. J. 599, 1449–1468 (2003) ADSCrossRefGoogle Scholar
  28. A. Courvoisier, D.W. Hughes, S.M. Tobias, The alpha effect in a family of chaotic flows. Phys. Rev. Lett. 96, 034503 (2006) ADSCrossRefGoogle Scholar
  29. T.G. Cowling, The Magnetic Field of Sunspots. Mon. Not. R. Astron. Soc. 94, 39–48 (1933) zbMATHADSGoogle Scholar
  30. E. Covas, R. Tavakol, P. Ashwin, A. Tworkowski, J.M. Brooke, In-out intermittency in PDE and ODE models. Chaos 11, 404–409 (2001) ADSCrossRefGoogle Scholar
  31. M. Dikpati, P. Charbonneau, A Babcock-Leighton flux transport dynamo with solar-like differential rotation. Astrophys. J. 518, 508–520 (1995) ADSCrossRefGoogle Scholar
  32. M. Dikpati, G. deToma, P.A. Gilman, Predicting the strength of solar cycle 24 using a flux transport dynamo-based tool. Geophys. Res. Lett. 33, L05102 (2006) CrossRefGoogle Scholar
  33. M. Dikpati, P.A. Gilman, Flux-transport solar dynamos. Space Sci. Rev. 144, 67–75 (2009) ADSCrossRefGoogle Scholar
  34. J.A. Eddy, The Maunder minimum. Science 192, 1189–1202 (1976) ADSCrossRefGoogle Scholar
  35. Y. Fan, Magnetic fields in the solar convection zone. Living Rev. Solar Phys. 1 (2004).
  36. D.J. Galloway, M.R.E. Proctor, N.O. Weiss, Formation of intense magnetic fields near the surface of the Sun. Nature 266, 686–689 (1977) ADSCrossRefGoogle Scholar
  37. D.J. Galloway, M.R.E. Proctor, Numerical calculations of fast dynamos for smooth velocity fields with realistic diffusion. Nature 356, 691–693 (1992) ADSCrossRefGoogle Scholar
  38. P.A. Gilman, Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell. II—Dynamos with cycles and strong feedbacks. Astrophys. J. Suppl. 53, 243–268 (1983) ADSCrossRefGoogle Scholar
  39. G.A. Glatzmaier, Numerical simulations of stellar convective dynamos. II—Field propagation in the convection zone. Astrophys. J. 291, 300–307 (1985) ADSCrossRefGoogle Scholar
  40. A.V. Gruzinov, P.H. Diamond, Self-consistent theory of mean-field electrodynamics. Phys. Rev. Lett. 72, 1651–1653 (1994) ADSCrossRefGoogle Scholar
  41. D.A. Haber, B.W. Hindman, J. Toomre, R.S. Bogart, R.M. Larsen, F. Hill, Evolving submerged meridional circulation cells within the upper convection zone revealed by ring-diagram analysis. Astrophys. J. 570, 855–864 (2002) ADSCrossRefGoogle Scholar
  42. G.E. Hale, On the probable existence of a magnetic field in sunspots. Astrophys. J. 28, 315–343 (1908) ADSCrossRefGoogle Scholar
  43. G.E. Hale, F. Ellerman, S.B. Nicholson, A.H. Joy, The magnetic polarity of sun-spots. Astrophys. J. 49, 153–185 (1919) ADSCrossRefGoogle Scholar
  44. R. Howe, J. Christensen-Dalsgaard, F. Hill, R.W. Komm, R.M. Larsen, J. Schou, M.J. Thompson, J. Toomre, Deeply penetrating banded zonal flows in the solar convection zone. Astrophys. J. 533, L163–L166 (2000a) ADSCrossRefGoogle Scholar
  45. R. Howe, J. Christensen-Dalsgaard, F. Hill, R.W. Komm, R.M. Larsen, J. Schou, M.J. Thompson, J. Toomre, Dynamic variations at the base of the solar convection zone. Science 287, 2456–2460 (2000b) ADSCrossRefGoogle Scholar
  46. D.W. Hughes, F. Cattaneo, The alpha-effect in rotating convection: size matters. J. Fluid Mech. 594, 445–461 (2008) zbMATHADSCrossRefMathSciNetGoogle Scholar
  47. A.B. Iskakov, A.A. Schekochihin, S.C. Cowley, J.C. McWilliams, M.R.E. Proctor, Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers. Phys. Rev. Lett. 98, 208501 (2007) ADSCrossRefGoogle Scholar
  48. S.A. Jepps, Numerical models of hydromagnetic dynamos. J. Fluid Mech. 67, 625–646 (1975) zbMATHADSCrossRefGoogle Scholar
  49. C.A. Jones, Dynamo theory, in Dynamos, ed. by P. Cardin, L.F. Cugliandiolo (Ecole de Physique de les Houches, Elsevier, Amsterdam, 2008) Google Scholar
  50. C.A. Jones, N.O. Weiss, F. Cattaneo, Nonlinear dynamos: a complex generalization of the Lorenz equations. Physica D 14D, 161–176 (1985) ADSCrossRefMathSciNetGoogle Scholar
  51. J. Jurc̆ak, L.R. Bellot Rubio, Penumbral models in the light of Hinode spectropolarimetric observations. Astron. Astrophys. 481, L17–L20 (2008) ADSCrossRefGoogle Scholar
  52. P.J. Käpylä, M.J. Korpi, A. Brandenburg, Large-scale dynamos in turbulent convection with shear. Astron. Astrophys. 491, 353–362 (2008) zbMATHADSCrossRefGoogle Scholar
  53. S.R. Keating, L.J. Silvers, P.H. Diamond, On crossphase and the quenching of the turbulent diffusion of magnetic fields in two dimensions. Astrophys. J. Lett. 678, L137 (2008) ADSCrossRefGoogle Scholar
  54. E. Knobloch, S.M. Tobias, N.O. Weiss, Modulation and symmetry changes in stellar dynamos. Mon. Not. R. Astron. Soc. 297, 1123–1138 (1998) ADSCrossRefGoogle Scholar
  55. A.G. Kosovichev, Helioseismic constraints on the gradient of angular velocity at the base of the solar convection zone. Astrophys. J. 469, L61–L64 (1996) ADSCrossRefGoogle Scholar
  56. F. Krause, K.-H. Rädler, Mean Field Magnetohydrodynamics and Dynamo Theory (Pergamon Press, New York, 1980) zbMATHGoogle Scholar
  57. A.S. Landsberg, E. Knobloch, Oscillatory bifurcation with broken translation symmetry. Phys. Rev. E 53, 3579–3600 (1996) ADSCrossRefMathSciNetGoogle Scholar
  58. R.B. Leighton, A magneto-kinematic model of the solar cycle. Astrophys. J. 156, 1–26 (1969) ADSCrossRefGoogle Scholar
  59. E.N. Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963) ADSCrossRefGoogle Scholar
  60. J.A. Markiel, J.H. Thomas, Solar interface dynamo profiles with a realistic rotation profile. Astrophys. J. 523, 827–837 (1999) ADSCrossRefGoogle Scholar
  61. M.S. Miesch, J. Toomre, Turbulence, magnetism, and shear in stellar interiors. Annu. Rev. Fluid Mech. 41, 317–345 (2009) ADSCrossRefGoogle Scholar
  62. H.K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, Cambridge, 1978) Google Scholar
  63. M.J.P.F.G. Monteiro, J. Christensen-Dalsgaard, M.J. Thompson, Seismic study of overshoot at the base of the solar convective envelope. Astron. Astrophys. 283, 247–262 (1994) ADSGoogle Scholar
  64. M. Ossendrijver, The solar dynamo. Astron. Astrophys. Rev. 11, 287 (2003) ADSCrossRefGoogle Scholar
  65. E.N. Parker, Hydromagnetic dynamo models. Astrophys. J. 122, 293 (1955) ADSCrossRefMathSciNetGoogle Scholar
  66. E.N. Parker, Cosmical Magnetic Fields, their Origin and Activity (Clarendon Press, Oxford, 1979) Google Scholar
  67. E.N. Parker, A solar dynamo surface wave at the interface between convection and nonuniform rotation. Astrophys. J. 408, 707 (1993) ADSCrossRefGoogle Scholar
  68. E.N. Parker, Solar dynamo, in Encyclopedia of Geomagnetism and Paleomagnetism, ed. by D. Gubbins, E. Herrero-Bervera (Springer, Dordrecht, 2007), p. 178 CrossRefGoogle Scholar
  69. K. Petrovay, J. Zsargo, On the validity of quasi-linear kinematic mean-field electrodynamics in astrophysical flows. Mon. Not. R. Astron. Soc. 296, 245 (1998) ADSCrossRefGoogle Scholar
  70. A. Pouquet, U. Frisch, J. Léorat, Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321–354 (1976) zbMATHADSCrossRefGoogle Scholar
  71. M.R.E. Proctor, Dynamo processes: the interaction of turbulence and magnetic fields, in Stellar Astrophysical Fluid Dynamics, ed. by M.J. Thompson, J. Christensen-Dalsgaard (Cambridge university Press, Cambridge, 2003) Google Scholar
  72. K.-H. Rädler, Mean-field magnetohydrodynamics as a basis of solar dynamo theory, in IAU Symposium 1971, ed. by V. Bumba, J. Kleczek (Dordrecht-Holland, Dordrecht, 1976), p. 323 Google Scholar
  73. S. Régnier, C.E. Parnell, A.L. Haynes, A new view of quiet-Sun topology from Hinode/SOT. Astron. Astrophys. 484, L47–L50 (2008) ADSCrossRefGoogle Scholar
  74. M. Rempel, Overshoot at the base of the solar convection zone: a semianalytical approach. Astrophys. J. 607, 1046–1064 (2004) ADSCrossRefGoogle Scholar
  75. J.C. Ribes, E. Nesme-Ribes, The solar sunspot cycle in the Maunder minimum AD-1645 to AD-1715. Astron. Astrophys. 276, 549–563 (1993) ADSGoogle Scholar
  76. A. Serebryanskiy, D.-Y. Chou, Comparison of solar cycle variations of solar p-mode frequencies from GONG and MDI. Astrophys. J. 633, 1187–1190 (2005) ADSCrossRefGoogle Scholar
  77. M. Schrinner, K.H. Rädler, D. Schmitt, M. Rheinhardt, U.R. Christensen, Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo. Geophys. Astrophys. Fluid Dyn. 101, 81–116 (2007) ADSCrossRefMathSciNetGoogle Scholar
  78. D. Sokoloff, H. Zhang, K.M. Kuzanyan, V.N. Obridko, D.N. Tomin, V.N. Tutubalin, Current helicity and twist as two indicators of the mirror asymmetry of solar magnetic fields. Solar Phys. 248, 17–28 (2008) ADSCrossRefGoogle Scholar
  79. E.A. Spiegel, Chaos and intermittency in the solar cycle. Space Sci. Rev. 144, 25–51 (2009) ADSCrossRefGoogle Scholar
  80. E.A. Spiegel, N.O. Weiss, Magnetic activity and variations in solar luminosity. Nature 287, 616 (1980) ADSCrossRefGoogle Scholar
  81. M. Steenbeck, F. Krause, K.-H. Rädler, A calculation of the mean electromotive force in an electrically conducting fluid in turbulent motion under the influence of Coriolis forces. Z. Naturforsch. 21a, 369–376 (1966) ADSGoogle Scholar
  82. R.F. Stein, A. Nordlund, Solar surface magneto-convection and dynamo action, in SOLMAG 2002. Proceedings of the Magnetic Coupling of the Solar Atmosphere Euroconference and IAU Colloquium 188, 11–15 June 2002, Santorini, Greece, ed. by H. Sawaya-Lacoste. ESA SP, vol. 505 (ESA Publications Division, Noordwijk, 2002), pp. 83–89 Google Scholar
  83. S. Stellmach, U. Hansen, Cartesian convection driven dynamos at Low Ekman number. Phys. Rev. E. 70, 056312:1–16 (2004) ADSCrossRefGoogle Scholar
  84. J.-C. Thelen, Non-linear αω-dynamos driven by magnetic buoyancy. Mon. Not. R. Astron. Soc. 315, 165–183 (2000) ADSCrossRefGoogle Scholar
  85. J.-C. Thelen, F. Cattaneo, Dynamo action driven by convection; the influence of magnetic boundary conditions. Mon. Not. R. Astron. Soc. 315, L13–L17 (2000) ADSCrossRefGoogle Scholar
  86. J.H. Thomas, N.O. Weiss, Sunspots and Starspots (Cambridge University Press, Cambridge, 2008) CrossRefGoogle Scholar
  87. M.J. Thompson, J. Christensen-Dalsgaard, M.S. Miesch, J. Toomre, The internal rotation of the Sun. Annu. Rev. Astron. Astrophys. 41, 599–643 (2003) ADSCrossRefGoogle Scholar
  88. S.M. Tobias, Grand minima in nonlinear dynamos. Astron. Astrophys. 307, L21 (1996) ADSGoogle Scholar
  89. S.M. Tobias, The solar cycle: parity interactions and amplitude modulation. Astron. Astrophys. 322, 1007–1017 (1997) ADSGoogle Scholar
  90. S.M. Tobias, Modulation of solar and stellar dynamos. Astron. Nachr. 323, 417–423 (2002) zbMATHADSCrossRefGoogle Scholar
  91. S.M. Tobias, The solar tachocline: Formation, stability and its role in the solar dynamo, in Fluid Dynamics and Dynamos in Astrophysics and Geophysics, ed. by A.M. Soward, C.A. Jones, D.W. Hughes, N.O. Weiss (CRC Press, Boca Raton, 2005), p. 193 Google Scholar
  92. S.M. Tobias, The Solar Dynamo: The role of penetration, rotation and shear on convective dynamos. Space Sci. Rev. 144, 77–86 (2009) ADSCrossRefGoogle Scholar
  93. S.M. Tobias, N.O. Weiss, V. Kirk, Chaotically modulated stellar dynamos. Mon. Not. R. Astron. Soc. 273, 1150–1166 (1995) ADSGoogle Scholar
  94. S.M. Tobias, F. Cattaneo, Dynamo action in complex flows: the quick and the fast. J. Fluid Mech. 601, 101–122 (2008) zbMATHADSCrossRefMathSciNetGoogle Scholar
  95. S.M. Tobias, F. Cattaneo, N.H. Brummell, Dynamo action with penetration, rotation and shear. Astrophys. J. 685, 596 (2008) ADSCrossRefGoogle Scholar
  96. S.I. Vainshtein, F. Cattaneo, Nonlinear restrictions on dynamo action. Astrophys. J. 393, 165–171 (1992) ADSCrossRefGoogle Scholar
  97. S.V. Vorontsov, J. Christensen-Dalsgaard, J. Schou, V.N. Strakhov, M.J. Thompson, Helioseismic measurement of solar torsional oscillations. Science 296, 101–103 (2002) ADSCrossRefGoogle Scholar
  98. A. Vögler, M. Schüssler, A solar surface dynamo. Astron. Astrophys. 465, L43–L46 (2007) CrossRefGoogle Scholar
  99. N.O. Weiss, The expulsion of magnetic flux by eddies. Proc. R. Soc. Lond. A 293, 310 (1966) ADSCrossRefGoogle Scholar
  100. N.O. Weiss, M.J. Thompson, The solar dynamo. Space Sci. Rev. 144, 53–66 (2009) ADSCrossRefGoogle Scholar
  101. N.O. Weiss, F. Cattaneo, C.A. Jones, Periodic and aperiodic dynamo waves. Geophys. Astrophys. Fluid Dyn. 30, 305–341 (1984) zbMATHADSCrossRefMathSciNetGoogle Scholar
  102. A. Yoshizawa, H. Kato, N. Yokoi, Mean field theory interpretation of solar polarity reversal. Astrophys. J. 537, 1039–1053 (2000) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Chris A. Jones
    • 1
    Email author
  • Michael J. Thompson
    • 2
  • Steven M. Tobias
    • 1
  1. 1.Department of Applied MathematicsUniversity of LeedsLeedsUK
  2. 2.School of Mathematics and StatisticsUniversity of SheffieldSheffieldUK

Personalised recommendations