Inside the Sun pp 385-402 | Cite as

The Solar Dynamo

  • K.-H. Rädler
Part of the Astrophysics and Space Science Library book series (ASSL, volume 159)


The phenomena of solar activity are connected with a general magnetic field of-the Sun which is due to a dynamo process essentially determined by the α-effect and the differential rotation in the convection zone. A few observational facts are summarized which are important for modelling this process. The basic ideas of the solar dynamo theory, with emphasis on the mean-field approach, are explained, and a critical review of the dynamo models investigated so far is given. Although several models reflect a number of essential features of the solar magnetic cycle there are many open questions. Part of them result from lack of knowledge of the structure of the convective motions and the differential rotation. Other questions concern, for example, details of the connection of the α-effect and related effects with the convective motions, or the way in which the behaviour of the dynamo is influenced by the back-reaction of the magnetic field on the motions.


Solar Cycle Flux Tube Convection Zone Differential Rotation Solar Magnetic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Belvedere, G. (1983) ‘Dynamo theory in the Sun and stars’, in P.B. Byrne and M. Rodonô (eds.), Activity in Red-Dwarf Stars, D. Reidel Publishing Co., Dordrecht, pp. 579–599.Google Scholar
  2. Belvedere, G., Paterné, L. and Stix, M. (1980a)‘Dynamo action of a mean flow caused by latitude-dependent heat transport’, Astron. Astrophys. 86, 40–45.ADSGoogle Scholar
  3. Belvedere, G., Patemô, L. and Stix M. (1980b) ‘Magnetic cycles of lower main sequence stars’, Astron. Astrophys. 91, 328–330.ADSGoogle Scholar
  4. Belvedere, G. and Proctor, M.R.E. (1989) ‘Nonlinear dynamo modes and timescales of stellar activity’, submitted to Proceedings IAU-Symp. 138.Google Scholar
  5. Brandenburg, A. (1988)’kinematic dynamo theory and the solar activity cycle’, Licenciate thesis, University of Helsinki.Google Scholar
  6. Brandenburg, A., Krause, F., Meinel, R., Moss, D. and Tuominen, I. (1989a) ‘The stability of nonlinear dynamos and the limited role of kinematic growth rates’, Astron. Astrophys. 213, 411–422.ADSGoogle Scholar
  7. Brandenburg, A., Krause, F., and Tuominen, I. (1989b) ‘Parity selection in nonlinear dynamos’, in M. Meneguzzi et al. (eds.), Turbulence and Nonlinear Dynamics in MHD Flows, Elsevier Science Publishers, North Holland.Google Scholar
  8. Brandenburg, A., Moss, D., Rédiger, G. and Tuominen. I. (1989c) ‘The nonlinear solar dynamo and differential rotation: A Taylor number puzzle, submitted to Solar Physics.Google Scholar
  9. Brandenburg, A., Moss, D. and Tuominen, I. (1989d) ‘On the nonlinear stability of dynamo models’, Geophys. Astrophys. Fluid Dyn., in press.Google Scholar
  10. Brandenburg, A. and Tuominen, I. (1988) ‘Variation of magnetic fields and flows during the solar cycle’, Adv. Space Res. 8, No 7, (7)185–(7)189.ADSCrossRefGoogle Scholar
  11. Brandenburg, A., Tuominen, I. and Rédler, K.-H. (1989e) ‘On the generation of non-axisymmetric magnetic fields in mean-field dynamos’, Geophys. Astrophys. Fluid Dyn., in press.Google Scholar
  12. Busse, F.H. (1979) ‘Some new results on spherical dynamos’, Physics Earth Planet. Inter. 20, 152–157.ADSCrossRefGoogle Scholar
  13. Busse, F.H. and Miin, S.W. (1979) ‘Spherical dynamos with anisotropic a-effect’, Geophys. Astrophys. Fluid Dyn. 14, 167–181.ADSzbMATHCrossRefGoogle Scholar
  14. Cowling, T.G. (1934) ‘The magnetic fields of sunspots’, Mon. Not. Roy. Astr. Soc. 94, 39–48.ADSGoogle Scholar
  15. Deinzer, W. and Stix, M. (1971) ‘On the eigenvalues of Krause-Steenbeck’s solar dynamo’, Astron. Astrophys. 12, 111–119.ADSGoogle Scholar
  16. Deinzer, W., von Kusserow, H.U. and Stix, M. (1974) ‘Steady and oscillatory aœ-dynamos’, Astron. Astrophys. 36, 69–78.ADSGoogle Scholar
  17. Deluca, E.E. and Gilman, P.A. (1986) ‘Dynamo theory for the interface between convection zone and the radiative interior of a star. Part I. Model equations and exact solutions’, Geophys. Astrophys. Fluid Dyn. 37, 85–127.ADSzbMATHCrossRefGoogle Scholar
  18. Dumey, B.R. (1988) ‘On a simple dynamo model and the anisotropic a—effect’, Astron. Astrophys. 191, 374.ADSGoogle Scholar
  19. Gilman, P.A. (1983) ‘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.ADSCrossRefGoogle Scholar
  20. Gilman, P.A. (1986) The solar dynamo: observations and theories of solar convection, global circulation, and magnetic fields’, in P.A. Sturrock et al. (eds.), Physics of the Sun, D. Reidel Publishing Co., Dordrecht, pp. 95–160.CrossRefGoogle Scholar
  21. Gilman, P.A. and Miller, J. (1981) ‘Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell’, Astrophys. J. Suppl. 46, 211–238.ADSCrossRefGoogle Scholar
  22. Gilman, P.A., Morrow, C.A. and Deluca, E.E. (1989) ‘Angular momentum transport and dynamo action in the Sun: Implications of recent oscillation measurements’, Astrophys. J. 338, 528–537.ADSCrossRefGoogle Scholar
  23. Glatzmaier, G.A. (1985) ‘Numerical simulations of stellar convective dynamos. II. Field propagation in the convection zone’, Astrophys. J. 291, 300–307.ADSCrossRefGoogle Scholar
  24. Ivanova, T.S. and Ruzmaikin, A.A. (1975) ‘A magnetohydrodynamic dynamo model of the solar cycle’, Soy. Astron. 20, 227–234.ADSGoogle Scholar
  25. Ivanova, T.S. and Ruzmaikin, A.A. (1977) ‘A nonlinear MHD-model of the dynamo of the Sun’, Astron. Zh. (USSR) 54, 846–858 (in Russian).ADSGoogle Scholar
  26. Ivanova, T.S. and Ruzmaikin, A.A. (1985)’Three-dimensional model for the generation of the mean solar magnetic field’, Astron. Nachr. 306, 177–186.ADSzbMATHCrossRefGoogle Scholar
  27. Jepps, S.A. (1975) Numerical models of hydromagnetic dynamos’, J. Fluid Mech. 67, 629–646.ADSCrossRefGoogle Scholar
  28. Kleeorin, N.I. and Ruzmaikin, A.A. (1984) ‘Mean-field dynamo with cubic non-linearity’, Astron. Nachr. 305, 265–275.MathSciNetADSCrossRefGoogle Scholar
  29. Köhler, H. (1973) The solar dynamo and estimates of the magnetic diffusivity and the a-effect’, Astron. Astrophys. 25, 467–476.ADSGoogle Scholar
  30. Krause, F. (1971) ‘Zur Dynamotheorie magnetischer Sterne: Der symmetrische Rotatorals Alternative zum mschiefen Rotator’, Astron. Nachr. 293, 187–193.ADSCrossRefGoogle Scholar
  31. Krause, F. and Meinel, R. (1988) ‘Stability of simple nonlinear a2-dynamos’, Geophys. Astrophys. Fluid dyn. 43, 95–117.ADSCrossRefGoogle Scholar
  32. Krause, F. and Rädler, K.-H. (1980) ‘Mean-Field Magnetohydrodynamics and Dynamo Theory’, Akademie-Verlag, Berlin and Pergamon Press, Oxford.Google Scholar
  33. Krivodubski, V.N. (1984) ‘Magnetic field transfer in the turbulent solar envelope’, Soy. Astron. 28, 205–211.ADSGoogle Scholar
  34. Kurths, J. (1987) ‘An attractor analysis of the sunspot relative number’, Preprint PRE-ZIAP (Potsdam) 87–02.Google Scholar
  35. Larmor, J. (1919) ‘How could a rotating body such as the Sun become a magnet?’ Rep. Brit. Assoc. adv. Sc. 1919, 159–160.Google Scholar
  36. Levy, E.H. (1972) ‘Effectiveness of cyclonic convertion for producing the geomagnetic field’, Astrophys. J. 171, 621–633.ADSCrossRefGoogle Scholar
  37. Malkus, W.V.R. and Proctor, M.R.E. (1975) The macrodynamics of a-effect dynamos in rotating fluids’, J. Fluid Mech. 67, 417–444.ADSzbMATHCrossRefGoogle Scholar
  38. Nicklaus, B. and Stix, M. (1988) ‘Corrections to first order smoothing in mean-field electrodynamics’, Geophys. Astrophys. Fluid Dyn. 43, 149–166.ADSzbMATHCrossRefGoogle Scholar
  39. Parker, E.N. (1955) ‘Hydromagnetic dynamo models’, Astrophys. J. 122, 293–314.MathSciNetADSCrossRefGoogle Scholar
  40. Parker, E.N. (1979) ‘Cosmical Magnetic fields’, Clarendon Press, Oxford.Google Scholar
  41. Rädler, K.-H. (1969) ’Über eine neue Möglichkeit eines Dynamomechanismus in turbulenten leitenden Medien’, Mber. Dtsch. Akad. Wiss. Berlin 11, 194–201.Google Scholar
  42. Rädler, K.-H. (1975) ‘Some new results on the generation of magnetic fields by dynamo action’, Mem. Soc. Roy. Sc. Liege VIII, 109–116.Google Scholar
  43. Rädler, K.-H. (1976) ‘Mean-field magnetohydrodynamics as a basis of solar dynamo theory’, in B. Bumba and J. Kleczek (eds.), Basic Mechanisms of Solar Activity, D. Reidel Publishing Co., Dordrecht, pp. 323–344.CrossRefGoogle Scholar
  44. Rädler, K.-H. (1980) ‘Mean-field approach to spherical dinamo models’, Astron. Nachr. 301, 101–129.CrossRefGoogle Scholar
  45. Rädler, K.-H. (1981a) ‘On the mean-field approach to spherical dynamo models’, in A.M. Soward (ed.), Stellar and Planetary Magnetism, Gordon and Breach Publishers, New York, pp. 17–36.Google Scholar
  46. Rädler, K.-H. (1981b) ‘Remarks on the a-effect and dynamo action in spherical models’, in A.M Soward (ed.), Stellar and Planetary Magnetism, Gordon and Breach Publishers, New York, pp. 37–48.Google Scholar
  47. Rädler, K.-H. (1986a) ‘Investigations of spherical kinematic mean-field dynamo models’, Astron. Nachr. 307, 89–113.ADSzbMATHCrossRefGoogle Scholar
  48. Rädler, K.-H. (1986b) ‘On the effect of differential rotation on axisymmetric and non-axisymmetric magnetic fields of cosmical bodies’, Plasma-Astrophysics, ESA SP-251, 569–574.Google Scholar
  49. Rädler, K. -H. and Bräuer, H.-J. (1987) ‘On the oscillatory behaviour of kinematic mean-field dynamos’, Astron. Nachr. 308, 101–109.zbMATHCrossRefGoogle Scholar
  50. Rédler, K.-H., Brandenburg, A. and Tuominen, I. (1989) ‘On the non-axisymmetric magnetic-field modes of the solar dynamo’, Poster IAU-Colloquium No 121, to be submitted to Solar Physics.Google Scholar
  51. Rédler, K.-H. and Wiedemann, E. (1989) ‘Numerical experiments with a simple nonlinear mean-field dynamo model’,Geophys. Astrophys. fluid Dyn., in press.Google Scholar
  52. Ribes, E., Mein, P. and Manganey, A. (1985) ‘A large scale meridional circulation in the convective zone’, Nature 318, 170–171.ADSCrossRefGoogle Scholar
  53. Ribes, E. and Laclare, F. (1988) ‘Toroidal convection rolls in the Sun’, Geophys. Astrophys. Fluid Dyn. 41, 171–180.ADSCrossRefGoogle Scholar
  54. Roberts, P.H. (1972) ‘Kinematic dynamo models’, Phil. Trans. Roy. Soc. A 272, 663–703.ADSCrossRefGoogle Scholar
  55. Roberts, P.H. and Stix, M. (1972) ‘a-effect dynamos, by the Bullard-Gellman formalism’, Astron. Astrophys. 18, 453–466.ADSGoogle Scholar
  56. Rüdiger, G. (1974a) ‘The influence of a uniform magnetic field of arbitrary strength on turbulence’, Astron. Nachr. 295, 275–283.ADSzbMATHCrossRefGoogle Scholar
  57. Rüdiger, G. (1974b) ‘Behandlung eines einfachen hydromagnetischen Dynamos mit Hilfe der Gitterpunktmethode’, Pub. Astrophys. Obs. Potsdam 32, 25–29.Google Scholar
  58. Rüdiger, G. (1980) ‘Rapidly rotating a2-dynamo models’, Astron. Nachr. 301, 181–187.ADSCrossRefGoogle Scholar
  59. Rüdiger, G. (1989) ‘Differential Rotation and Stellar Convection’, Akademie-Verlag, Berlin and Gordon and Breach Science Publishers, New York.Google Scholar
  60. Rüdiger, G. Tuominen, I., Krause, F. and Virtanen, H. (1986) ‘Dynamo generated flows in the Sun’, Astron. Astrophys. 166, 306–318.ADSzbMATHGoogle Scholar
  61. Ruzmaikin, A.A. (1985) ‘The solar dynamo’, Solar Physics 100, 125–140.ADSCrossRefGoogle Scholar
  62. Ruzmaikin, A.A., Sokoloff, D.D. and Starchenko, S.V. (1988) ‘Excitation of non-axially symmetric modes of the Sun’s magnetic field’, Solar Phys. 115, 5–15.ADSCrossRefGoogle Scholar
  63. Schmitt, D. (1985) ‘Dynamowirkung magnetischer Wellen’, Thesis, Univ. Göttingen.Google Scholar
  64. Schmitt, D. (1987) ‘An a-dynamo with an a-effect due to magnetostrophic waves’, Astron. Astrophys. 174, 281–287.ADSzbMATHGoogle Scholar
  65. Steenbeck, M. and Krause, F. (1969a) ‘Zur Dynamotheorie stellarer und planetarer Magnetfelder. I. Berechnung sonnenähnlicher Wechselfeldgeneratoren’, Astron. Nachr. 291, 49–84.ADSzbMATHCrossRefGoogle Scholar
  66. Steenbeck, M. and Krause, F. (1969b) ‘Zur Dynamotheorie stellarer und planetarer Magnetfelder. II. Berechnung planetenähnlicher Gleichfeldgeneratoren’, Astron. Nachr. 291, 271–286.ADSzbMATHCrossRefGoogle Scholar
  67. Steenbeck, M., Krause, F. and Rädler, K.-H. (1966) ‘Berechnung der mittleren Lorentz-Feldstärken vxB für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflubter Bewegung’, Z. Naturforsch. 21a, 369–376.ADSGoogle Scholar
  68. Stenflo, J.O. (1973) ‘Magnetic-field structure of the photospheric network’, Solar Physics 32, 41–63.ADSCrossRefGoogle Scholar
  69. Stenflo, J.O. and Vogel, M. (1986) ‘Global resonances in the evolution of solar magnetic fields’, Nature 319, 285.ADSCrossRefGoogle Scholar
  70. Stenflo, J.O. and Güdel, M. (1987) ‘Evolution of solar magnetic fields: Modal stucture’, Astron. Astrophys. 191, 137.ADSGoogle Scholar
  71. Stix, M. (1971) ‘A non-axisymmetric a-effect dynamo’, Astron. Astrophys. 13, 203–208.ADSGoogle Scholar
  72. Stix, M. (1972) ‘non-linear dynamo waves’, Astron. Astrophys. 20, 9–12.ADSzbMATHGoogle Scholar
  73. Stix, M. (1973) ‘Spherical a-dynamos, by a variational method’, Astron. Astrophys. 24, 275–281.ADSGoogle Scholar
  74. Stix, M. (1976a) ‘Dynamo theory and the solar cycle’, in V. Bumba and J. Kleczek (eds.), Basic Mechanisms of Solar Activity, D. Reidel Publishing Co., Dordrecht, pp. 367–388.CrossRefGoogle Scholar
  75. Stix, M. (1976b) ‘Differential rotation and the solar dynamo’, Astron. Astrophys. 47, 243–254.ADSGoogle Scholar
  76. Stix, M. (1981) ‘Theory of the solar cycle’, Solar Physics 74, 79–101.ADSCrossRefGoogle Scholar
  77. Stix, M. (1983) ‘Helicity and a-effect of simple convection cells’, Astron. Astrophys. 118, 363–364.MathSciNetADSzbMATHGoogle Scholar
  78. Stix, M. (1989) ‘The Sun’, Springer-Verlag Berlin.Google Scholar
  79. Tuominen, I., Rüdiger, G. and Brandenburg, A. (1988) Observational constraints for solar-type dynamos’, in O. Havens et al. (eds.), Activity in Cool Star Envelopes, Kluwer Academic Publishers, London, pp. 13–20.CrossRefGoogle Scholar
  80. Walder, M., Deinzer, W. and Stix, M. (1980) ‘Dynamo action associated with random waves in a rotating stratified fluid’, J. Fluid Mech. 96, 207–222.ADSzbMATHCrossRefGoogle Scholar
  81. Weiss, N.O. (1985) ‘Chaotic behaviour in stellar dynamos’, Journal of Statistical Physics 39, 477–491.MathSciNetADSCrossRefGoogle Scholar
  82. Weisshaar, E. (1982) ‘A numerical study of a2-dynamos with anisotropic a-effect’, Geophys. Astrophys. Fluid dyn. 21, 285.ADSzbMATHCrossRefGoogle Scholar
  83. Yoshimura, H. (1975a) ‘Solar-cycle dynamo wave propagation’, Astrophys. J. 201, 740–748.MathSciNetADSCrossRefGoogle Scholar
  84. Yoshimura, H. (1975b) ‘A model of the solar cycle driven by the dynamo action of the global convection in the solar convection zone’, Astrophys. J. Suppl. 29, 467–494.ADSCrossRefGoogle Scholar
  85. Yoshimura, H. (1976) ‘Phase relation between the poloidal and toroidal solar-cycle general magnetic fields and location of the origin of the surface magnetic fields’, Solar Physics 50, 3–23.ADSCrossRefGoogle Scholar
  86. Yoshimura, H. (1978a) ‘Nonlinear astrophysical dynamos: The solar cycle as the non-linear oscillation of the general magnetic field driven by the non-linear dynamo and the associated modulation of the differential-rotation-global-convection system’, Astrophys. J. 220, 692–711.ADSCrossRefGoogle Scholar
  87. Yoshimura, H. (1978b) ‘Nonlinear astrophysical dynamos: multiple-period dynamo wave oscillations and long-term modulations of the 22 years solar cycle’, Astrophys. J. 226, 706–719.ADSCrossRefGoogle Scholar
  88. Yoshimura, H. (1981) ‘Solar cycle Lorentz force waves and the torsional oscillations of the Sun’, Astrophys. J. 247, 1102–1112.ADSCrossRefGoogle Scholar
  89. Yoshimura, H., Wang, Z. and Wu, F. (1984a) ‘Linear astrophysical dynamos in rotating spheres: Differential rotation, anisotropic turbulent magnetic diffusivity, and solar-stellar cycle magnetic parity’, Astrophys. J. 280, 865–872.ADSCrossRefGoogle Scholar
  90. Yoshimura, H., Wang, Z. and Wu, F. (1984b) ‘Linear astrophysical dynamos in rotating spheres: Mode transition between steady and oscillatory dynamos as a function of the dynamo strength and anisotropie turbulent magnetic diffusivity’, Astrophys. J. 283, 870–878.ADSCrossRefGoogle Scholar
  91. Yoshimura, H., Wu, F. and Wang, Z. (1984c) ‘Linear astrophysical dynamos in rotating spheres: Solar and stellar cycle north-south hemisphere parity selection mechanism and turbulent magnetic diffusivity’, Astrophys. J. 285, 325–338.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • K.-H. Rädler
    • 1
  1. 1.Sternwarte BabelsbergPotsdamGermany

Personalised recommendations