Solar Physics

, Volume 280, Issue 2, pp 321–333 | Cite as

Spontaneous Formation of Magnetic Flux Concentrations in Stratified Turbulence

  • Koen Kemel
  • Axel Brandenburg
  • Nathan Kleeorin
  • Dhrubaditya Mitra
  • Igor Rogachevskii


The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNSs) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in the formation of large-scale inhomogeneous magnetic structures from an initially uniform magnetic field. Earlier investigations of this instability in DNSs of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma β are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L 2/η t, where η t is the turbulent diffusivity and L is the scale of the domain. DNSs are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number.


Magnetohydrodynamics (MHD) Sun: dynamo Sunspots Turbulence 



We thank the anonymous referee for making detailed suggestions. We acknowledge the NORDITA dynamo programs of 2009 and 2011 for providing a stimulating scientific atmosphere. Computing resources were provided by the Swedish National Allocations Committee at the Center for Parallel Computers at the Royal Institute of Technology in Stockholm and the High Performance Computing Center North in Umeå. This work was supported in part by the European Research Council under the AstroDyn Research Project No. 227952.


  1. Brandenburg, A.: 2005, Astrophys. J. 625, 539. ADSCrossRefGoogle Scholar
  2. Brandenburg, A., Procaccia, I., Segel, D.: 1995, Phys. Plasmas 2, 1148. MathSciNetADSCrossRefGoogle Scholar
  3. Brandenburg, A., Kleeorin, N., Rogachevskii, I.: 2010, Astron. Nachr. 331, 5. ADSMATHCrossRefGoogle Scholar
  4. Brandenburg, A., Jennings, R.L., Nordlund, Å., Rieutord, M., Stein, R.F., Tuominen, I.: 1996, J. Fluid Mech. 306, 325. MathSciNetADSMATHCrossRefGoogle Scholar
  5. Brandenburg, A., Kemel, K., Kleeorin, N., Mitra, D., Rogachevskii, I.: 2011, Astrophys. J. 740, L50 (BKKMR). ADSCrossRefGoogle Scholar
  6. Brandenburg, A., Kemel, K., Kleeorin, N., Rogachevskii, I.: 2012, Astrophys. J. doi: 10.1088/0004-637X/748/1/1. arXiv:1005.5700. Google Scholar
  7. Cally, P.S., Dikpati, M., Gilman, P.A.: 2003, Astrophys. J. 582, 1190. ADSCrossRefGoogle Scholar
  8. Cheung, M.C.M., Rempel, M., Title, A.M., Schüssler, M.: 2010, Astrophys. J. 720, 233. ADSCrossRefGoogle Scholar
  9. Cline, K.S., Brummell, N.H., Cattaneo, F.: 2003, Astrophys. J. 599, 1449. ADSCrossRefGoogle Scholar
  10. Golub, L., Rosner, R., Vaiana, G.S., Weiss, N.O.: 1981, Astrophys. J. 243, 309. ADSCrossRefGoogle Scholar
  11. Guerrero, G., Käpylä, P.J.: 2011, Astron. Astrophys. 533, A40. ADSCrossRefGoogle Scholar
  12. Käpylä, P.J., Brandenburg, A., Kleeorin, N., Mantere, M.J., Rogachevskii, I.: 2011, Mon. Not. Roy. Astron. Soc. in press. arXiv:1105.5785.
  13. Kemel, K., Brandenburg, A., Kleeorin, N., Rogachevskii, I.: 2012, Astron. Nachr. 333, 95. ADSCrossRefGoogle Scholar
  14. Kitchatinov, L.L., Mazur, M.V.: 2000, Solar Phys. 191, 325. ADSCrossRefGoogle Scholar
  15. Kitchatinov, L.L., Olemskoy, S.V.: 2006, Astron. Lett. 32, 320. ADSCrossRefGoogle Scholar
  16. Kitiashvili, I.N., Kosovichev, A.G., Wray, A.A., Mansour, N.N.: 2010, Astrophys. J. 719, 307. ADSCrossRefGoogle Scholar
  17. Kleeorin, N., Rogachevskii, I.: 1994, Phys. Rev. E 50, 2716. ADSCrossRefGoogle Scholar
  18. Kleeorin, N.I., Rogachevskii, I.V., Ruzmaikin, A.A.: 1989, Sov. Astron. Lett. 15, 274. ADSGoogle Scholar
  19. Kleeorin, N.I., Rogachevskii, I.V., Ruzmaikin, A.A.: 1990, Sov. Phys. JETP 70, 878. Google Scholar
  20. Kleeorin, N., Mond, M., Rogachevskii, I.: 1996, Astron. Astrophys. 307, 293. ADSGoogle Scholar
  21. Newcomb, W.A.: 1961, Phys. Fluids 4, 391. MathSciNetADSMATHCrossRefGoogle Scholar
  22. Nordlund, Å., Brandenburg, A., Jennings, R.L., Rieutord, M., Ruokolainen, J., Stein, R.F., Tuominen, I.: 1992, Astrophys. J. 392, 647. ADSCrossRefGoogle Scholar
  23. Ossendrijver, M.: 2003, Astron. Astrophys. Rev. 11, 287. ADSCrossRefGoogle Scholar
  24. Parker, E.N.: 1966, Astrophys. J. 145, 811. ADSCrossRefGoogle Scholar
  25. Parker, E.N.: 1979, Cosmical Magnetic Fields, Oxford University Press, New York. Google Scholar
  26. Parker, E.N.: 1982, Astrophys. J. 256, 302. ADSCrossRefGoogle Scholar
  27. Parker, E.N.: 1984, Astrophys. J. 283, 343. ADSCrossRefGoogle Scholar
  28. Priest, E.R.: 1982, Solar Magnetohydrodynamics, Reidel, Dordrecht. CrossRefGoogle Scholar
  29. Rempel, M.: 2011a, Astrophys. J. 729, 5. ADSCrossRefGoogle Scholar
  30. Rempel, M.: 2011b, Astrophys. J. 740, 15. ADSCrossRefGoogle Scholar
  31. Rempel, M., Schüssler, M., Knölker, M.: 2009, Astrophys. J. 691, 640. ADSCrossRefGoogle Scholar
  32. Rempel, M., Schüssler, M., Cameron, R.H., Knölker, M.: 2009, Science 325, 171. ADSCrossRefGoogle Scholar
  33. Rogachevskii, I., Kleeorin, N.: 2007, Phys. Rev. E 76, 056307. MathSciNetADSCrossRefGoogle Scholar
  34. Rüdiger, G.: 1989, Differential Rotation and Stellar Convection: Sun and Solar-Type Stars, Gordon & Breach, New York. Google Scholar
  35. Stein, R.F., Lagerfjärd, A., Nordlund, Å., Georgobiani, D.: 2011, Solar Phys. 268, 271. ADSCrossRefGoogle Scholar
  36. Sur, S., Brandenburg, A., Subramanian, K.: 2008, Mon. Not. Roy. Astron. Soc. 385, L15. ADSCrossRefGoogle Scholar
  37. Tao, L., Weiss, N.O., Brownjohn, D.P., Proctor, M.R.E.: 1998, Astrophys. J. 496, L39. ADSCrossRefGoogle Scholar
  38. Tserkovnikov, Y.A.: 1960, Sov. Phys. Dokl. 5, 87. ADSMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Koen Kemel
    • 1
    • 2
  • Axel Brandenburg
    • 1
    • 2
  • Nathan Kleeorin
    • 1
    • 3
  • Dhrubaditya Mitra
    • 1
  • Igor Rogachevskii
    • 1
    • 3
  1. 1.NorditaAlbaNova University CenterStockholmSweden
  2. 2.Department of AstronomyStockholm UniversityStockholmSweden
  3. 3.Department of Mechanical EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael

Personalised recommendations