Title: Thermal Diagnostics of
1Thermal 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)
2A 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)
Ta - -Scaling law of width with temperature w(T)
Tb - 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.
3TRACE Response functions 171, 195, 284
A T0.7-2.8 MK
4Model
Forward- Fitting to 3 filters varying T
5171AonJune 12 1998120520Loop 3A T1.39
MK w2.84 Mm
6Loop_19980612_A
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9Observational constraints Distribution of
-loop width N(w), ltwloopgt -loop temperature
N(T), ltTloopgt -loop density N(n_e), ltn_eloopgt
-goodness-of-fit, N(chi2), ltch2gt -total flux
171 A, N(F1), ltF1corgt -total flux 195 A, N(F2),
ltF2corgt -total flux 284 A, N(F3), ltF3corgt
-ratio of good fits q_fit
N(chi2lt1.5)/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_det17,908 (positions) (Aschwa
nden Nightingale 2005, ApJ 633, 499)
10Forward-fitting of CELTIC Model Distribution
of -loop width N(w), ltwloopgt -loop temperature
N(T), ltTloopgt -loop density N(n_e), ltn_eloopgt
-goodness-of-fit, N(chi2), ltch2gt -total flux
171 A, N(F1), ltF1corgt -total flux 195 A, N(F2),
ltF2corgt -total flux 284 A, N(F3), ltF3corgt
-ratio of good fits q_fit
N(chi2lt1.5)/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)
12Loop 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)Intne2(x,z)dz
/cos(theta) -loop inclination
angle theta -point-spread function
wobswi q_PSF EMobsEM_i /
q_PSF q_PSFsqrt 1 (w_PSF/w_i)2
13Parameter distributions of CELTIC model N(T),
N(n,T), N(w,T) Scaling laws in CELTIC model
n(T)Ta, w(T)Tb
a0 b0
a1 b2
14Concept 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)
15Superposition 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 chi2-fit sensitive to
N_L
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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 (a1,b2)
- Inversion of DEM with
- AIA data and CELTIC
- model will extend DEM
- to larger temperature
- range
- 3-4 Gaussian DEM peaks
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_g0.50 Mm
- which corresponds to an average FWHM
- ltFWHMgtw_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) T2.0
- which could be explained by cross-sectional
19Scaling 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-? ltlt 1, and thus
- cross-section w is formed in TR at ?gt1
- Thermal conduction across loop widths
- In TR predicts scaling law
20CONCLUSIONS
- 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)T1.0, and loop widths - w(T) T2. (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 lt T lt 2.7 MK for TRACE).
This range can be extended to - 0.3 lt T lt 30 MK with AIA/SDO.
- (4) The CELTIC model constrains the
cross-sectional area (1 granulation size) - and the plasma-beta (gt1), both pointing to
the transition region and upper