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Thermal Diagnostics of Elementary and Composite Coronal Loops with AIAPowerPoint Presentation

Thermal Diagnostics of Elementary and Composite Coronal Loops with AIA

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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

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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)

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.

TRACE

Response functions

171, 195, 284 A

T=0.7-2.8 MK

Model:

Forward-

Fitting

to 3 filters

varying T

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)

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

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

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]

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

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)

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

- 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

- 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.

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:

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!