Reconstructing Active Region Thermodynamics

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Reconstructing Active Region Thermodynamics

• Loraine Lundquist
• Joint MURI Meeting
• Dec. 5, 2002

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Motivation

• Reconstructing an expected emission picture is an
  excellent way to compare with observations
• Most current MHD models do not give a
  satisfactory treatment of the energy equation
• Allows us to test assumptions about the coronal
  loop heating function
• A temperature, density, and magnetic field vector
  map of the corona would allow us to model type II
  bursts, EIT and Moreton wave propagation, and
  shocks which may accelerate particles

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Reconstruct temperature and density structure of
active regions from first principles
Magnetic field data (from Régnier FFF data or MHD)
Interpolate to a regular grid
Integrate fieldlines
Construct X-ray and EUV false images
Assume a form for the loop heating function
Compare with observations
Solve static energy equation along each
fieldline, (with some simplifying assumptions)
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Integrate fieldlines
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Static Coronal Loop ModelDescription
Solve Static Energy Equation
EH Plasma heating function
ER Energy losses due to radiation
FC Conductive heat flux along loop.
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Heating Function
Empirical relationship from Pevtsov et al. soft
x-ray data.
Solar Active Regions
X-Ray Bright Points
T-Tauri stars
G, K, M dwarfs
Quiet Sun
Solar Disc Averages
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Solve Static Energy EquationAssumptions

• Static
• (bulk plasma velocity vanishes)
• Thin straight loop
• (ignore area variations)
• Uniform heating
• Radiative losses approximated with a power law
• No gravity
• No losses through footpoints

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Solve Static Energy EquationAssumptions

• Static
• (bulk plasma velocity vanishes)
• Straight
• (ignore curvature effects)
• Uniform heating
• Radiative losses approximated with a power law
• No gravity
• No losses through footpoints

Delta function at base
Look-up table or piecewise power law
Add gravity
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Construct False Images

• Interpolate onto a regular grid.
• (This is easy in theory, but in practice,
  
• there are many difficulties, depending
• on the spatial coverage of the
  fieldlines.)
• Plot emissivity integrated along line of sight
• If desired, integrate over known band passes to
  simulate pictures from Yohkoh, EIT, etc.

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Preliminary Results
1401
1940
1757
2112
Yohkoh SXT AR 8210 May 1, 1998 MURI case study
Reconstructed Active Region (emission integrated
over line of sight)
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Future Applications

• Compare with results, and refine assumptions.
• Do a statistical study to see which coronal
  heating functions give the best results over a
  broad range of data.
• Create maps of the coronal Alfvén speeds and
  sound speeds for modeling EIT and Moreton waves,
  Type II bursts, and particle acceleration.