UNNOFIT inversion 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
Dec 26, 2015
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)
0
5000
1 104
1.5 104
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
2000
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)
0
1000
2000
3000
4000
5000
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)
0
1 104
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
Magnetic field strength * filling factor
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
Magnetic field line-of-sight inclination
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
Magnetic field slit azimuth
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
comparisonUNNOFIT 8 parameters / UNNOFIT 9 parameters
UNNOFIT 8 parameters(no filling factor)
UNNOFIT 9 parameters(with filling factor)
comparisonUNNOFIT 8 parameters / UNNOFIT 9 parameters
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 OF UNNOFIT WITH PCA RESULTS
initialisation (and acceleration) of UNNOFIT: 2 proposed methods– initialisation with PCA analysis results
("PCA initialisation")– initialisation with results of neighbour pixels
("neighbour initialisation)
INITIALISATION OF UNNOFIT WITH PCA RESULTS
0
5000
1 104
1.5 104
2 104
2.5 104
3 104
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
Magnetic field line-of-sight inclination
Count
ψ (degree)
0
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
Magnetic field slit azimuth
Count
ϕ (degree)
PCAinitialisation
neighbourinitialisation
difference with the "normal" (i.e., non accelerated) solution
0
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
Magnetic field strength * filling factor
Count
% difference
0
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
Magnetic field strength * filling factor
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
Magnetic field line-of-sight inclination
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
Magnetic field slit azimuth
Count
ϕ (degree)
INITIALISATION OF UNNOFIT WITH PCA RESULTS
0
5000
1 104
1.5 104
2 104
2.5 104
3 104
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
Magnetic field line-of-sight inclination
Count
ψ (degree)
0
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
Magnetic field slit azimuth
Count
ϕ (degree)
PCAinitialisation
22.0%of
"bad" pixels
neighbourinitialisation
1.2%of
"bad" pixels
0
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
Magnetic field strength * filling factor
Count
% difference
0
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
Magnetic field strength * filling factor
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
Magnetic field line-of-sight inclination
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
Magnetic field slit azimuth
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
0
1000
2000
3000
4000
5000
-1 -0.8 -0.6 -0.4 -0.20 0.2 0.4 0.6 0.8 1
Magnetic field strength * filling factor
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
500
1000
1500
2000
2500
-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)
0
500
1000
1500
2000
2500
3000
3500
-135-120-105-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 105120
Magnetic field line-of-sight inclination
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
5000
1 104
1.5 104
2 104
2.5 104
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
0
5000
1 104
1.5 104
2 104
2.5 104
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
comparisonUNNOFIT 9 parameters / UNNOFIT 10 parameters
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