Solar Physics

, 294:14 | Cite as

Large-scale Model of the Axisymmetric Dynamo with Feedback Effects

  • Laura SraibmanEmail author
  • Fernando Minotti


A dynamo model is presented, based on a previously introduced kinematic model, in which the effect of the magnetic field on the mass flow through the Lorentz force is included. Given the base mass flow corresponding to the case with no magnetic field, and assuming that the modification of this flow through the Lorentz force can be treated as a perturbation, a complete model of the large-scale magnetic field dynamics can be obtained. The input needed consists of the large-scale meridional and zonal flows, the small-scale magnetic diffusivity, and a constant parameter entering the expression of the \(\alpha \)-effect. When applied to a Sun-like star, the model shows realistic dynamics of the magnetic field, including cycle duration, consistent field amplitudes with the correct parity, progression of the zonal magnetic field toward the equator, and motion toward the poles of the radial field at high latitudes. In addition, the radial and zonal components show a correct phase relation, and at the surface level, the magnetic helicity is predominantly negative in the northern hemisphere and positive in the southern hemisphere.


Solar cycle, models Magnetic fields, models 



We acknowledge the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and the University of Buenos Aires for institutional support.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.


  1. Belucz, B., Dikpati, M., Forgács-Dajka, E.: 2015, A Babcock–Leighton solar dynamo model with multi-cellular meridional circulation in advection- and diffusion-dominated regimes. Astrophys. J. 806, 169. ADSCrossRefGoogle Scholar
  2. Bonanno, A., Elstner, D., Rüdiger, G., Belvedere, G.: 2002, Parity properties of an advection dominated solar \(\alpha ^{2}\omega \)-dynamo. Astron. Astrophys. 390, 673. ADSCrossRefGoogle Scholar
  3. Brandenburg, A., Moss, D., Tuominen, I.: 1992, Stratification and thermodynamics in mean-field dynamos. Astron. Astrophys. 265, 328. ADSGoogle Scholar
  4. Brandenburg, A., Moss, D., Rüdiger, G., Tuominen, I.: 1990, The nonlinear solar dynamo and differential rotation: a Taylor number puzzle? Solar Phys. 128, 243. ADSCrossRefGoogle Scholar
  5. Cameron, R.H., Dikpati, M., Brandenburg, A.: 2017, The global solar dynamo. Space Sci. Rev., 367. Google Scholar
  6. Cameron, R.H., Schüssler, M.: 2015, The crucial role of surface magnetic fields for the solar dynamo. Science, 1333. Google Scholar
  7. Charbonneau, P.: 2010, Dynamo models of the solar cycle. Living Rev. Solar Phys. 7, 3. ADSCrossRefGoogle Scholar
  8. Charbonneau, P., Christensen-Dalsgaard, J., Henning, R., Larsen, R.M.: 1999, Helioseismic constraints on the structure of the solar tachocline. Astrophys. J. 527, 445. ADSCrossRefGoogle Scholar
  9. Choudhuri, A.R., Schussler, M., Dikpati, M.: 1995, The solar dynamo with meridional circulation. Astron. Astrophys. 303, L29. ADSGoogle Scholar
  10. Clark, R.A., Ferziger, J.H., Reynolds, W.C.: 1979, Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1. ADSCrossRefGoogle Scholar
  11. Dikpati, M., Charbonneau, P.: 1999, A Babcock–Leighton flux transport dynamo with solar-like differential rotation. Astrophys. J. Lett. 518, 508. ADSCrossRefGoogle Scholar
  12. Durney, B.R.: 1995, On a Babcock–Leighton dynamo model with a deep-seated generating layer for the toroidal magnetic field. Solar Phys. 63, 3. Google Scholar
  13. Gnevyshev, M.N., Ohl, A.I.: 1948, Solar activity and its terrestrial manifestations. Astron. Zh. 25, 18. Google Scholar
  14. Guererro, G.A., Munoz, J.D.: 2004, Kinematic solar dynamo models with a deep meridional flow. Mon. Not. Roy. Astron. Soc. 350, 317. ADSCrossRefGoogle Scholar
  15. Hathaway, D.H.: 2015, The solar cycle. Living Rev. Solar Phys. 12, 4. ADSCrossRefGoogle Scholar
  16. Hathaway, D.H., Rightmire, L.: 2010, Variations in the sun’s meridional flow over a solar cycle. Science 327, 1350. ADSCrossRefGoogle Scholar
  17. Hazra, G., Choudhuri, A.R.: 2017, A theoretical model of the variation of the meridional circulation with the solar cycle. Mon. Not. Roy. Astron. Soc. 472, 2728. ADSCrossRefGoogle Scholar
  18. Hazra, G., Karak, B.B., Choudhuri, A.R.: 2014, Is a deep one-cell meridional circulation essential for the flux transport solar dynamo? Astrophys. J. 782, 93. ADSCrossRefGoogle Scholar
  19. Howe, R., Christensen-Dalsgaard, J., Hill, F., Komm, R.W., Larsen, R.M., Schou, J.: 2000, Dynamic variations at the base of the solar convection zone. Science 287, 2456. ADSCrossRefGoogle Scholar
  20. Hung, C.P., Jouve, L., Brun, A.S., Fournier, A., Talagrand, O.: 2015, Estimating the deep solar meridional circulation using magnetic observations and a dynamo model: a variational approach. Astrophys. J. 814, 151. ADSCrossRefGoogle Scholar
  21. Jackiewicz, J., Serebryanskiy, A., Kholikov, S.: 2015, Meridional flow in the solar convection zone. ii. Helioseismic inversions of GONG data. Astrophys. J. 805, 133. ADSCrossRefGoogle Scholar
  22. Jouve, L., Brun, A.S.: 2007, On the role of meridional flows in flux transport dynamo models. Astron. Astrophys. 474, 239. ADSCrossRefGoogle Scholar
  23. Karak, B.B., Cameron, R.: 2016, Babcock–Leighton solar dynamo: the role of downward pumping and the equatorward propagation of activity. Astrophys. J. 832, 94. ADSCrossRefGoogle Scholar
  24. Kitchatinov, L.L., Nepomnyashchikh, A.A.: 2017, A joined model for solar dynamo and differential rotation. Astron. Lett. 43, 332. ADSCrossRefGoogle Scholar
  25. Küker, M., Arlt, R., Rüdiger, G.: 1999, The Maunder minimum as due to magnetic Open image in new window-quenching. Astron. Astrophys. 343, 977. ADSGoogle Scholar
  26. Küker, M., Rüdiger, G., Schultz, M.: 2001, Circulation-dominated solar shell dynamo models with positive alpha effect. Astron. Astrophys. 374, 301. ADSCrossRefGoogle Scholar
  27. Lemerle, A., Charbonneau, P.: 2017, A coupled 2 × 2d Babcock–Leighton solar dynamo model. ii. Reference dynamo solutions. Astrophys. J. 834, 133. ADSCrossRefGoogle Scholar
  28. Leonard, A.: 1974, Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18(A), 237. ADSGoogle Scholar
  29. Miesch, M.S., Dikpati, M.: 2014, A three-dimensional Babcock–Leighton solar dynamo model. Astrophys. J. Lett. 785, 1. ADSCrossRefGoogle Scholar
  30. Miesch, M.S., Teweldebirhan, K.: 2016, A three-dimensional Babcock–Leighton solar dynamo model: initial results with axisymmetric flows. Adv. Space Res. 58, 1571. ADSCrossRefGoogle Scholar
  31. Minotti, F.O.: 2000, Self-consistent derivation of subgrid stresses for large-scale fluid equations. Phys. Rev. E 61, 429. ADSCrossRefGoogle Scholar
  32. Passos, D., Charbonneau, P., Miesch, M.: 2015, Meridional circulation dynamics from 3d magnetohydrodynamic global simulations of solar convection. Astrophys. J. Lett. 800, L18. ADSCrossRefGoogle Scholar
  33. Passos, D., Nandy, D., Hazra, S., Lopes, I.: 2014, A solar dynamo model driven by mean-field alpha and Babcock–Leighton sources: fluctuations, grand-minima-maxima, and hemispheric asymmetry in sunspot cycles. Astron. Astrophys. 563, A18. ADSCrossRefGoogle Scholar
  34. Pope, S.B.: 2000, Turbulent Flows, Cambridge University Press, UK, 587. CrossRefGoogle Scholar
  35. Rempel, M.: 2006, Flux-transport dynamos with Lorentz force feedback on differential rotation and meridional flow: saturation mechanism and torsional oscillations. Astrophys. J. Lett. 647, 662. ADSCrossRefGoogle Scholar
  36. Rüdiger, G., Hollerbach, R.: 2004, The Magnetic Universe: Geophysical and Astrophysical Dynamo Theory, Wiley, Germany, 137. CrossRefGoogle Scholar
  37. Schad, A., Timmer, J., Roth, M.: 2013, Global helioseismic evidence for a deeply penetrating solar meridional flow consisting of multiple flow cells. Astrophys. J. Lett. 778, 38. ADSCrossRefGoogle Scholar
  38. Schou, J., Antia, H.M., Basu, S., Bogart, R.S., Bush, R.I., Chitre, S.M.: 1998, Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the Michelson Doppler Imager. Astrophys. J. 505, 390. ADSCrossRefGoogle Scholar
  39. Schumann, U.: 1975, Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376. ADSCrossRefGoogle Scholar
  40. Scotti, A., Meneveau, C., Lilly, D.K.: 1993, Generalized Smagorinsky model for anisotropic grids. Phys. Fluids A 5, 2306. ADSCrossRefGoogle Scholar
  41. Sraibman, L., Minotti, F.: 2016, Large-scale model of the axisymmetric kinematic dynamo. Mon. Not. Roy. Astron. Soc. 456, 3715. ADSCrossRefGoogle Scholar
  42. Thompson, M.J.: 2004, Helioseismology and the sun’s interior. Astron. Geophys. 45, 4.21. CrossRefGoogle Scholar
  43. Wang, Y.-M., Sheeley, N.R. Jr.: 1991, Magnetic flux transport and the sun’s dipole moment – new twists to the Babcock–Leighton model. Astrophys. J. Lett. 375, 761. CrossRefGoogle Scholar
  44. Zhao, J., Bogart, R.S., Kosovichev, A.G., Duvall Jr, T.L., Hartlep, T.: 2013, Detection of equatorward meridional flow and evidence of double-cell meridional circulation inside the sun. Astrophys. J. Lett. 774, L29. ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Facultad de Ciencias Exactas y Naturales, Departamento de FísicaUniversidad de Buenos AiresBuenos AiresArgentina
  2. 2.Instituto de Física del Plasma (INFIP)CONICET-Universidad de Buenos AiresBuenos AiresArgentina

Personalised recommendations