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.

Brief Outline I.Why I Chose this paper II.Develop the Governing Equations (Quickly!!!) A.Flux Equation B.Emission Measure C.Differential Emission Measure III.SERTS Analysis A.Method B.Results C.Limitations IV.DEM Analysis A.Method B.Results C.Possible problems V.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

Under “Coronal Equilibrium” Conditions

Forms of the Flux Equation Many transformations later

Emission Measure

Differential Emission Measure

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 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? C ij is a function of electron density and temperature 1.A value for N e was used as an input to the emissivity function calculation 2.A DEM curve was generated and a reduced chi- square value obtained 3.The above process was repeated for other input values of N e 4.The reduced chi-square for all DEM curves were evaluated. The value of N e with the lowest chi- square value wins!

Problems Black Boxes everywhere C ij approximation C ij calculation

Problems Isn’t DEM proportional to N e 2 ? 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 N e from DEM