Estimating the magnetic energy in solar magnetic configurations

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Estimating the magnetic energy in solar magnetic
configurations
Stéphane Régnier
Reconnection seminar on Thursday 15 December 2005
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Goals estimating the magnetic energy in a
magnetic configuration, finding the amount of
magnetic energy which can be released during an
eruption, determining where and how the
magnetic energy is stored in the corona
Plan 1) What can we learn from the potential
field extrapolations? 2) How does the
magnetic energy differ from on model to another
(potential-linear force-free, nonlinear
force-free fields)? 3) What is the evolution
in time of the magnetic energy in a
flaring active region using the nonlinear
force-free approximation?
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Definition
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1) What can we learn from the potential field
extrapolations?
Halloween event X17 flare on Oct. 28, 2003
The solar X-ray flux measured by GOES-10 exhibits
a peak on Oct 28 at 1110 UT characterizing the
X17 flare which occurred in AR 0486
As shown by the 195Å EIT image at 1112 UT, the
X-class flare occurred in AR0486. A CME was
observed by LASCO C2-C3. In addition, a fast
emerging active region (AR 0488) was observed.
AR0488
AR0486
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Potential field extrapolations of AR 10486
1000 UT
1105 UT
1110 UT
Background image smoo-thed MDI magnetograms on
the computational grid (215x150x150) Field lines
red (green) field lines coming from the positive
(negative) polarity
1115 UT
1120 UT
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Potential field extrapolation of AR 10486 at
1110 UT on Oct. 28, 2003
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Magnetic energy of AR 0486 from the potential
field
We compute the magnetic energy of the potential
field for every 96 min MDI magnetograms from Oct.
27 to Oct 29 and for every 1 min MDI magnetograms
on Oct. 28 before and after the flare. Over this
three day period, the magnetic energy (or the
unsigned magnetic flux) is rising by a factor of
1.6 (from 1.1 1034 erg to 1.8 1034 erg).
Solid line flare time, Dashed lines separate
each day (AR0486 crossed the disk center around
1800 UT on Oct. 29)
Magnetic energy of the potential field from 1 min
cadence MDI magnetogram
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Time series of 1 min cadence SOHO/MDI
magnetograms during the eruption
parasitic polarities are observed in the active
region starting from the flare site and
propagating away in strong field regions.
Conclusion instrumental effect
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2) How does the magnetic energy differ from on
model to another (potential-linear force-free,
nonlinear force-free fields)?
Ordering Epot lt Elff, Enlff Elff(dHm) lt
Enlff Em lt Eopen
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3) What is the evolution in time of the magnetic
energy in a flaring active region using the
nonlinear force-free approximation?
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Overview of AR 8210
X-ray flux observed on May 1, 1998, site of
numerous flares (4 C-class and 2 B-class
flares) H? events blue-shift events were
observed at location A before and during the
first series of C-class flares from 1707 UT to
1756 UT
Vector magnetograms time series of 15
magnetograms averaged over 15 min, observed by
IVM on May 1 from 1713 UT to 2129 UT
Moving feature
A
Photospheric motions Clockwise rotation of the
sunspot Fast moving parasitic polarity
Flare site
IVM movie of AR8210
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Rotating sunspot
E E E A E E e
Scenario of the flares Topology of the field
dome-like separatrice surface above the red field
lines Photospheric motion clockwise rotation of
the negative main polarities Reconnection
process field lines moving toward the
separatrice surface due to the rotation can
reconnect from the red domain to the green
domain Signatures blue-shift events at one
foot-point of the reconnected field lines
dome
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Emerging and moving parasitic polarity
Scenario of the flux emergence Pre-existing
topology red field lines inside two different
connectivity domains (NE and SW) separate by a
separatrice surface Emergence flux emergence of
a parasitic polarity close to the
separatrice Photospheric motion fast motion of
the parasitic polarity toward the South-West
Reconnection process field lines in NE
approaching the separatrice surface are
reconnected into SW
Emerging and moving parasitic polarity
NE
Pre-existing magnetic configuration
SW
Separatrix
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Time evolution of the magnetic energy in AR 10486

• Magnetic energy of the potential field (dashed
  line)
• Magnetic energy of the nonlinear force-free
  field (solid line)
• Measurement of the rate of change (1029 erg.s-1)

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Time evolution of the magnetic energy in AR 10486

• Magnetic energy due to transverse motion on the
  photosphere (Longcope 2004, MEF -Minimum Energy
  Fit- technique)
• Free magnetic energy budget difference between
  the magnetic energy of the nonlinear force-free
  field and of the potential field

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Comparison between different active regions
Relevant quantities to study the evolution and
the differences of active regions the magnetic
energy in the corona and the relative magnetic
helicity (relative to the potential field).
Twisted flux tubes
Confined flares
Two-ribbon flare
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Conclusions

• Magnetic energy budget, flare and reconnection
• The most relevant quantity is the free magnetic
  energy budget
• The combination of 3D magnetic field geometry
  and magnetic energy values gives information on
  the nature and the location of the flare and the
  reconnection site
• Small scale flares do not modify significantly
  the magnetic energy budget
• - The transverse photospheric motions contribute
  to injection of magnetic energy in the corona,
  they seem to be precursors of flaring activity
• Space Weather
• Need first to understand the capabilities of the
  instrument .