Transcript Using Forward Folding of SERTS and Densities of Coronal Plasma

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/
Brief Outline
I.
II.
A.
B.
C.
III.
A.
B.
C.
IV.
A.
B.
C.
V.
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 (I’ll never make it!)
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
• I’ve been think about electron densities lately
• I’ve never felt quite right about this paper
• I wanted to show the work I’ve done and what I’m
currently working on
Forms of the Flux Equation
Flux  constants   ij dV
 ij   N j Aji
hc
ij
Forms of the Flux Equation
Under “Coronal Equilibrium” Conditions
N i N eCij  N j Aji
N j A ji
Cij 
hc
ij
Ni N e
hc
ij
Forms of the Flux Equation
Many transformations later
Flux   Abund  Ionization Balance  0.8  Cij 
GT   Ionization Balance  0.8  Cij 
Flux   Abund  G T   N e2dV
hc
 ji
hc
 ji
 N e2dV
Emission Measure
Flux  Abund  G Te    N dV
2
e
dV
 N dl   N Pixel Size 2
2
e
2
e
Differential Emission Measure


N
dl


T
dT


2
e
 T   N
2
e
Fluxk  Abund k   Gk T   T  dT
SERTS Analysis
• Observed AR 7963 (Aug. 17, 1997)
• Acquired data along a 2.7’x 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
SERTS Results
Density ranges from 1.5E+9 to 2.0E+10
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 there’s
no reason to assume it would be at the peak
formation temperature.
Pretty Pictures
Monster Analysis
• Does not make an isothermal approximation
Fluxk  Abund k   Gk T    T  dT
• 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
How Does That Derive
Density?
Cij is a function of electron density and temperature
1. A value for Ne was used as an input to the
emissivity function calculation
2. A DEM curve was generated and a reduced chisquare value obtained
3. The above process was repeated for other input
values of Ne
4. The reduced chi-square for all DEM curves were
evaluated. The value of Ne with the lowest chisquare value wins!
Problems
• Black Boxes everywhere
Cij approximation
Cij calculation
N j A ji
Cij 
hc
ij
Ni N e
Problems
• Isn’t DEM proportional to Ne2?
Recursive processes
Topology is hard
• Ill-posed problems
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