Solar Physics

, Volume 290, Issue 2, pp 491–506 | Cite as

Time Evolution of Force-Free Parameter and Free Magnetic Energy in Active Region NOAA 10365

  • G. ValoriEmail author
  • P. Romano
  • A. Malanushenko
  • I. Ermolli
  • F. Giorgi
  • K. Steed
  • L. van Driel-Gesztelyi
  • F. Zuccarello
  • J.-M. Malherbe


We describe the variation of the accumulated coronal helicity derived from the magnetic helicity flux through the photosphere in active region (AR) NOAA 10365, where several large flares and coronal mass ejections (CMEs) occurred. We used SOHO/MDI full-disk line-of-sight magnetograms to measure the helicity flux, and the integral of GOES X-ray flux as a proxy of the coronal energy variations due to flares or CMEs. Using the linear force-free field model, we transformed the accumulated helicity flux into a time sequence of the force-free parameter α accounting for flares or CMEs via the proxy derived from GOES observations. This method can be used to derive the value of α at different times during the AR evolution, and is a partial alternative to the commonly used match of field lines with EUV loops. By combining the accumulated helicity obtained from the observations with the linear force-free theory, we describe the main phases of the emergence process of the AR, and relate them temporally with the occurrence of flares or CMEs. Additionally, a comparison with the loop-matching method of fixing alpha at each time independently shows that the proposed method may be helpful in avoiding unrealistic or undetermined values of alpha that may originate from an insufficient quality of the image used to identify coronal loops at a given time. For the relative intensity of the considered events, the linear force-free field theory implies that there is a direct correlation between the released energy on the one hand and the product of the coronal helicity with the variation of α due to the event on the other. Therefore, the higher the value of the accumulated coronal helicity, the smaller the force-free parameter variation required to produce the same decrease in the free energy during the CMEs.


Magnetic fields, photosphere Velocity fields, photosphere 



The research leading to these results has received funding from the European Commissions Seventh Framework Programme under the grant agreements no. 284461 (eHEROES project), no. 312495 (SOLARNET project), and from no. 263340 (SWIFF project), and from the Leverhulme Trust, Research Project Grant no. RPG-2014-051. LvDG’s work was supported by the Hungarian Research grants OTKA K-081421 and K-109276, and the STFC Consolidated Grant ST/H00260/1. PR, IE, FG, FZ work was partially supported by the INAF grant PRIN-INAF-2010. The SOHO/LASCO CME catalogue is generated and maintained at the CDAW Data Center by NASA and The Catholic University of America in cooperation with the Naval Research Laboratory. SOHO is a project of international cooperation between ESA and NASA. TRACE is a mission of the Stanford-Lockheed Institute for Space Research, and part of the NASA Small Explorer programme.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • G. Valori
    • 1
    • 2
    • 7
    Email author
  • P. Romano
    • 3
  • A. Malanushenko
    • 4
  • I. Ermolli
    • 1
  • F. Giorgi
    • 1
  • K. Steed
    • 5
  • L. van Driel-Gesztelyi
    • 2
    • 6
    • 7
  • F. Zuccarello
    • 8
  • J.-M. Malherbe
    • 2
  1. 1.INAFOsservatorio Astronomico di RomaMonte Porzio CatoneItaly
  2. 2.LESIA-Observatoire de Paris, CNRS, UPMC Univ. Paris 06Univ. Paris-DiderotMeudon CedexFrance
  3. 3.INAFOsservatorio Astrofisico di CataniaCataniaItaly
  4. 4.Department of PhysicsMontana State UniversityBozemanUSA
  5. 5.Centre for Mathematical Plasma Astrophysics, Department of MathematicsKU LeuvenLeuvenBelgium
  6. 6.Konkoly Observatory of the Hungarian Academy of SciencesBudapestHungary
  7. 7.Mullard Space Science LaboratoryUniversity College LondonDorkingUK
  8. 8.Dipartimento di Fisica e AstronomiaUniversitá di CataniaCataniaItaly

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