Estimating Free Energy in AR 8210

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Estimating Free Energy in AR 8210
Acknowledgements Graham Barnes (Colarado
Research Associates, NWRA) Ravi Belur (Dept. of
Physics, Montana State Univ) Colin Beveridge
(Dept. of Physics, MSU) K. D. Leka (Colarado
Research Associates, NWRA) Dana Longcope (Dept.
of Physics, MSU) Jim McTiernan (Space Sciences
Lab, UC Berkeley) Tom Metcalf (Colarado Research
Associates, NWRA) Blame Brian Welsch (Space
Sciences Lab, UC Berkeley)
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The central question we hope to address is Can
we accurately estimate free energy in AR 8210?
AR 8210 is rare for its long-duration set of
high-quality vector magnetograms near the time
of a CME. We hope that new vector magnetographs
SOLIS/VSM, Solar-B/FPP, and SDO/HMI should
give us many more such data sets. Acknowledgement
(again) K.D. Leka worked hard to reduce
average the IVM magnetograms for our analyses.
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The data are 21 vector mgrams with 20 min.
cadence, averaged from 5 consecutive mgrams with
4 min. cadence.
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Approach Compare free energy estimates from
several methods, study consistency or lack
thereof.

• Nonlinear Force-free Field Extrapolation, Jim
  McTiernan (15 min.)
• (Modified) Magnetic Virial Theorem, Tom Metcalf
  (15 min.)
• gtgt Break (30 min.) ltlt
• Minimum Current Corona Model, Graham Barnes,
  Colin Beveridge, Dana Longcope (20 min.)
• Free Energy Flux, Brian Welsch Ravi Belur
  (remaining)

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GOES data other estimates of coronal energy
losses provide a measure of ground truth.
s are flares NOAA ascribed to AR 8210 s
are thermal energies from GOES, at flare peak
?s are kinetic energies from halo CMEs from
CDAW list http//cdaw.gsfc.nasa.gov/CME_list/
solid curve is cumulative radiative loss from
GOES (neglects conductive loss) dotted curve
is heating rate from Pevtsov et al., ApJL 598
(2003), with ? 1022 Mx
Plot courtesy D. Longcope
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Regnier Canfield (AA, v. 451, p. 319) also
studied magnetic energy changes in AR 8210.
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Regniers Caption
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Temporal Coverage
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Longcopes Plot Caption
After reading Emslie et al. JGR 109, A10104
(2004) I realized there might be a few other
elements capable of providing a ground-truth for
energetics.   The attached plot works as
follows   top panel GOES as before, s denote 4
large flares IDed by NOAA as originating
in 8210 bottom energies of various
kinds (key at top). these are accumulated
beginning after the M6.8 flare on
April-28. the different quantities are  
Uth (squares) use GOES to calculate the total
thermal energy in the flare plasma, at
its peak. I've made guesses for the
flare plasma volume in each flare.
Halo CMEs (diamonds) this is the kinetic
energy reported on
http//cdaw.gsfc.nasa.gov/CME_list/ I
expect there to be an interesting discussion on
the relevance of this energy to
free-energy content of the AR.
Radiation this is the same thing i
plotted before, but now the
integration is begun after the decay of the
M6.8 flare. It is the total radiative
losses for the plasma observed by
GOES. If you assume the plasma cools
in equal measures from radiation and condution
then the actual losses would be twice
this large. Heating this is
the BG radiation loss rate reported in Pevtsov
et al. ApJL 598 (2003) w/ Phi1.0e22 Mx.
It is intended as a kind of lower
bound.