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Thermal Diagnostics of Elementary and Composite Coronal Loops with AIA

This study focuses on conducting thermal studies of coronal loops using a forward-fitting technique with AIA data. The goal is to parameterize the distribution of physical parameters of coronal loops and simulate cross-sectional profiles in different filters. The study also aims to perform a self-consistent simulation of the coronal background and detected loops.

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Thermal Diagnostics of Elementary and Composite Coronal Loops with AIA

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  1. Thermal Diagnostics of Elementary and Composite Coronal Loops with AIA Markus J. Aschwanden & Richard W. Nightingale (LMSAL) AIA/HMI Science Teams Meeting, Monterey, Feb 13-17, 2006 Session C9: Coronal Heating and Irradiance (Warren/Martens)

  2. A Forward-Fitting Technique to conduct Thermal Studies with AIA Using the Composite and Elementary Loop Strands in a Thermally Inhomogeneous Corona (CELTIC) • Parameterize the distribution of physical parameters of coronal loops • (i.e. elementary loop strands): • -Distribution of electron temperatures N(T) • Distribution of electron density N(n_e,T) • Distribution of loop widths N(w,T) • Assume general scaling laws: • -Scaling law of density with temperature: n_e(T) ~ T^a • -Scaling law of width with temperature: w(T) ~ T^b • Simulate cross-sectional loop profiles F_f(x) in different filters • by superimposing N_L loop strands • Self-consistent simulation of coronal background and detected loops Forward-fitting of CELTIC model to observed flux profiles F_i(x) in 3-6 AIA filters F_i yields inversion of physical loop parameters T, n_e, w as well as the composition of the background corona [N(T), N(n_e,T), N(w,T)] in a self-consistent way.

  3. TRACE Response functions 171, 195, 284 A T=0.7-2.8 MK

  4. Model: Forward- Fitting to 3 filters varying T

  5. 171AonJune 12 199812:05:20Loop #3A T=1.39 MK w=2.84 Mm

  6. Loop_19980612_A

  7. Observational constraints: Distribution of -loop width N(w), <w^loop> -loop temperature N(T), <T^loop> -loop density N(n_e), <n_e^loop> -goodness-of-fit, N(chi^2), <ch^2> -total flux 171 A, N(F1), <F1^cor> -total flux 195 A, N(F2), <F2^cor> -total flux 284 A, N(F3), <F3^cor> -ratio of good fits q_fit =N(chi^2<1.5)/N_det Observables obtained from Fitting Gaussian cross-sectional profiles F_f(x) plus linear slope to observed flux profiles in TRACE triple-filter data (171 A, 195, A, 284 A) N_det=17,908 (positions) (Aschwanden & Nightingale 2005, ApJ 633, 499)

  8. Forward-fitting of CELTIC Model: Distribution of -loop width N(w), <w^loop> -loop temperature N(T), <T^loop> -loop density N(n_e), <n_e^loop> -goodness-of-fit, N(chi^2), <ch^2> -total flux 171 A, N(F1), <F1^cor> -total flux 195 A, N(F2), <F2^cor> -total flux 284 A, N(F3), <F3^cor> -ratio of good fits q_fit =N(chi^2<1.5)/N_det With the CELTIC model we Perform a Monte-Carlo simulation of flux profiles F_i(x) in 3 Filters (with TRACE response function and point-spread function) by superimposing N_L structures with Gaussian cross-section and reproduce detection of loops to Measure T, n and w of loop and Total (background) fluxes F1,F2,F3

  9. (Aschwanden, Nightingale, & Boerner 2006, in preparation)

  10. Loop cross-section profile In CELTIC model: -Gaussian density distribution with width w_i n_e(x-x_i) -EM profile with width w_i/sqrt(2) EM(x)=Int[n^e^2(x,z)dz] /cos(theta) -loop inclination angle theta -point-spread function w^obs=w^i * q_PSF EM^obs=EM_i / q_PSF q_PSF=sqrt[ 1 + (w_PSF/w_i)^2]

  11. Parameter distributions of CELTIC model: N(T), N(n,T), N(w,T) Scaling laws in CELTIC model: n(T)~T^a, w(T)~T^b a=0 b=0 a=1 b=2

  12. Concept of CELTIC model: -Coronal flux profile F_i(x) measured in a filter i is constructed by superimposing the fluxes of N_L loops, each one characterized with 4 independent parameters: T_i,N_i,W_i,x_i drawn from random distributions N(T),N(n),N(w),N(x) The emission measure profile EM_i(x) of each loop strand is convolved with point-spread function and temperature filter response function R(T)

  13. Superposition of flux profiles f(x) of individual strands  Total flux F_f(x) The flux contrast of a detected (dominant) loop decreases with the number N_L of superimposed loop structures  makes chi^2-fit sensitive to N_L

  14. AIA Inversion of DEM • AIA covers temperature • range of log(T)=5.4-7.0 • Inversion of DEM with • TRACE triple-filter data • and CELTIC model • constrained in range of • log(T)=5.9-6.4 •  2 Gaussian DEM peaks • and scaling law (a=1,b=2) • Inversion of DEM with • AIA data and CELTIC • model will extend DEM • to larger temperature • range • 3-4 Gaussian DEM peaks and scaling laws: n_e(T) ~ T^a w(T) ~ T^b

  15. Constraints from CELTIC model • for coronal heating theory • (1) The distribution of loop widths N(w), • [corrected for point-spread function] • in the CELTIC model is consistent • with a semi-Gaussian distribution • with a Gaussian width of • w_g=0.50 Mm • which corresponds to an average FWHM • <FWHM>=w_g * 2.35/sqrt(2)=830 km • which points to heating process of • fluxtubes separated by a granulation size. • There is no physical scaling law known for • the intrinsic loop width with temperature • The CELTIC model yields • w(T) ~ T^2.0 • which could be explained by cross-sectional • expansion by overpressure in regions where • thermal pressure is larger than magnetic • pressure  plasma-beta > 1, which points • again to heating below transition region.

  16. Scaling law of width with temperature in elementary loop strands Observational result from TRACE Triple-filter data analysis of elementary loop strands (with isothermal cross-sections): • Loop widths cannot adjust to temperature in • corona because plasma- << 1, and thus • cross-section w is formed in TR at >1 • Thermal conduction across loop widths In TR predicts scaling law:

  17. CONCLUSIONS • The Composite and Elementary Loop Strands in a Thermally Inhomogeneous • Corona (CELTIC) model provides a self-consistent statistical model to quantify • the physical parameters (temperature, density, widths) of detected elementary • loop strands and the background corona, observed with a multi-filter instrument. • (2) Inversion of the CELTIC model from triple-filter measurements of 18,000 • loop structures with TRACE quantifies the temperature N(T), density N(n_e), • and width distribution N(w) of all elementary loops that make up the corona • and establish scaling laws for the density, n_e(T)~T^1.0, and loop widths • w(T) ~ T^2. (e.g., hotter loops seen in 284 and Yohkoh are “fatter” than in 171) • (3) The CELTIC model attempts an instrument-independent description of the • physical parameters of the solar corona and can predict the fluxes and • parameters of detected loops with any other instrument in a limited temperature • range (e.g., 0.7 < T < 2.7 MK for TRACE). This range can be extended to • 0.3 < T < 30 MK with AIA/SDO. • (4) The CELTIC model constrains the cross-sectional area (~1 granulation size) • and the plasma-beta (>1), both pointing to the transition region and upper • chromosphere as the location of the heating process, rather than the corona!

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