What can we learn from nonlinear forcefree extrapolations

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Hinode Science Meeting, Dublin 23 Aug.
2007
What can we learn from nonlinear force-free
extrapolations?
Stéphane Régnier University of St Andrews
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Hinode Science Meeting, Dublin 23 Aug.
2007
Understanding solar eruptions from flares to CMEs
What are the most suitable magnetic
configurations for flares and
CMEs? How to store magnetic energy in the
corona? What is the amount of magnetic helicity
needed to trigger a flare? How much magnetic
flux can be reconnected
during an eruptive event? What is the importance
of separator field lines
in the flaring mechanism?
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Hinode Science Meeting, Dublin 23 Aug.
2007
What are the main properties of a magnetic
configuration?
Geometry length, height, magnetic field
strength of field lines as well as twist and
shear (Régnier et al. 2002, 2004, Régnier and
Canfield 2006, Régnier and Priest
2007) Magnetic Energy free magnetic energy
budget, deposit of energy in the corona (Régnier
and Priest 2007) Magnetic Helicity injection of
helicity through photosphere, expelled in CMEs
(Régnier et al. 2005) Connectivity defining
flux domains (if they exist) Magnetic
Topology null points, separatrix surfaces,
separator, and quasi-topology.
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Hinode Science Meeting, Dublin 23 Aug.
2007
Pre-requisites
Magnetic Energy Woltjers Theorem (1958) If the
normal field is fixed on the boundary,
the
minimum-energy state is the linear force-free
field that
conserves the total magnetic helicity Free
Magnetic Energy
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Hinode Science Meeting, Dublin 23 Aug.
2007
See Régnier and Priest, ApJ submitted
AR 8210 Obs. on 1 May 1998 Activity C-class
flares Free Energy 1.3 (2.3)
AR 8151 Obs. on 11 Feb. 1998 Activity failed
filament eruption and CME, no flare Free Energy
8 (70)
AR 0486 Obs. on 28 Oct. 2003 Activity X17 flare
CME Free Energy 11.4 (34.4)
?
7.23 1032 erg
x
AR 9077 Obs. on 14 July 2000 Activity post-flare
loops (X5) Free Energy 12.8 (18.4)
?
1.62 1032 erg
x
0.05 1032 erg
?
x
?
0.14 1032 erg
? Nonlinear force-free energy x Linear
force-free energy
x
AR9077
AR8210
AR8151
AR0486
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Hinode Science Meeting, Dublin 23 Aug.
2007
Courtesy of T. Amari

• Hinode vector magnetogram
• Nonlinear force-free reconstruction
• Obs. on 12 Dec. 2006
• AR 10930
• Existence of a twisted flux tube
• Non-uniform twist (see also Régnier et al. 2004)
• 40 of free energy above potential
• Enlff 6.51 1033 erg ( AR 0486)

More about AR 10930 NLFFF Talks by M. DeRosa and
S. Inoue (this afternoon) Poster by T.
Wiegelmann
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Hinode Science Meeting, Dublin 23 Aug.
2007
Conclusions

• Magnetic Energy
• Free magnetic energy computed both above
  potential and above the linear force-free field
  satisfying Woltjers theorem
• Both values needed to distinguish between the
  different eruptive mechanisms
• NLFF extrapolations
• Richness of the magnetic configuration ?
  geometry (twist and shear), magnetic energy,
  magnetic helicity, connectivity, topology
• More physical insights to study flaring activity
  (e.g., confined and eruptive flares, CMEs)

• Future directions
• Magnetohydrostatic modeling of the corona
• Incorporating plasma information in magnetic
  configurations
• Faster algorithms