Solar Physics

, Volume 290, Issue 2, pp 335–350 | Cite as

Spatio-Temporal Scaling of Turbulent Photospheric Line-of-Sight Magnetic Field in Active Region NOAA 11158

  • J. A. GuerraEmail author
  • A. Pulkkinen
  • V. M. Uritsky
  • S. Yashiro


We studied the structure and dynamics of the turbulent photospheric magnetic field in active region NOAA 11158 by characterizing spatial and temporal scaling properties of the line-of-sight (LOS) component. Using high-resolution high-cadence LOS magnetograms from SDO/HMI, we measured the power-law exponents α and β that describe Fourier power spectra in wavenumber (k) and frequency (f) domains, and we investigated their evolution during the passage of the active region through the field of view of HMI. The flaring active region NOAA 11158 produces a one-dimensional spatial power spectral density that approximately follows a k −2 power law – a spectrum that suggests parallel MHD fluctuations in an anisotropic turbulent medium. In addition, we found that the values of α capture systematically change in the configuration of the LOS photospheric magnetic field during flaring activity in the corona. Position-dependent values of the temporal scaling exponent β showed that, on an average, the core of the active region scales with β>3 surrounded by a diffusive region with an approximately f −2-type spectrum. Our results indicate that only about 1 – 3 % of the studied LOS photospheric magnetic flux displays βα, implying that Taylor’s hypothesis of frozen-in-flow turbulence is typically invalid for this scalar field in the presence of turbulent photospheric flows. In consequence, both spatial and temporal variations of the plasma and magnetic field must be included in a complete description of the turbulent evolution of active regions.


Active regions Flares, relation to magnetic field Magnetic fields, photosphere Photospheric turbulence 



We thank the SDO/HMI and SDO/AIA teams for the data used in this study. This work was done under CEPHEUS cooperative agreement between The Catholic University of America and NASA Goddard Space Flight Center. We thank Karin Muglach for useful discussions.


  1. Abramenko, V.I.: 2005, Astrophys. J. 629, 1141.  DOI. ADSCrossRefGoogle Scholar
  2. Abramenko, V., Yurchyshyn, V.: 2010, Astrophys. J. 720, 717.  DOI. ADSCrossRefGoogle Scholar
  3. Abramenko, V., Yurchyshyn, V., Wang, H., Goode, P.R.: 2001, Solar Phys. 201, 225.  DOI. ADSCrossRefGoogle Scholar
  4. Abramenko, V.I., Yurchyshyn, V.B., Wang, H., Spirock, T.J., Goode, P.R.: 2002, Astrophys. J. 577, 487.  DOI. ADSCrossRefGoogle Scholar
  5. Aschwanden, M.J.: 2011, Self-Organized Criticality in Astrophysics, Springer, Berlin, 122. CrossRefzbMATHGoogle Scholar
  6. Barnes, G., Leka, K.D.: 2008, Astrophys. J. Lett. 688, L107.  DOI. ADSCrossRefGoogle Scholar
  7. Beauregard, L., Verma, M., Denker, C.: 2012, Astron. Nachr. 333, 125.  DOI. ADSCrossRefGoogle Scholar
  8. Biskamp, D.: 1993, Nonlinear Magnetohydrodynamics, Cambridge University Press, Cambridge, 196. CrossRefGoogle Scholar
  9. Biskamp, D., Welter, H.: 1989, Phys. Fluids, B Plasma Phys. 1, 1964.  DOI. CrossRefGoogle Scholar
  10. Borrero, J.M., Tomczyk, S., Kubo, M., Socas-Navarro, H., Schou, J., Couvidat, S., Bogart, R.: 2011, Solar Phys. 273, 267.  DOI. ADSCrossRefGoogle Scholar
  11. Falconer, D.A., Moore, R.L., Gary, G.A.: 2002, Astrophys. J. 569, 1016.  DOI. ADSCrossRefGoogle Scholar
  12. Falconer, D.A., Moore, R.L., Gary, G.A.: 2003, J. Geophys. Res. 108, 1380.  DOI. CrossRefGoogle Scholar
  13. Georgoulis, M.K.: 2008, Geophys. Res. Lett. 35, 6.  DOI. CrossRefGoogle Scholar
  14. Georgoulis, M.K., Rust, D.M.: 2007, Astrophys. J. Lett. 661, L109.  DOI. ADSCrossRefGoogle Scholar
  15. Hergarten, S.: 2002, Self-Organized Criticality in Earth Systems, Springer, Berlin, 48. CrossRefGoogle Scholar
  16. Kolmogorov, A.: 1941, Dokl. Akad. Nauk SSSR 30, 301. ADSGoogle Scholar
  17. Leka, K.D., Barnes, G.: 2003a, Astrophys. J. 595, 1277.  DOI. ADSCrossRefGoogle Scholar
  18. Leka, K.D., Barnes, G.: 2003b, Astrophys. J. 595, 1296.  DOI. ADSCrossRefGoogle Scholar
  19. Lemen, J., Title, A., Akin, D., Boerner, P., Chou, C., Drake, J.F., et al.: 2012, Solar Phys. 275, 17.  DOI. ADSCrossRefGoogle Scholar
  20. Li, Y., Jing, J., Fan, Y., Wang, H.: 2011, Astrophys. J. Lett. 727, L19.  DOI. ADSCrossRefGoogle Scholar
  21. Liu, C., Deng, N., Liu, Y., Falconer, D., Goode, P.R., Denker, C., Wang, H.: 2005, Astrophys. J. 622, 722.  DOI. ADSCrossRefGoogle Scholar
  22. Mandelbrot, B.B.: 1982, The Fractal Geometry of Nature, Freeman, San Francisco, 247. zbMATHGoogle Scholar
  23. McAteer, R.T.J., Gallagher, P.T., Conlon, P.A.: 2010, Adv. Space Res. 45, 1067.  DOI. ADSCrossRefGoogle Scholar
  24. McIntosh, P.: 1990, Solar Phys. 125, 251.  DOI. ADSCrossRefGoogle Scholar
  25. Moin, P.: 2009, J. Fluid Mech. 640, 1.  DOI. ADSCrossRefzbMATHMathSciNetGoogle Scholar
  26. Pesnell, W.D., Thompson, B.J., Chamberlin, P.C.: 2012, Solar Phys. 275, 3.  DOI. ADSCrossRefGoogle Scholar
  27. Petrie, G.J.D., Sudol, J.J.: 2010, Astrophys. J. 724, 1218.  DOI. ADSCrossRefGoogle Scholar
  28. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: 1992, Numerical Recipes in FORTRAN. The Art of Scientific Computing 1, Cambridge University Press, Cambridge, 547. zbMATHGoogle Scholar
  29. Roberts, B.: 2003, Solar Photospheric Magnetic Flux Tubes: Theory, Taylor & Francis, London, 1. Google Scholar
  30. Schekochihin, A.A., Cowley, S.C., Dorland, W., Hammett, G.W., Howes, G.G., Quataert, E., Tatsuno, T.: 2009, Astrophys. J. Suppl. 182, 310.  DOI. ADSCrossRefGoogle Scholar
  31. Scherrer, P.H., Bogart, R.S., Bush, R.I., Hoeksema, J.T., Kosovichev, A.G., Schou, J., et al.: 1995, Solar Phys. 162, 129.  DOI. ADSCrossRefGoogle Scholar
  32. Scherrer, P.H., Schou, J., Bush, R.I., Kosovichev, A.G., Bogart, R.S., Hoeksema, J.T., et al.: 2012, Solar Phys. 275, 207.  DOI. ADSCrossRefGoogle Scholar
  33. Schrijver, C.J., Aulanier, G., Title, A.M., Pariat, E., Delannée, C.: 2011, Astrophys. J. 738, 167.  DOI. ADSCrossRefGoogle Scholar
  34. Shibata, K., Magara, T.: 2011, Living Rev. Solar Phys. 8(6),
  35. Shine, R.A., Simon, G.W., Hurlburt, N.E.: 2000, Solar Phys. 193, 313. ADSCrossRefGoogle Scholar
  36. Simon, G.W., Title, A.M., Weiss, N.O.: 2001, Astrophys. J. 561, 427.  DOI. ADSCrossRefGoogle Scholar
  37. Stenflo, J.O.: 2012, Astron. Astrophys. 541, A17.  DOI. ADSCrossRefGoogle Scholar
  38. Taylor, G.I.: 1938, Proc. Roy. Soc. London A 164, 476.  DOI. ADSCrossRefGoogle Scholar
  39. Uritsky, V.M., Davila, J.M.: 2012, Astrophys. J. 748, 60.  DOI. ADSCrossRefGoogle Scholar
  40. Uritsky, V.M., Davila, J.M., Ofman, L., Coyner, A.J.: 2013, Astrophys. J. 769, 62.  DOI. ADSCrossRefGoogle Scholar
  41. Vemareddy, P., Ambastha, A., Maurya, R.A., Chae, J.: 2012, Astrophys. J. 761, 86.  DOI. ADSCrossRefGoogle Scholar
  42. Wang, S., Liu, C., Liu, R., Deng, N., Liu, Y., Wang, H.: 2012, Astrophys. J. Lett. 745, L17.  DOI. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • J. A. Guerra
    • 1
    • 2
    Email author
  • A. Pulkkinen
    • 2
  • V. M. Uritsky
    • 1
    • 2
  • S. Yashiro
    • 1
    • 2
  1. 1.The Catholic University of AmericaWashingtonUSA
  2. 2.NASA Goddard Space Flight CenterGreenbeltUSA

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