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.
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.
Belvedere, G., Patemô, L. and Stix M. (1980b) ‘Magnetic cycles of lower main sequence stars’, Astron. Astrophys. 91, 328–330.
Belvedere, G. and Proctor, M.R.E. (1989) ‘Nonlinear dynamo modes and timescales of stellar activity’, submitted to Proceedings IAU-Symp. 138.
Brandenburg, A. (1988)’kinematic dynamo theory and the solar activity cycle’, Licenciate thesis, University of Helsinki.
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.
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.
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.
Brandenburg, A., Moss, D. and Tuominen, I. (1989d) ‘On the nonlinear stability of dynamo models’, Geophys. Astrophys. Fluid Dyn., in press.
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.
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.
Busse, F.H. (1979) ‘Some new results on spherical dynamos’, Physics Earth Planet. Inter. 20, 152–157.
Busse, F.H. and Miin, S.W. (1979) ‘Spherical dynamos with anisotropic a-effect’, Geophys. Astrophys. Fluid Dyn. 14, 167–181.
Cowling, T.G. (1934) ‘The magnetic fields of sunspots’, Mon. Not. Roy. Astr. Soc. 94, 39–48.
Deinzer, W. and Stix, M. (1971) ‘On the eigenvalues of Krause-Steenbeck’s solar dynamo’, Astron. Astrophys. 12, 111–119.
Deinzer, W., von Kusserow, H.U. and Stix, M. (1974) ‘Steady and oscillatory aœ-dynamos’, Astron. Astrophys. 36, 69–78.
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.
Dumey, B.R. (1988) ‘On a simple dynamo model and the anisotropic a—effect’, Astron. Astrophys. 191, 374.
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.
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.
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.
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.
Glatzmaier, G.A. (1985) ‘Numerical simulations of stellar convective dynamos. II. Field propagation in the convection zone’, Astrophys. J. 291, 300–307.
Ivanova, T.S. and Ruzmaikin, A.A. (1975) ‘A magnetohydrodynamic dynamo model of the solar cycle’, Soy. Astron. 20, 227–234.
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).
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.
Jepps, S.A. (1975) Numerical models of hydromagnetic dynamos’, J. Fluid Mech. 67, 629–646.
Kleeorin, N.I. and Ruzmaikin, A.A. (1984) ‘Mean-field dynamo with cubic non-linearity’, Astron. Nachr. 305, 265–275.
Köhler, H. (1973) The solar dynamo and estimates of the magnetic diffusivity and the a-effect’, Astron. Astrophys. 25, 467–476.
Krause, F. (1971) ‘Zur Dynamotheorie magnetischer Sterne: Der symmetrische Rotatorals Alternative zum mschiefen Rotator’, Astron. Nachr. 293, 187–193.
Krause, F. and Meinel, R. (1988) ‘Stability of simple nonlinear a2-dynamos’, Geophys. Astrophys. Fluid dyn. 43, 95–117.
Krause, F. and Rädler, K.-H. (1980) ‘Mean-Field Magnetohydrodynamics and Dynamo Theory’, Akademie-Verlag, Berlin and Pergamon Press, Oxford.
Krivodubski, V.N. (1984) ‘Magnetic field transfer in the turbulent solar envelope’, Soy. Astron. 28, 205–211.
Kurths, J. (1987) ‘An attractor analysis of the sunspot relative number’, Preprint PRE-ZIAP (Potsdam) 87–02.
Larmor, J. (1919) ‘How could a rotating body such as the Sun become a magnet?’ Rep. Brit. Assoc. adv. Sc. 1919, 159–160.
Levy, E.H. (1972) ‘Effectiveness of cyclonic convertion for producing the geomagnetic field’, Astrophys. J. 171, 621–633.
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.
Nicklaus, B. and Stix, M. (1988) ‘Corrections to first order smoothing in mean-field electrodynamics’, Geophys. Astrophys. Fluid Dyn. 43, 149–166.
Parker, E.N. (1955) ‘Hydromagnetic dynamo models’, Astrophys. J. 122, 293–314.
Parker, E.N. (1979) ‘Cosmical Magnetic fields’, Clarendon Press, Oxford.
Rädler, K.-H. (1969) ’Über eine neue Möglichkeit eines Dynamomechanismus in turbulenten leitenden Medien’, Mber. Dtsch. Akad. Wiss. Berlin 11, 194–201.
Rädler, K.-H. (1975) ‘Some new results on the generation of magnetic fields by dynamo action’, Mem. Soc. Roy. Sc. Liege VIII, 109–116.
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.
Rädler, K.-H. (1980) ‘Mean-field approach to spherical dinamo models’, Astron. Nachr. 301, 101–129.
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.
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.
Rädler, K.-H. (1986a) ‘Investigations of spherical kinematic mean-field dynamo models’, Astron. Nachr. 307, 89–113.
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.
Rädler, K. -H. and Bräuer, H.-J. (1987) ‘On the oscillatory behaviour of kinematic mean-field dynamos’, Astron. Nachr. 308, 101–109.
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.
Rédler, K.-H. and Wiedemann, E. (1989) ‘Numerical experiments with a simple nonlinear mean-field dynamo model’,Geophys. Astrophys. fluid Dyn., in press.
Ribes, E., Mein, P. and Manganey, A. (1985) ‘A large scale meridional circulation in the convective zone’, Nature 318, 170–171.
Ribes, E. and Laclare, F. (1988) ‘Toroidal convection rolls in the Sun’, Geophys. Astrophys. Fluid Dyn. 41, 171–180.
Roberts, P.H. (1972) ‘Kinematic dynamo models’, Phil. Trans. Roy. Soc. A 272, 663–703.
Roberts, P.H. and Stix, M. (1972) ‘a-effect dynamos, by the Bullard-Gellman formalism’, Astron. Astrophys. 18, 453–466.
Rüdiger, G. (1974a) ‘The influence of a uniform magnetic field of arbitrary strength on turbulence’, Astron. Nachr. 295, 275–283.
Rüdiger, G. (1974b) ‘Behandlung eines einfachen hydromagnetischen Dynamos mit Hilfe der Gitterpunktmethode’, Pub. Astrophys. Obs. Potsdam 32, 25–29.
Rüdiger, G. (1980) ‘Rapidly rotating a2-dynamo models’, Astron. Nachr. 301, 181–187.
Rüdiger, G. (1989) ‘Differential Rotation and Stellar Convection’, Akademie-Verlag, Berlin and Gordon and Breach Science Publishers, New York.
Rüdiger, G. Tuominen, I., Krause, F. and Virtanen, H. (1986) ‘Dynamo generated flows in the Sun’, Astron. Astrophys. 166, 306–318.
Ruzmaikin, A.A. (1985) ‘The solar dynamo’, Solar Physics 100, 125–140.
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.
Schmitt, D. (1985) ‘Dynamowirkung magnetischer Wellen’, Thesis, Univ. Göttingen.
Schmitt, D. (1987) ‘An a-dynamo with an a-effect due to magnetostrophic waves’, Astron. Astrophys. 174, 281–287.
Steenbeck, M. and Krause, F. (1969a) ‘Zur Dynamotheorie stellarer und planetarer Magnetfelder. I. Berechnung sonnenähnlicher Wechselfeldgeneratoren’, Astron. Nachr. 291, 49–84.
Steenbeck, M. and Krause, F. (1969b) ‘Zur Dynamotheorie stellarer und planetarer Magnetfelder. II. Berechnung planetenähnlicher Gleichfeldgeneratoren’, Astron. Nachr. 291, 271–286.
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.
Stenflo, J.O. (1973) ‘Magnetic-field structure of the photospheric network’, Solar Physics 32, 41–63.
Stenflo, J.O. and Vogel, M. (1986) ‘Global resonances in the evolution of solar magnetic fields’, Nature 319, 285.
Stenflo, J.O. and Güdel, M. (1987) ‘Evolution of solar magnetic fields: Modal stucture’, Astron. Astrophys. 191, 137.
Stix, M. (1971) ‘A non-axisymmetric a-effect dynamo’, Astron. Astrophys. 13, 203–208.
Stix, M. (1972) ‘non-linear dynamo waves’, Astron. Astrophys. 20, 9–12.
Stix, M. (1973) ‘Spherical a-dynamos, by a variational method’, Astron. Astrophys. 24, 275–281.
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.
Stix, M. (1976b) ‘Differential rotation and the solar dynamo’, Astron. Astrophys. 47, 243–254.
Stix, M. (1981) ‘Theory of the solar cycle’, Solar Physics 74, 79–101.
Stix, M. (1983) ‘Helicity and a-effect of simple convection cells’, Astron. Astrophys. 118, 363–364.
Stix, M. (1989) ‘The Sun’, Springer-Verlag Berlin.
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.
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.
Weiss, N.O. (1985) ‘Chaotic behaviour in stellar dynamos’, Journal of Statistical Physics 39, 477–491.
Weisshaar, E. (1982) ‘A numerical study of a2-dynamos with anisotropic a-effect’, Geophys. Astrophys. Fluid dyn. 21, 285.
Yoshimura, H. (1975a) ‘Solar-cycle dynamo wave propagation’, Astrophys. J. 201, 740–748.
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.
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.
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.
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.
Yoshimura, H. (1981) ‘Solar cycle Lorentz force waves and the torsional oscillations of the Sun’, Astrophys. J. 247, 1102–1112.
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.
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.
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.
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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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