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Inside the Sun pp 385–402Cite as

The Solar Dynamo

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Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 159))

Abstract

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.

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References

  • 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 

  • 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.

    ADS  Google Scholar 

  • Belvedere, G., Patemô, L. and Stix M. (1980b) ‘Magnetic cycles of lower main sequence stars’, Astron. Astrophys. 91, 328–330.

    ADS  Google Scholar 

  • Belvedere, G. and Proctor, M.R.E. (1989) ‘Nonlinear dynamo modes and timescales of stellar activity’, submitted to Proceedings IAU-Symp. 138.

    Google Scholar 

  • Brandenburg, A. (1988)’kinematic dynamo theory and the solar activity cycle’, Licenciate thesis, University of Helsinki.

    Google Scholar 

  • 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.

    ADS  Google Scholar 

  • 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 

  • 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 

  • Brandenburg, A., Moss, D. and Tuominen, I. (1989d) ‘On the nonlinear stability of dynamo models’, Geophys. Astrophys. Fluid Dyn., in press.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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 

  • Busse, F.H. (1979) ‘Some new results on spherical dynamos’, Physics Earth Planet. Inter. 20, 152–157.

    Article  ADS  Google Scholar 

  • Busse, F.H. and Miin, S.W. (1979) ‘Spherical dynamos with anisotropic a-effect’, Geophys. Astrophys. Fluid Dyn. 14, 167–181.

    Article  ADS  MATH  Google Scholar 

  • Cowling, T.G. (1934) ‘The magnetic fields of sunspots’, Mon. Not. Roy. Astr. Soc. 94, 39–48.

    ADS  Google Scholar 

  • Deinzer, W. and Stix, M. (1971) ‘On the eigenvalues of Krause-Steenbeck’s solar dynamo’, Astron. Astrophys. 12, 111–119.

    ADS  Google Scholar 

  • Deinzer, W., von Kusserow, H.U. and Stix, M. (1974) ‘Steady and oscillatory aœ-dynamos’, Astron. Astrophys. 36, 69–78.

    ADS  Google Scholar 

  • 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.

    Article  ADS  MATH  Google Scholar 

  • Dumey, B.R. (1988) ‘On a simple dynamo model and the anisotropic a—effect’, Astron. Astrophys. 191, 374.

    ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Glatzmaier, G.A. (1985) ‘Numerical simulations of stellar convective dynamos. II. Field propagation in the convection zone’, Astrophys. J. 291, 300–307.

    Article  ADS  Google Scholar 

  • Ivanova, T.S. and Ruzmaikin, A.A. (1975) ‘A magnetohydrodynamic dynamo model of the solar cycle’, Soy. Astron. 20, 227–234.

    ADS  Google Scholar 

  • 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).

    ADS  Google Scholar 

  • 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.

    Article  ADS  MATH  Google Scholar 

  • Jepps, S.A. (1975) Numerical models of hydromagnetic dynamos’, J. Fluid Mech. 67, 629–646.

    Article  ADS  Google Scholar 

  • Kleeorin, N.I. and Ruzmaikin, A.A. (1984) ‘Mean-field dynamo with cubic non-linearity’, Astron. Nachr. 305, 265–275.

    Article  MathSciNet  ADS  Google Scholar 

  • Köhler, H. (1973) The solar dynamo and estimates of the magnetic diffusivity and the a-effect’, Astron. Astrophys. 25, 467–476.

    ADS  Google Scholar 

  • Krause, F. (1971) ‘Zur Dynamotheorie magnetischer Sterne: Der symmetrische Rotatorals Alternative zum mschiefen Rotator’, Astron. Nachr. 293, 187–193.

    Article  ADS  Google Scholar 

  • Krause, F. and Meinel, R. (1988) ‘Stability of simple nonlinear a2-dynamos’, Geophys. Astrophys. Fluid dyn. 43, 95–117.

    Article  ADS  Google Scholar 

  • Krause, F. and Rädler, K.-H. (1980) ‘Mean-Field Magnetohydrodynamics and Dynamo Theory’, Akademie-Verlag, Berlin and Pergamon Press, Oxford.

    Google Scholar 

  • Krivodubski, V.N. (1984) ‘Magnetic field transfer in the turbulent solar envelope’, Soy. Astron. 28, 205–211.

    ADS  Google Scholar 

  • Kurths, J. (1987) ‘An attractor analysis of the sunspot relative number’, Preprint PRE-ZIAP (Potsdam) 87–02.

    Google Scholar 

  • 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 

  • Levy, E.H. (1972) ‘Effectiveness of cyclonic convertion for producing the geomagnetic field’, Astrophys. J. 171, 621–633.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  MATH  Google Scholar 

  • Nicklaus, B. and Stix, M. (1988) ‘Corrections to first order smoothing in mean-field electrodynamics’, Geophys. Astrophys. Fluid Dyn. 43, 149–166.

    Article  ADS  MATH  Google Scholar 

  • Parker, E.N. (1955) ‘Hydromagnetic dynamo models’, Astrophys. J. 122, 293–314.

    Article  MathSciNet  ADS  Google Scholar 

  • Parker, E.N. (1979) ‘Cosmical Magnetic fields’, Clarendon Press, Oxford.

    Google Scholar 

  • Rädler, K.-H. (1969) ’Über eine neue Möglichkeit eines Dynamomechanismus in turbulenten leitenden Medien’, Mber. Dtsch. Akad. Wiss. Berlin 11, 194–201.

    Google Scholar 

  • 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 

  • 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.

    Chapter  Google Scholar 

  • Rädler, K.-H. (1980) ‘Mean-field approach to spherical dinamo models’, Astron. Nachr. 301, 101–129.

    Article  Google Scholar 

  • 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 

  • 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 

  • Rädler, K.-H. (1986a) ‘Investigations of spherical kinematic mean-field dynamo models’, Astron. Nachr. 307, 89–113.

    Article  ADS  MATH  Google Scholar 

  • 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 

  • Rädler, K. -H. and Bräuer, H.-J. (1987) ‘On the oscillatory behaviour of kinematic mean-field dynamos’, Astron. Nachr. 308, 101–109.

    Article  MATH  Google Scholar 

  • 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 

  • 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 

  • Ribes, E., Mein, P. and Manganey, A. (1985) ‘A large scale meridional circulation in the convective zone’, Nature 318, 170–171.

    Article  ADS  Google Scholar 

  • Ribes, E. and Laclare, F. (1988) ‘Toroidal convection rolls in the Sun’, Geophys. Astrophys. Fluid Dyn. 41, 171–180.

    Article  ADS  Google Scholar 

  • Roberts, P.H. (1972) ‘Kinematic dynamo models’, Phil. Trans. Roy. Soc. A 272, 663–703.

    Article  ADS  Google Scholar 

  • Roberts, P.H. and Stix, M. (1972) ‘a-effect dynamos, by the Bullard-Gellman formalism’, Astron. Astrophys. 18, 453–466.

    ADS  Google Scholar 

  • Rüdiger, G. (1974a) ‘The influence of a uniform magnetic field of arbitrary strength on turbulence’, Astron. Nachr. 295, 275–283.

    Article  ADS  MATH  Google Scholar 

  • Rüdiger, G. (1974b) ‘Behandlung eines einfachen hydromagnetischen Dynamos mit Hilfe der Gitterpunktmethode’, Pub. Astrophys. Obs. Potsdam 32, 25–29.

    Google Scholar 

  • Rüdiger, G. (1980) ‘Rapidly rotating a2-dynamo models’, Astron. Nachr. 301, 181–187.

    Article  ADS  Google Scholar 

  • Rüdiger, G. (1989) ‘Differential Rotation and Stellar Convection’, Akademie-Verlag, Berlin and Gordon and Breach Science Publishers, New York.

    Google Scholar 

  • Rüdiger, G. Tuominen, I., Krause, F. and Virtanen, H. (1986) ‘Dynamo generated flows in the Sun’, Astron. Astrophys. 166, 306–318.

    ADS  MATH  Google Scholar 

  • Ruzmaikin, A.A. (1985) ‘The solar dynamo’, Solar Physics 100, 125–140.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Schmitt, D. (1985) ‘Dynamowirkung magnetischer Wellen’, Thesis, Univ. Göttingen.

    Google Scholar 

  • Schmitt, D. (1987) ‘An a-dynamo with an a-effect due to magnetostrophic waves’, Astron. Astrophys. 174, 281–287.

    ADS  MATH  Google Scholar 

  • Steenbeck, M. and Krause, F. (1969a) ‘Zur Dynamotheorie stellarer und planetarer Magnetfelder. I. Berechnung sonnenähnlicher Wechselfeldgeneratoren’, Astron. Nachr. 291, 49–84.

    Article  ADS  MATH  Google Scholar 

  • Steenbeck, M. and Krause, F. (1969b) ‘Zur Dynamotheorie stellarer und planetarer Magnetfelder. II. Berechnung planetenähnlicher Gleichfeldgeneratoren’, Astron. Nachr. 291, 271–286.

    Article  ADS  MATH  Google Scholar 

  • 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.

    ADS  Google Scholar 

  • Stenflo, J.O. (1973) ‘Magnetic-field structure of the photospheric network’, Solar Physics 32, 41–63.

    Article  ADS  Google Scholar 

  • Stenflo, J.O. and Vogel, M. (1986) ‘Global resonances in the evolution of solar magnetic fields’, Nature 319, 285.

    Article  ADS  Google Scholar 

  • Stenflo, J.O. and Güdel, M. (1987) ‘Evolution of solar magnetic fields: Modal stucture’, Astron. Astrophys. 191, 137.

    ADS  Google Scholar 

  • Stix, M. (1971) ‘A non-axisymmetric a-effect dynamo’, Astron. Astrophys. 13, 203–208.

    ADS  Google Scholar 

  • Stix, M. (1972) ‘non-linear dynamo waves’, Astron. Astrophys. 20, 9–12.

    ADS  MATH  Google Scholar 

  • Stix, M. (1973) ‘Spherical a-dynamos, by a variational method’, Astron. Astrophys. 24, 275–281.

    ADS  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Stix, M. (1976b) ‘Differential rotation and the solar dynamo’, Astron. Astrophys. 47, 243–254.

    ADS  Google Scholar 

  • Stix, M. (1981) ‘Theory of the solar cycle’, Solar Physics 74, 79–101.

    Article  ADS  Google Scholar 

  • Stix, M. (1983) ‘Helicity and a-effect of simple convection cells’, Astron. Astrophys. 118, 363–364.

    MathSciNet  ADS  MATH  Google Scholar 

  • Stix, M. (1989) ‘The Sun’, Springer-Verlag Berlin.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  ADS  MATH  Google Scholar 

  • Weiss, N.O. (1985) ‘Chaotic behaviour in stellar dynamos’, Journal of Statistical Physics 39, 477–491.

    Article  MathSciNet  ADS  Google Scholar 

  • Weisshaar, E. (1982) ‘A numerical study of a2-dynamos with anisotropic a-effect’, Geophys. Astrophys. Fluid dyn. 21, 285.

    Article  ADS  MATH  Google Scholar 

  • Yoshimura, H. (1975a) ‘Solar-cycle dynamo wave propagation’, Astrophys. J. 201, 740–748.

    Article  MathSciNet  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Yoshimura, H. (1981) ‘Solar cycle Lorentz force waves and the torsional oscillations of the Sun’, Astrophys. J. 247, 1102–1112.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  Google Scholar 

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  1. Sternwarte Babelsberg, DDR-1591, Potsdam, Germany

    K.-H. Rädler

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  1. K.-H. Rädler
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  1. Observatoire de la Côte d’Azur, Nice, France

    Gabrielle Berthomieu

  2. CEN, Saclay, France

    Michel Cribier

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Rädler, KH. (1990). The Solar Dynamo. In: Berthomieu, G., Cribier, M. (eds) Inside the Sun. Astrophysics and Space Science Library, vol 159. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0541-2_32

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  • DOI: https://doi.org/10.1007/978-94-009-0541-2_32

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