Modeling Magnetic Reconnection in a Complex Solar Corona

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Modeling Magnetic Reconnection in a ComplexSolar
Corona

• Dana Longcope
• Montana State University
• Institute for Theoretical Physics

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The Changing Magnetic Field
PHOTOSPHERE
THE CORONA
TRACE 171 1,000,000 K
8/10/01 1251 UT
8/11/01 925 UT (movie)
8/11/01 1739 UT
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Is this Reconnection?
PHOTOSPHERE
THE CORONA
TRACE 171 1,000,000 K
8/10/01 1251 UT
8/11/01 925 UT (movie)
8/11/01 1739 UT
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Outline

• Developing a model magnetic field
• A simple example of 3d reconnection
• The general (complex) case --- approached via
  variational calculus.
• A complex example

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The Sun and its field
Focus on the p-phere
And the corona just above
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Modeling the coronal field
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Example X-ray bright points
EIT 195A image of quiet solar corona
(1,500,000 K)
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Example X-ray bright points
Small specks occur above pair of magnetic
poles (Golub et al. 1977)
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Example X-ray bright points
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When 2 Poles Collide
All field lines from positive source P1
All field lines to negative source N1
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When 2 Poles Collide
Regions overlap when poles approach
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How its done in 2 dimensions
Stress applied at boundary Concentrated at
X-point to form current sheet Reconnection
releases energy
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A Case Study
TRACE SOI/MDI observations 6/17/98 (Kankelborg
Longcope 1999)
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The Magnetic Model

• Poles
• Converging v 218 m/sec
• Potential field
• - bipole
• - changing
• ? 1.6 MegaVolts
• (on separator)

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Reconnection Energetics

• Flux transferred intermittently
• Current builds between transfers
• Minimum energy drops _at_ transfer

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Post-reconnection Flux Tube
Flux Accumulated over Releases stored
Energy Into flux tube just inside bipole
(under separator)
Projected to bipole location
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Post-reconnection Flux Tube
Flux Accumulated over Releases stored
Energy Into flux tube just inside bipole
(under separator)
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A view of the model
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More complexity
Defines connectivity
Find coronal coronal field
From p-spheric field (obs).
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Minimum Energy Equilibrium

• Magnetic energy
• Variation
• Fixed at photosphere
• ? Potential field

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Minimization with constraints

• Ideal variations only
• ? force-free field
• Constrain helicity
• ( w/ undetd multiplier a )
• ? constant-a fff

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A new type of constraint
flux in each domain
Photospheric field f(x,y) -- the sources
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Domain fluxes

• Domain Dij connects sources Pi Nj
• Flux in source i
• Flux in Domain Dij
• Q how are fluxes related
• A through the graphs incidence matrix

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The incidence matrix

• Ns Rows sources
• Nd Columns domains
• ? Nc Nd Ns 1 circuits

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The incidence matrix
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Reconnection
possible allocation of flux
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Reconnection
another possibility
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Reconnection
Related to circuit in the domain graph
Must apply 1 constraint to every circuit in
graph
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Separators where domains meet
4 distinct flux domains
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Separators where domains meet
4 distinct flux domains
Separator at interface
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Separators where domains meet
4 distinct flux domains
Separator at interface
Closed loop encloses all flux linking P2?N1
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Minimum W subj. to constraint
Current-free within each domain
Constraint on P2?N1 flux
? current sheet at separator
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Minimum W subj. to constraint
2d version X-point _at_ boundary of 4 domains
becomes current sheet
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A complex example
Ns 20
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A complex example
Ns 20 ? Nc 33
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The original case study
Approximate p-spheric field using discrete
sources
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The domain of new flux
Emerging bipole P01-N03
New flux connects P01-N07
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Summary

• 3d reconnection occurs at separators
• Currents accumulate at separators
• ? store magnetic energy
• Reconnection there releases energy
• Complex field has numerous separators