Preliminary Results from Nonlinear Field Extrapolations using Hinode Boundary Data

1
Preliminary Results from Nonlinear Field
Extrapolations using Hinode Boundary Data

• Marc DeRosa (LMSAL), on behalf of the NLFFF Team
• WG1 SHINE 2007
• Karel Schrijver, Tom Metcalf, Graham Barnes,
  Bruce Lites, Ted Tarbell, Aad van Ballegooijen,
  Jim McTiernan, Gherardo Valori, Thomas
  Wiegelmann, Mike Wheatland, Tahar Amari,
  Guillaume Aulanier, Pascal Démoulin, Kanya
  Kusano, Stéphane Régnier, Julia Thalmann, Marcel
  Fuhrmann

2
Rationale

• Understanding the structure and evolution of the
  solar corona requires a quantitative
  understanding of the coronal magnetic field and
  its currents.
• Nonlinear force-free fields (NLFFFs) provide a
  useful model. These are computed by
  extrapolating upward from a surface (usually
  photospheric) vector magnetogram.
• Three popular methods
• Optimization minimize a metric containing (? ?
  B) ? B and ? ? B
• Current-field iteration compute field, apply
  currents, recompute field,
• Magneto-frictional solves a MHD-like system of
  equations that include an ad-hoc friction term
  that drives the system toward a force-free state

3
Recap of previous work

• We have previously used analytic solutions as
  blind test cases, and found that these algorithms
  are viable. However, the fields from these test
  cases do not resemble solar fields. Schrijver
  et al. 2006
• We also tested the methods on a solar-like model,
  and found Metcalf et al. 2008
• Correct solution is largely recovered by all
  methods when a chromospheric vector magnetogram
  is used (i.e., a magnetogram containing no net
  Lorentz force or magnetic torque).
• Correct solution is not recovered when a
  photospheric vector magnetogram is used (i.e.,
  a magnetogram containing forces and torques).
• Photospheric boundary data can be pre-processed
  to remove forces and torques. However, getting
  accurate measurements of physical quantities
  (such as free energies) remains difficult.

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Hinode dataset

• Two vector magnetograms derived from
  Hinode/SOT-SP scans bracketing X flare on 2006
  Dec 13 from AR10930
• native spatial sampling is 0.16?0.16?
• slit is 164? long (1024 pixels)
• 90min for a 160?-wide scan
• binned 44 for our purposes
• SOT-SP magnetogram embedded in MDI magnetogram
• resulting cutout is 320320 pixels (205?205?)
• Links to Ca H flare movie, and to Hinode/XRT
  flare movie

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Pre-flare magnetogram
Hinode/SOT-BFI
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Pre-flare magnetogram
Hinode/SOT-BFI
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2006.12.12 2030 case
2006.12.12_2030
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Comparison with observations

• Start with an image with prominent loops (e.g.,
  TRACE).
• Trace some loops by hand.
• Draw fieldlines in the model that interesect
  midpoint of each hand-traced line.
• Determine the best-fit fieldline for each
  hand-traced fieldline.

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Comparison with observations

• Best match determined by evaluating length of
  several spokes in vicinity of crossing point.
• Minimum aggregate length wins.

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Hinode/XRT overlay - preflare
fieldlines contained within a 320320128 pixel
volume
2006.12.12_2030
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Volume renderings of current
pre-flare
post-flare
E/Epot1.32
E/Epot1.14
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Volume renderings of current
pre-flare
post-flare
E/Epot1.32
E/Epot1.14
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Summary

• NLFFF algorithms do not reach a consensus for
  this case.
• Still, we can determine a best-matching model by
  comparing model fieldlines to observations in
  the EUV (from TRACE) and/or in x-rays (from
  Hinode/XRT).
• In the best-matching model, free energy drops
  from 32 to 14 of potential energy,
  corresponding to a drop in free energy of 3?1032
  erg, even as total field energy increased by
  1032 erg during this time.
• Issue 1 EUV and x-ray coverage was not optimal
  for this region, making it hard to determine
  best-fit model. (TRACE had only 285 binned 2?2,
  and x-ray images not the best for identifying
  loops.)
• Issue 2 Lower boundary did not fully contain
  both flare ribbons. We are currently enlarging
  the lower boundary footprint and will repeat the
  analysis.