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Loop cross-section profile. In CELTIC model: -Gaussian density distribution ... (4) The CELTIC model constrains the cross-sectional area (~1 granulation size) ... – PowerPoint PPT presentation

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Title: Thermal Diagnostics of


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)
    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.

3
TRACE Response functions 171, 195, 284
A T0.7-2.8 MK
4
Model
Forward- Fitting to 3 filters varying T
5
171AonJune 12 1998120520Loop 3A T1.39
MK w2.84 Mm
6
Loop_19980612_A
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9
Observational 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)
10
Forward-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)
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)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
13
Parameter 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
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 chi2-fit sensitive to
N_L
16
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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

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-? ltlt 1, and thus
  • cross-section w is formed in TR at ?gt1
  • Thermal conduction across loop widths
  • In TR predicts scaling law

20
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)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
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