Thermal Diagnostics of Elementary and Composite Coronal Loops with AIA Markus J. Aschwanden &...
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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, 2006Session C9: Coronal Heating and Irradiance (Warren/Martens)
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A Forward-Fitting Technique to conduct Thermal Studies with AIAUsing 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 filtersby superimposing N_L loop strandsSelf-consistent simulation of coronal background and detected loops
Forward-fitting of CELTIC model to observed flux profiles F_i(x) in 3-6AIA filters F_i yields inversion of physical loop parameters T, n_e, was well as the composition of the background corona[N(T), N(n_e,T), N(w,T)] in a self-consistent way.
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TRACEResponse functions171, 195, 284 AT=0.7-2.8 MK
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Model:
Forward-Fitting to 3 filtersvarying T
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171Aon
June 12 1998
12:05:20
Loop #3A T=1.39 MK w=2.84 Mm
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Loop_19980612_A
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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 fromFitting 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)
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Forward-fittingof 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 wePerform a Monte-Carlo simulationof flux profiles F_i(x) in 3 Filters(with TRACE response functionand point-spread function) bysuperimposing N_L structureswith Gaussian cross-section andreproduce detection of loops toMeasure T, n and w of loop andTotal (background) fluxes F1,F2,F3
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(Aschwanden, Nightingale, & Boerner 2006, in preparation)
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Loop cross-section profileIn 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]
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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=0b=0
a=1b=2
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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)
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Superposition of flux profiles f(x) of individual strands Total flux F_f(x)
The flux contrast of a detected (dominant) loop decreases with thenumber N_L of superimposed loop structures makes chi^2-fit sensitive to N_L
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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 range3-4 Gaussian DEM peaks and scaling laws: n_e(T) ~ T^a w(T) ~ T^b
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Constraints from CELTIC modelfor 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.
(2) There is no physical scaling law known for the intrinsic loop width with temperature
The CELTIC model yieldsw(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.
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Scaling law of width with temperaturein elementary loop strands
Observational result from TRACETriple-filter data analysis of elementaryloop strands (with isothermal cross-sections):
97.1)( TTw
2
2/72/7
L
T
s
T
sFE cH
75.14/7)( TTTw
Loop widths cannot adjust to temperature incorona because plasma- << 1, and thuscross-section w is formed in TR at >1Thermal conduction across loop widthsIn TR predicts scaling law:
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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!