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. 171A on June 12 1998 12:05:20 Loop #3A T=1.39 MK w=2.84 Mm

6. Loop_19980612_A

9. Observational constraints: Distribution of -loop width N(w), -loop temperature N(T), -loop density N(n_e), -goodness-of-fit, N(chi^2), -total flux 171 A, N(F1), -total flux 195 A, N(F2), -total flux 284 A, N(F3), -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)

10. Forward-fitting of CELTIC Model: Distribution of -loop width N(w), -loop temperature N(T), -loop density N(n_e), -goodness-of-fit, N(chi^2), -total flux 171 A, N(F1), -total flux 195 A, N(F2), -total flux 284 A, N(F3), -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

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

12. 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]

13. 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

14. 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)

15. 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

17. 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

18. 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 =w_g * 2.35/sqrt(2)=830 km which points to heating process of fluxtubes separated by a granulation size. (2)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.

19. 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:

20. CONCLUSIONS (1)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!