UNNOFIT inversion

UNNOFITinversion

V. Bommier, J. Rayrole,M. Martínez González, G. Molodij

Paris-Meudon Observatory (France)

THEMIS

Atelier "Inversion et transfert multidimensionnel", Beaulieu sur mer, France, 8-10 Octobre 2007

UNNOFIT INVERSION

presentation of UNNOFIT, accuracy

Comparison UNNOFIT 8 parameters / UNNOFIT 9 parameters

Initialisation of UNNOFIT with PCA results

Comparison UNNOFIT / SIR results (M. Martínez González)

Introduction of a velocity gradient (J. Rayrole, G. Molodij)

UNNOFITLandolfi, M., Landi Degl'Innocenti, E., Arena, P., 1984, Solar Physics 93, 269

• Unno-Rachkowsky analytical solution in a Milne-Eddington atmosphere• Marquardt algorithm to reach the minimum 2 (Harvey et al., 1972, Auer et al., 1977)

• Magneto-optical and damping effects (Landolfi & Landi Degl'Innocenti, 1982)

typical INTRANETWORK low polarized pixel

UNNOFIT

• Present work: introduction of a 9th fitted parameter: the magnetic filling factor

⇒

I = (1−α )Inm +α ImQ = αQm

U = αUm

V = αVm

⎧

⎨⎪⎪

⎩⎪⎪

Skumanich & Lites (1987): Inm constant (average of the observation) our work: same physical conditions (except the magnetic field) for Inm and Im

Inm varies throughout the map (umbra, penumbra, plages, faculæ, quiet, etc...)

• 8 fitted parameters:1 – the line strength 0

2 – the Zeeman splitting H

3 – the Doppler width D

4 – the damping parameter of the Voigt function 5 – one single parameter b describing the Milne-Eddington atmosphere6 – the line central wavelength7 & 8 – the field inclination and azimuth angles

UNNOFITminimum of per pixelfor two varying parameters:

– the magnetic field intensity– the magnetic filling factor

full scale: the polarimetric sensitivity N

UNNOFITminimum of per pixelfor two varying parameters:

– the magnetic field inclination– the magnetic field azimuth

full scale: the polarimetric sensitivity N

noise level measurement

point standard deviation photon noisex,y std in Q std in U std in V phot in Q phot in U phot in V

0,0 0.00324177 0.00284607 0.00264669 0.00151052 0.00150339 0.00150640,100 0.00111572 0.00102486 0.00128867 0.00151471 0.00153136 0.0015328550,200 0.00156507 0.00101591 0.00104588 0.00150802 0.00150579 0.00150346100,100 0.00115483 0.00096431 0.00213768 0.00152452 0.00151273 0.00152062150,150 0.00087806 0.00097765 0.00111934 0.00148089 0.00147595 0.0014757200,50 0.00105883 0.0010295 0.001039 0.00151575 0.00151188 0.00151393250,250 0.00129234 0.00129322 0.00111852 0.00145689 0.00145491 0.00145175300,150 0.00226823 0.00098293 0.0012045 0.00152382 0.00151804 0.00151826

average 0.0014296 0.001503

by wavelet filtering techniqueand determination of the standard deviation

1 line (in the visible range) Determination of the local average magnetic field strength

test:comparisonknown inputvsinverted output:

the filling factor and the field strength Bare not separately recovered,

but their productB, the local average magnetic field strength,is recovered.

histograms of the differences inverted-initial(UNNOFIT accuracy)

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5000

1 104

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2 104

-30 -20 -10 0 10 20 30 40 50 60 70 80 90 100110 120130140

Magnetic field strength * filling factor

Count

B (Gauss)

0

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4000

6000

8000

1 104

1.2 104

1.4 104

-120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120

Magnetic field line-of-sight inclination

Count

ψ (degree)

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4000

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6000

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

Magnetic field slit azimuth

Count

ϕ (degree)

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2 104

3 104

4 104

5 104

6 104

-160-140-120-100-80 -60 -40 -20 0 20 40 60 80 100 120


Count

B (Gauss)

0

1 104

2 104

3 104

4 104

5 104

6 104

-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70


Count

ψ (degree)

0

1 104

2 104

3 104

4 104

5 104

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90


Count

ϕ (degree)

(input)B >= 45GNETWORK

(input)B < 45GINTER-NETWORK

comparisonUNNOFIT 8 parameters / UNNOFIT 9 parameters

UNNOFIT 8 parameters(no filling factor)

Blim= 100 Gauss

UNNOFIT 9 parameters(with filling factor)

Blim= 20 Gauss

Accuracy

polarimetric noise level: 1.5×10−3

⇓circular polarization longitudinal field 10 Gauss

linear polarization transverse field 100 Gauss

⇓UNNOFIT inversion without filling factor

accuracy 100 Gauss

butUNNOFIT inversion with filling factor

accuracy 20 Gauss on B?

Orders of magnitude

circular polarization V I ∝ B

D

: mag. filling factor

B: Zeeman splitting

D: Doppler width

⎧

⎨⎪

⎩⎪

linear polarization Q I and U I ∝ B

D

⎛

⎝⎜⎞

⎠⎟

2

no filling factor( = 1)

with filling factor( 1)

weak magnetic field

B << D

⇓Q I and U I <<V I

small filling factor

<<1strong magnetic field

B ≈D

⇓Q I and U I ≈V I


UNNOFIT 8 parameters(no filling factor)

UNNOFIT 9 parameters(with filling factor)

Symmetrisation of the profiles

beam exchange:

recenter (spectrally)

the I+X and I–X profilesobtained in the same channel

at different times(for Q and U)

the idea is thatthe l.o.s. velocity

has changedbetween the two times

the result issymmetrised

profiles

comparisonunsymmetrised / symmetrised

unsymmetrised(no recentering

before subtraction)

symmetrised(with recentering

before subtraction)

QUIET SUN25 July 2007TIP-TILT ON

pixel size 0.2 arcsec

INITIALISATION OF UNNOFIT WITH PCA RESULTS

data: active region, 6 November 2004provided by BASS2000 (codes runned by BASS2000):– polarimetric analysis results

SQUV code A. Sainz Stokes profiles(submitted to UNNOFIT inversion)

– PCA analysis resultsA. Lopez's code magnetic field vector and filling factor


initialisation (and acceleration) of UNNOFIT: 2 proposed methods– initialisation with PCA analysis results

("PCA initialisation")– initialisation with results of neighbour pixels

("neighbour initialisation)


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5000

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1.5 104

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-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100


Count

ψ (degree)

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1.5 104

2 104

2.5 104

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90


Count

ϕ (degree)

PCAinitialisation

neighbourinitialisation

difference with the "normal" (i.e., non accelerated) solution

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5000

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1.5 104

2 104

2.5 104

3 104

-1 -0.8 -0.6 -0.4 -0.20 0.2 0.4 0.6 0.8


Count

% difference

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1.5 104

2 104

-1 -0.8 -0.6 -0.4 -0.20 0.2 0.4 0.6 0.8


Count

% difference

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5000

1 104

1.5 104

2 104

-150-135-120-105-90 -75 -60 -45 -30 -15 0 15 30 45 60 75


Count

ψ (degree)

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1.5 104

2 104

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90


Count

ϕ (degree)


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1.5 104

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2.5 104

3 104

-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100


Count

ψ (degree)

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5000

1 104

1.5 104

2 104

2.5 104

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90


Count

ϕ (degree)

PCAinitialisation

22.0%of

"bad" pixels

neighbourinitialisation

1.2%of

"bad" pixels

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5000

1 104

1.5 104

2 104

2.5 104

3 104

-1 -0.8 -0.6 -0.4 -0.20 0.2 0.4 0.6 0.8


Count

% difference

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5000

1 104

1.5 104

2 104

-1 -0.8 -0.6 -0.4 -0.20 0.2 0.4 0.6 0.8


Count

% difference

0

5000

1 104

1.5 104

2 104

-150-135-120-105-90 -75 -60 -45 -30 -15 0 15 30 45 60 75


Count

ψ (degree)

0

5000

1 104

1.5 104

2 104

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90


Count

ϕ (degree)

proportion of "bad" pixels where the magnetic field vector differs with:– more than 25% in field strength– or more than 20 degrees in inclination or azimuth anglewith respect to the "normal" (i.e., non accelerated) solution:

COMPARISON UNNOFIT/PCAdata: active region, 6 November 2004, provided by BASS2000 (codes runned by BASS2000):– polarimetric analysis results: SQUV code A. Sainz Stokes profiles (submitted to UNNOFIT inversion)– PCA analysis results: A. Lopez's code magnetic field vector and filling factor

UNNOFIT PCA

COMPARISON UNNOFIT/PCA

UNNOFIT PCA

inclinationangle

anglewith the

horizontalplane

COMPARISON UNNOFIT/PCA

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1000

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4000

5000

-1 -0.8 -0.6 -0.4 -0.20 0.2 0.4 0.6 0.8 1


Count

% difference

data: active region, 6 November 2004, provided by BASS2000 (codes runned by BASS2000):– polarimetric analysis results: SQUV code A. Sainz Stokes profiles (submitted to UNNOFIT inversion)– PCA analysis results: A. Lopez's code magnetic field vector and filling factor

0

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1000

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2500

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90


Count

ϕ (degree)

0

500

1000

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2000

2500

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3500

-135-120-105-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 105120


Count

ψ (degree)

COMPARISON UNNOFIT/SIR

As UNNOFIT provides only the product B,

SIR was runned with:– one signe line Fe I 6302.5 Å– one single magnetic component (homogeneous field)– 11 free parameters:

– the temperature (5 nodes)– the microturbulent velocity– the macroturbulent velocity– the line-of-sight velocity– the magnetic field strength– the magnetic field inclination and azimuth angles

UNNOFIT/SIR Comparison : Sunspot

field strength

inclination azimuth

differences in

UNNOFIT/SIR Comparison : Quiet Sun

inclination azimuth

differences infield strength

Validity of the Milne-Eddington Approximation

0.001

0.01

0.1

1

0

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2 104

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10-10 10-8 10-6 0.0001 0.01 1 100 104

Source function

Temperature

Source function

Temperature

optical depth in Fe I 6302.5

non-LTE solution (zero magnetic field)

0

0.005

0.01

0.015

0.02

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2 104

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0 2 4 6 8 10

Source function

Temperature

Source function

Temperature

optical depth in Fe I 6302.5

non-LTE solution (zero magnetic field)

logarithmic linear

Linearity of the source function at 1

NLTE computation of the source function in a VALC atmosphereFe I 6302.5 Å opacity

VELOCITY GRADIENT

Observation by J. RAYROLE

concerns theline bisector

I+V I-V

theory:the 2 line bisectorsof I+V and I-Vare symmetrical

I+V I-V

observation by J. Rayrole:the 2 line bisectors of I+V and I-Vare not symmetrical but are RECTILINEAR(in )

VELOCITY GRADIENT

Empirical law by J. RAYROLE and G. MOLODIJ

absorption coefficient (that enters the Unno-Rachkowsky solution):

p = η0 e−λ −λ 0

ΔλD+δVp

⎛

⎝⎜⎞

⎠⎟

2

ηb = η0 e−λ −λ 0

ΔλD+

Δλ BΔλD

+δVb⎛

⎝⎜⎞

⎠⎟

2

η r = η0 e−λ −λ 0

ΔλD−

Δλ BΔλD

+δVr⎛

⎝⎜⎞

⎠⎟

2

⎧

⎨

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

where

δVp =ΔVmÅ

ΔλD e

−λ −λ 0

ΔλD

⎛

⎝⎜⎞

⎠⎟

2

δVb =ΔVmÅ

ΔλD e

−λ −λ 0

ΔλD+

Δλ BΔλD

⎛

⎝⎜⎞

⎠⎟

2

δVr =ΔVmÅ

ΔλD e

−λ −λ 0

ΔλD−

Δλ BΔλD

⎛

⎝⎜⎞

⎠⎟

2

⎧

⎨

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

modification of UNNOFITto determine a 10th parameter, V

V (m/s) is the line continuum level minus line center level velocity difference


UNNOFIT 9 parameters(symmetrical profiles)

UNNOFIT 10 parameters(including asymmetry)

V = 1.1 km/s

VELOCITY GRADIENT

with this empirical law,UNNOFIT is enabled

to treat asymmetric profiles

the convergence is quicker

tests: OK

0

5000

1 104

1.5 104

2 104

2.5 104

-0.44-0.4-0.36-0.32-0.28-0.24-0.2-0.16-0.12-0.08-0.040

0.040.080.120.160.2 0.24

velocity gradient dv

Count

V (km/s)

output vs input histogram output–input

VELOCITY GRADIENT26 August 2006

UNNOFIT 9 parameters UNNOFIT 10 parameters

fieldhorizontality

(angle between

the vectorand the

horizontalplane)

fieldstrength(global)

VELOCITY GRADIENT26 August 2006

map of the velocity gradient V

UNNOFIT inversion

Documents

Transcript of UNNOFIT inversion