Solar Physics

, Volume 282, Issue 2, pp 389–404 | Cite as

Instrumental and Observational Artifacts in Quiet Sun Magnetic Flux Cancellation Functions

  • A. PietarilaEmail author
  • J. Pietarila Graham


Under the assumption that the photospheric quiet Sun magnetic field is turbulent, the cancellation function has previously been used to estimate the true, resolution-independent mean, unsigned vertical flux 〈|B z |〉true. We show that the presence of network elements, noise, and seeing complicate the measurement of accurate cancellation functions and their power law exponents κ. Failure to exclude network elements previously led to estimates that were too low for both the cancellation exponent κ and 〈|B z |〉true. However, both κ and 〈|B z |〉true are overestimated due to noise in magnetograms. While no conclusive value can be derived with data from current instruments, our Hinode/SP results of κ⪅0.38 and 〈|B z |〉true⪅270 gauss can be taken as upper bounds.


Solar magnetic fields Photosphere Quiet Sun 



JPG gratefully acknowledges the support of the U.S. Department of Energy through the LANL/LDRD Program for this work. Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in cooperation with ESA and NSC (Norway) data provided by the SOHO/MDI consortium. SOHO is a mission of international cooperation between ESA and NASA. SDO is a mission for NASA’s Living With a Star program.


  1. Abramenko, V.: 2003, Pre-flare changes in current helicity and turbulent regime of the photospheric magnetic field. Adv. Space Res. 32, 1937. ADSCrossRefGoogle Scholar
  2. Abramenko, V., Yurchyshyn, V.: 2010a, Intermittency and multifractality spectra of the magnetic field in solar active regions. Astrophys. J. 722, 122. ADSCrossRefGoogle Scholar
  3. Abramenko, V., Yurchyshyn, V.: 2010b, Magnetic energy spectra in solar active regions. Astrophys. J. 720, 717. ADSCrossRefGoogle Scholar
  4. Brandenburg, A.: 1995, Flux tubes and scaling in MHD dynamo simulations. Chaos Solitons Fractals 5, 2023. ADSCrossRefGoogle Scholar
  5. Brandenburg, A., Procaccia, I., Segel, D., Vincent, A.: 1992, Fractal level sets and multifractal fields in direct simulations of turbulence. Phys. Rev. A 46, 4819. ADSCrossRefGoogle Scholar
  6. Cadavid, A.C., Lawrence, J.K., Ruzmaikin, A.A., Kayleng-Knight, A.: 1994, Multifractal models of small-scale solar magnetic fields. Astrophys. J. 429, 391. ADSCrossRefGoogle Scholar
  7. Frisch, U.: 1995, Turbulence. The Legacy of A.N. Kolmogorov. Cambridge University Press. Cambridge, 136–148, 185–189. zbMATHGoogle Scholar
  8. Georgoulis, M.K.: 2012, Are solar active regions with major flares more fractal, multifractal, or turbulent than others? Solar Phys. 276, 161. ADSCrossRefGoogle Scholar
  9. Goldreich, P., Sridhar, S.: 1995, Toward a theory of interstellar turbulence. 2: Strong Alfvénic turbulence. Astrophys. J. 438, 763. ADSCrossRefGoogle Scholar
  10. Goode, P.R., Yurchyshyn, V., Cao, W., Abramenko, V., Andic, A., Ahn, K., Chae, J.: 2010, Highest resolution observations of the quietest Sun. Astrophys. J. Lett. 714, L31. ADSCrossRefGoogle Scholar
  11. Iroshnikov, P.S.: 1964, Turbulence of a conducting fluid in a strong magnetic field. Soviet Astron. 7, 566. MathSciNetADSGoogle Scholar
  12. Janßen, K., Vögler, A., Kneer, F.: 2003, On the fractal dimension of small-scale magnetic structures in the Sun. Astron. Astrophys. 409, 1127. ADSCrossRefGoogle Scholar
  13. Kraichnan, R.H.: 1965, Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8, 1385. MathSciNetADSCrossRefGoogle Scholar
  14. Lee, E., Brachet, M.E., Pouquet, A., Mininni, P.D., Rosenberg, D.: 2010, Lack of universality in decaying magnetohydrodynamic turbulence. Phys. Rev. E 81, 016318. ADSCrossRefGoogle Scholar
  15. Lites, B.W., Kubo, M., Socas-Navarro, H., Berger, T., Frank, Z., Shine, R., et al.: 2008, The horizontal magnetic flux of the quiet-Sun internetwork as observed with the Hinode Spectro-Polarimeter. Astrophys. J. 672, 1237. ADSCrossRefGoogle Scholar
  16. Manso Sainz, R., Landi Degl’Innocenti, E., Trujillo Bueno, J.: 2006, A qualitative interpretation of the second solar spectrum of Ce ii. Astron. Astrophys. 447, 1125. ADSCrossRefGoogle Scholar
  17. Moll, R., Pietarila Graham, J., Pratt, J., Cameron, R.H., Müller, W.-C., Schüssler, M.: 2011, Universality of the small-scale dynamo mechanism. Astrophys. J. 736, 36. ADSCrossRefGoogle Scholar
  18. Ott, E., Du, Y., Sreenivasan, K.R., Juneja, A., Suri, A.K.: 1992, Sign-singular measures – fast magnetic dynamos, and high-Reynolds-number fluid turbulence. Phys. Rev. Lett. 69, 2654. ADSCrossRefGoogle Scholar
  19. Pietarila Graham, J., Cameron, R., Schüssler, M.: 2010, Turbulent small-scale dynamo action in solar surface simulations. Astrophys. J. 714, 1606. ADSCrossRefGoogle Scholar
  20. Pietarila Graham, J., Danilovic, S., Schüssler, M.: 2009, Turbulent magnetic fields in the quiet Sun: implications of Hinode observations and small-scale dynamo simulations. Astrophys. J. 693, 1728. ADSCrossRefGoogle Scholar
  21. Pietarila Graham, J., Mininni, P.D., Pouquet, A.: 2005, Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modeling. Phys. Rev. E 72, 045301. ADSCrossRefGoogle Scholar
  22. Pietarila Graham, J., Mininni, P.D., Pouquet, A.: 2011, High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model. Phys. Rev. E 84, 016314. ADSCrossRefGoogle Scholar
  23. Sánchez Almeida, J., Martínez González, M.: 2011, The magnetic fields of the quiet Sun. In: Kuhn, J.R., Harrington, D.M., Lin, H., Berdyugina, S.V., Trujillo-Bueno, J., Keil, S.L., Rimmele, T. (eds.) Solar Polarization 6, ASP Conf. Ser. 437, 451. Google Scholar
  24. Scherrer, P.H., Bogart, R.S., Bush, R.I., Hoeksema, J.T., Kosovichev, A.G., Schou, J., et al.: 1995, The Solar Oscillations Investigation – Michelson Doppler Imager. Solar Phys. 162, 129. ADSCrossRefGoogle Scholar
  25. Scherrer, P.H., Schou, J., Bush, R.I., Kosovichev, A.G., Bogart, R.S., Hoeksema, J.T., et al.: 2012, The Helioseismic and Magnetic Imager (HMI) investigation for the Solar Dynamics Observatory (SDO). Solar Phys. 275, 207. ADSCrossRefGoogle Scholar
  26. Solanki, S.K., Barthol, P., Danilovic, S., Feller, A., Gandorfer, A., Hirzberger, J., et al.: 2010, SUNRISE: Instrument, mission, data, and first results. Astrophys. J. Lett. 723, L127. ADSCrossRefGoogle Scholar
  27. Sorriso-Valvo, L., Carbone, V., Noullez, A., Politano, H., Pouquet, A., Veltri, P.: 2002, Analysis of cancellation in two-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 9, 89. MathSciNetADSCrossRefGoogle Scholar
  28. Sorriso-Valvo, L., Abramenko, V., Carbone, V., Noullez, A., Politano, H., Pouquet, A., Veltri, P., Yurchyshyn, V.: 2003, Cancellations analysis of photospheric magnetic structures and flares. Mem. Soc. Astron. Ital. 74, 631. ADSGoogle Scholar
  29. Sorriso-Valvo, L., Carbone, V., Veltri, P., Abramenko, V.I., Noullez, A., Politano, H., Pouquet, A., Yurchyshyn, V.: 2004, Topological changes of the photospheric magnetic field inside active regions: A prelude to flares? Planet. Space Sci. 52, 937. ADSCrossRefGoogle Scholar
  30. Stenflo, J.O.: 2011, Collapsed, uncollapsed, and hidden magnetic flux on the quiet Sun. Astron. Astrophys. 529, A42. ADSCrossRefGoogle Scholar
  31. Tsuneta, S., Ichimoto, K., Katsukawa, Y., Nagata, S., Otsubo, M., Shimizu, T., et al.: 2008, The solar optical telescope for the Hinode mission: an overview. Solar Phys. 249, 167. ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.National Solar ObservatoryTucsonUSA
  2. 2.Solid Mechanics and Fluid Dynamics (T-3) & Center for Nonlinear Studies; Los Alamos National Laboratory MS-B258Los AlamosUSA

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