Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A Comparison Between Nonlinear Force-Free Field and Potential Field Models Using Full-Disk SDO/HMI Magnetogram


Measurements of magnetic fields and electric currents in the pre-eruptive corona are crucial to the study of solar eruptive phenomena, like flares and coronal mass ejections (CMEs). However, spectro-polarimetric measurements of certain photospheric lines permit a determination of the vector magnetic field only at the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field above multiple active regions with the help of a potential field and a nonlinear force-free field (NLFFF) extrapolation code over the full solar disk using Helioseismic and Magnetic Imager (SDO/HMI) data as boundary conditions. We compare projections of the resulting magnetic field lines with full-disk coronal images from the Atmospheric Imaging Assembly (SDO/AIA) for both models. This study has found that the NLFFF model reconstructs the magnetic configuration closer to observation than the potential field model for full-disk magnetic field extrapolation. We conclude that many of the trans-equatorial loops connecting the two solar hemispheres are current-free.

This is a preview of subscription content, log in to check access.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7


  1. Aly, J.J.: 1989, Solar Phys. 120, 19.

  2. Amari, T., Aly, J.: 2010, Astron. Astrophys. 522, A52.

  3. Amari, T., Luciani, J.F., Aly, J.J., Tagger, M.: 1996, Astrophys. J. Lett. 466, L39.

  4. Aschwanden, M.J., Malanushenko, A.: 2012, Solar Phys. doi: 10.1007/s11207-012-0070-1 .

  5. Borrero, J.M., Tomczyk, S., Kubo, M., Socas-Navarro, H., Schou, J., Couvidat, S., Bogart, R.: 2011, Solar Phys. 273, 267.

  6. DeRosa, M.L., Schrijver, C., Barnes, G., Leka, K., Lites, B., Aschwanden, M., et al.: 2009, Astrophys. J. 696, 1780.

  7. Gary, G.A.: 2001, Solar Phys. 203, 71.

  8. Guo, Y., Ding, M.D., Liu, Y., Sun, X.D., DeRosa, M.L., Wiegelmann, T.: 2012, Astrophys. J. 760, 47.

  9. Inhester, B., Wiegelmann, T.: 2006, Solar Phys. 235, 201.

  10. Jiang, C., Feng, X.: 2012, Astrophys. J. 749, 135.

  11. Jiang, C., Feng, X., Xiang, C.: 2012, Astrophys. J. 755, 62.

  12. Leka, K.D., Barnes, G., Crouch, A.D., Metcalf, T.R., Gary, G.A., Jing, J., Liu, Y.: 2009, Solar Phys. 260, 83.

  13. Lemen, J.R., Title, A.M., Akin, D.J., Boerner, P.F., Chou, C., Drake, J.F., et al.: 2012, Solar Phys. 275, 17.

  14. Lin, H., Penn, M.J., Tomczyk, S.: 2000, Astrophys. J. Lett. 541, L83.

  15. Liu, Y., Lin, H.: 2008, Astrophys. J. 680, 1496.

  16. Metcalf, T.R.: 1994, Solar Phys. 155, 235.

  17. Metcalf, T.R., Leka, K.D., Barnes, G., Lites, B.W., Georgoulis, M.K., Pevtsov, A.A., et al.: 2006, Solar Phys. 237, 267.

  18. Metcalf, T.R., De Rosa, M.L., Schrijver, C.J., Barnes, G., vanô Ballegooijen, A.A., Wiegelmann, T., Wheatland, M.S., Valori, G., McTtiernan, J.M.: 2008, Solar Phys. 247, 269.

  19. Molodensky, M.M.: 1969, Soviet Astron. 12, 585.

  20. Pesnell, W.D., Thompson, B.J., Chamberlin, P.C.: 2012, Solar Phys. 275, 3.

  21. Régnier, S., Priest, E.R.: 2007, Astrophys. J. Lett. 669, L53.

  22. Sakurai, T.: 1989, Space Sci. Rev. 51, 11.

  23. Schatten, K.H., Wilcox, J.M., Ness, N.F.: 1969, Solar Phys. 6, 442.

  24. Schmidt, H.U.: 1964, In: Hess, W.N. (ed.) The Physics of Solar Flares, NASA SP-50, 107.

  25. Schou, J., Scherrer, P.H., Bush, R.I., Wachter, R., Couvidat, S., Rabello-Soares, M.C., et al.: 2012, Solar Phys. 275, 229.

  26. Schrijver, C.J., De Rosa, M.L.: 2003, Solar Phys. 212, 165.

  27. Schrijver, C.J., Title, A.M.: 2005, Astrophys. J. 619, 1077.

  28. Schrijver, C.J., Derosa, M.L., Metcalf, T.R., Liu, Y., McTiernan, J., Régnier, S., Valori, G., Wheatland, M.S., Wiegelmann, T.: 2006, Solar Phys. 235, 161.

  29. Tadesse, T., Wiegelmann, T., Inhester, B.: 2009, Astron. Astrophys. 508, 421.

  30. Tadesse, T., Wiegelmann, T., Inhester, B., Pevtsov, A.: 2011, Astron. Astrophys. 527, A30.

  31. Tadesse, T., Wiegelmann, T., Inhester, B., Pevtsov, A.: 2012a, Solar Phys. 277, 119.

  32. Tadesse, T., Wiegelmann, T., Inhester, B., Pevtsov, A.: 2012b, Solar Phys. 281, 53.

  33. Tadesse, T., Wiegelmann, T., Inhester, B., MacNeice, P., Pevtsov, A., Sun, X.: 2013, Astron. Astrophys. 550, A14.

  34. Thalmann, J.K., Wiegelmann, T., Raouafi, N.E.: 2008, Astron. Astrophys. 488, L71.

  35. Turmon, M., Jones, H.P., Malanushenko, O.V., Pap, J.M.: 2010, Solar Phys. 262, 277.

  36. Valori, G., Kliem, B., Keppens, R.: 2005, Astron. Astrophys. 433, 335.

  37. Wang, Y.M., Sheeley, N.R. Jr.: 1990, Astrophys. J. 365, 372.

  38. Wheatland, M.S.: 2004, Solar Phys. 222, 247.

  39. Wheatland, M.S., Leka, K.D.: 2011, Astrophys. J. 728, 112.

  40. Wheatland, M.S., Régnier, S.: 2009, Astrophys. J. Lett. 700, L88.

  41. Wheatland, M.S., Sturrock, P.A., Roumeliotis, G.: 2000, Astrophys. J. 540, 1150.

  42. Wiegelmann, T.: 2004, Solar Phys. 219, 87.

  43. Wiegelmann, T.: 2007, Solar Phys. 240, 227.

  44. Wiegelmann, T., Inhester, B.: 2010, Astron. Astrophys. 516, A107.

  45. Wiegelmann, T., Inhester, B., Sakurai, T.: 2006, Solar Phys. 233, 215.

  46. Wiegelmann, T., Sakurai, T.: 2012, Living Rev. Solar Phys. 9(5). http://solarphysics.livingreviews.org/Articles/lrsp-2012-5/ .

  47. Wiegelmann, T., Thalmann, J.K., Inhester, B., Tadesse, T., Sun, X., Hoeksema, J.T.: 2012, Solar Phys. 281, 37.

Download references


The authors thank the anonymous referee for helpful and detailed comments. Data are courtesy of NASA/SDO and the AIA and HMI science teams. SOLIS/VSM vector magnetograms are produced cooperatively by NSF/NSO and NASA/LWS. The National Solar Observatory (NSO) is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. This research was partly supported by NASA grant NNX07AU64G and by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center (GSFC), administered by Oak Ridge Associated Universities through a contract with NASA.

Author information

Correspondence to Tilaye Tadesse.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tadesse, T., Wiegelmann, T., MacNeice, P.J. et al. A Comparison Between Nonlinear Force-Free Field and Potential Field Models Using Full-Disk SDO/HMI Magnetogram. Sol Phys 289, 831–845 (2014). https://doi.org/10.1007/s11207-013-0364-y

Download citation


  • Active regions, magnetic fields
  • Active regions, models
  • Magnetic fields, corona
  • Magnetic fields, models
  • Magnetic fields, photosphere