Using Forward Folding of SERTS and Yohkoh Data to Estimate the Electron Densities of Coronal Plasma J.T. Schmelz

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Using Forward Folding of SERTS and Yohkoh Data to
Estimate the Electron Densities of Coronal Plasma
J.T. Schmelz H.D. Winter III
Presented by Henry (Trae) D. Winter III Montana
State University, Bozeman, Physics Dept.
http//solar.physics.montana.edu/winter/
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Brief Outline

• Why I Chose this paper
• Develop the Governing Equations (Quickly!!!)
• Flux Equation
• Emission Measure
• Differential Emission Measure
• SERTS Analysis
• Method
• Results
• Limitations
• DEM Analysis
• Method
• Results
• Possible problems
• Current and Future Work (Ill never make it!)

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Why I chose this paper

• I wanted to introduce DEM analysis and forward
  modeling to first years and the group
• I wanted my naïve assumptions about DEM exposed
• Ive been think about electron densities lately
• Ive never felt quite right about this paper
• I wanted to show the work Ive done and what Im
  currently working on

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Forms of the Flux Equation
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Forms of the Flux Equation
Under Coronal Equilibrium Conditions
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Forms of the Flux Equation
Many transformations later
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Emission Measure
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Differential Emission Measure
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SERTS Analysis

• Observed AR 7963 (Aug. 17, 1997)
• Acquired data along a 2.7x 4.4 slit
• Yohkoh SXT was simultaneously obtained in the
  thin Al, AlMgMn, and thick Al filters
• Took ratios of eleven lines whose G(T) function
  was sensitive to electron density and less
  sensitive to temperature
• Assumed that all of the emission of a line
  occurred at the peak formation temperature of
  that line

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SERTS Results
Density ranges from 1.5E9 to 2.0E10
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Limitations of SERTS Analysis

• Line ratios are sensitive to atomic physics
  errors
• SERTS was observing a slice along the solar disk.
  Isothermal is out!
• Even if the plasma was isothermal theres no
  reason to assume it would be at the peak
  formation temperature.

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Pretty Pictures
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Monster Analysis

• Does not make an isothermal approximation

• Model DEM curves are folded through the flux
  equation and through the SXT response curve so
  that the two observations can be directly
  combined
• The DEM curve is then iteratively adjusted until
  the predicted fluxes best approximate the
  observed values

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How Does That Derive Density?

• Cij is a function of electron density and
  temperature
• A value for Ne was used as an input to the
  emissivity function calculation
• A DEM curve was generated and a reduced
  chi-square value obtained
• The above process was repeated for other input
  values of Ne
• The reduced chi-square for all DEM curves were
  evaluated. The value of Ne with the lowest
  chi-square value wins!

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Problems

• Black Boxes everywhere
• Cij approximation
• Cij calculation

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Problems

• Isnt DEM proportional to Ne2?
• Recursive processes
• Topology is hard
• Ill-posed problems

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Current and Future Work

• Measure error on the DEM curve arising from
  photon statistics
• Developed a program that transforms a DEM curve
  to a Fourier Series
• Using the minimization program AMOEBA to adjust
  Fourier coefficients so that the output DEM
  minimizes the chi-square value of the predicted
  to observed fluxes
• Improve knowledge of fundamental atomic physics
  to improve calculations
• Investigate topology assumptions that may lead to
  the extraction of Ne from DEM