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

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)

UNNOFIT Landolfi, 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 9 th fitted parameter: the magnetic filling factor   Skumanich & Lites (1987): I nm constant (average of the observation)  our work: same physical conditions (except the magnetic field) for I nm and I m I nm 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 atmosphere 6 – the line central wavelength 7 & 8 – the field inclination and azimuth angles

UNNOFIT minimum of  per pixel for two varying parameters: – the magnetic field intensity – the magnetic filling factor full scale: the polarimetric sensitivity

UNNOFIT minimum of  per pixel for two varying parameters: – the magnetic field inclination – the magnetic field azimuth full scale: the polarimetric sensitivity

noise level measurement by wavelet filtering technique and determination of the standard deviation

1 line (in the visible range)  Determination of the local average magnetic field strength test: comparison known input vs inverted output: the filling factor  and the field strength B are not separately recovered, but their product  B, the local average magnetic field strength, is recovered.

histograms of the differences inverted-initial (UNNOFIT accuracy) (input)  B >= 45G NETWORK (input)  B < 45G INTER- NETWORK

comparison UNNOFIT 8 parameters / UNNOFIT 9 parameters UNNOFIT 8 parameters (no filling factor) B lim = 100 Gauss UNNOFIT 9 parameters (with filling factor) B lim = 20 Gauss

Accuracy

Orders of magnitude no filling factor (  = 1) with filling factor (   1)

comparison UNNOFIT 8 parameters / UNNOFIT 9 parameters UNNOFIT 8 parameters (no filling factor) UNNOFIT 9 parameters (with filling factor)

comparison UNNOFIT 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 profiles obtained in the same channel at different times (for Q and U) the idea is that the l.o.s. velocity has changed between the two times the result is symmetrised profiles

comparison unsymmetrised / symmetrised unsymmetrised (no recentering before subtraction) symmetrised (with recentering before subtraction) QUIET SUN 25 July 2007 TIP-TILT ON pixel size 0.2 arcsec

INITIALISATION OF UNNOFIT WITH PCA RESULTS 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

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

INITIALISATION OF UNNOFIT WITH PCA RESULTS PCA initialisation 22.0% of "bad" pixels neighbour initialisation 1.2% of "bad" pixels 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 angle with respect to the "normal" (i.e., non accelerated) solution:

COMPARISON UNNOFIT/PCA 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 UNNOFIT PCA

COMPARISON UNNOFIT/PCA UNNOFIT PCA inclination angle with the horizontal plane

COMPARISON UNNOFIT/PCA 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

COMPARISON UNNOFIT/SIR As UNNOFIT provides only the product  B, SIR was runned with: – one signe line Fe I 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 inclinationazimuth differences in

UNNOFIT/SIR Comparison : Quiet Sun inclinationazimuth differences in field strength

Validity of the Milne-Eddington Approximation logarithmic linear Linearity of the source function at   1 NLTE computation of the source function in a VALC atmosphere Fe I Å opacity

VELOCITY GRADIENT Observation by J. RAYROLE concerns the line bisector I+V I-V theory: the 2 line bisectors of I+V and I-V are symmetrical I+V I-V observation by J. Rayrole: the 2 line bisectors of I+V and I-V are not symmetrical but are RECTILINEAR (in )

VELOCITY GRADIENT Empirical law by J. RAYROLE and G. MOLODIJ absorption coefficient (that enters the Unno-Rachkowsky solution):  modification of UNNOFIT to determine a 10 th parameter,  V  V (m/s) is the line continuum level minus line center level velocity difference

comparison UNNOFIT 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 output vs input histogram output–input

VELOCITY GRADIENT 26 August 2006 UNNOFIT 9 parameters UNNOFIT 10 parameters field horizontality (angle between the vector and the horizontal plane) field strength (global)

VELOCITY GRADIENT 26 August 2006 map of the velocity gradient  V