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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, 2006 Session C9: Coronal Heating and Irradiance (Warren/Martens).

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Thermal Diagnostics of Elementary and Composite Coronal Loops with AIA

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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, 2006

Session C9: Coronal Heating and Irradiance (Warren/Martens)


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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.


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TRACE

Response functions

171, 195, 284 A

T=0.7-2.8 MK


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Model:

Forward-

Fitting

to 3 filters

varying T


171a on june 12 1998 12 05 20 loop 3a t 1 39 mk w 2 84 mm l.jpg

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


Loop 19980612 a l.jpg

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 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)


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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


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


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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]


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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=0

b=0

a=1

b=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 the

number 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

  • range

  • 3-4 Gaussian DEM peaks

    and scaling laws:

    n_e(T) ~ T^a

    w(T) ~ T^b


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  • 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.


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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:


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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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