SPINOR

SPINOR 

Inversions based on RFs 

A. Lagg - Abisko Winter School 1

Asymmetric profiles and ME (1) ) 

MHD MHD-Simulations Simulations (Vögler et al. 2005) 

) 


Asymmetric profiles and ME (2) ) 

MHD MHD-Simulations Simulations (Vögler et al. 2005) 

) 

� Fe I 630.1 and 630.2 profiles 

degraded to SP pixel size 

� Maps of inferred B and v 

very similar to real ones! 

� Maps of inferred B and v LOS 


Inversions with gradients 

� Inversion codes capable of f deealing 

with gradients 

� Are based on numerical solution 

of RTE 

�� Provide reliable thermal info ormation 

� Use less free parameters thhan 

ME codes (7 vs 8) 

�� Infer stratifications of physic cal parameters with depth 

� Produce better fits to asymmmetric 

Stokes profiles 

� Height dependence of atmosppheric 

parameters is needed for 

� easier solution of the 180 o a 

� 3D structure of sunspots annd 

pores 

� Magnetic flux cancellation eevents 

� Polarity inversion lines 

� Dynamical state of coronal 

� wave propagation analysis 

� … 

azimuth disambiguity g y 

loop footpoints 


Example: SIR inversion 

+ 

• Spatial resolution: ∼0.4" 

VIP TESOS KAOS 

1.0 

0.8 

0.6 

0.4 

Stok tokes I/I I/IQS Stokes V/I V/IQS 0.2 

0 20 40 4 60 80 

7.5 

7.0 

6.5 

6.0 

5.5 

• VIP + TESOS + KAOS -2 

• Inversion: SIR with 10 free 

Temper erature [kK] 

Field strength [kG] 

5.0 

4.5 

-4 -3 -2 - -1 0 

-4 

parameters -4 -3 --2 

lo log tau 

-1 0 

4 

2 

0 

Bellot Rubio et al. (2007) 

0.02 

0.01 

0.00 

-0.01 

-0.02 

-0.03 

-0.04 

0 20 40 60 80 

0.4 

LOS velo elocity [km/s] Field inclination [deg] 

0.7 

0.6 

0.5 

0.3 

0.2 

-4 -3 -2 -1 0 

145 145 

140 

135 

130 

125 

-4 -3 -2 

log tau 

-1 0 


Non Non-ME ME Inversion Codes 

SIR Ruiz Cobo & 

del Toro Iniesta (1992) 

1CC 

& 2C atmospheres, arbitrary 

stratifications, 

any photospheric line 

SIR/FT Bellot Rubio et al. (1996) Thin 

flux tube model, arbitrary stratifications, 

anyy 

photospheric line 

SIR/NLTE Socas-Navarro Socas Navarro et al al. (1998) NL LTE line transfer, transfer arbitrary stratifications 

SIR/GAUS Bellot Rubio (2003) Unncombed 

penumbral model, arbitrary 

stratifications 

SPINOR Frutiger & Solanki (2001) 1CC 

& 2C (nC) atmospheres, arbitrary 

stratifications, 

any photospheric line, 

moolecular 

lines, flux tube model, 

un combed model 

LILIA Socas-Navarro (2001) 1CC 

atmospheres, arbitrary stratifications 

MISMA IC Sánchez Almeida (1997) MI SMA model, arbitrary stratifications, 

anyy 

photospheric line 


SPINOR core: the synthesis 

RTE has h tto bbe solved l d ffor 

each spectral line 

each line-of sight 

each h it iteration ti 

� efficient computation 

required! 

height / tau depen ndent 

height independ dent 

atmospheric parameters: 

T ... gas temperature 

B ... magn magn. field strength 

γ,φ ... incl. / azimuth angle of B 

vLOS ... line-of sight velocity 

v vmic ... micro micro-turbulent turbulent velocity 

AX ... abundance (AH=12) G ... grav. acc. at surface 

vmac... macro-turbulence 

vinst ... instr. broadening 

vabs ... abs. velocity Sun-Earth 


Stokes sepctrum diagn nostics 

CFs and RFs 


Contribution Functions (1) 

The contribution function (CF) 

describes how different atmospheric 

layers y contribute to the observed 

spectrum. 

Mathematical definition: 

CF ≡ integrand of formal sol sol. of RTE 

(here isotropic case, no B field): 

line core: highest formation 

wings: lowest formation 

Intuitively: profile shape indicates 

atmospheric opacity. Medium is more 

transparent (less heavily absorbed) in wings. 

�� one can see „deeper deeper“ into the atmosphere 

at the wings. 


Contribution functions (2) 

The general case: 

Height of formation: 

„This This line is formed at x km 

above the reference, the 

other line is formed at y km 

…“ “ 

�� caution caution with this 

statement is highly 

recommended! 

� CF CFs are strongly t l 

dependent on model 

atmosphere 

� different physical 

quantities are measured 

at different atmospheric 

heights 


Response Functions 


Response Functions 

„brute force method“: 

1. synthesis of Stokes spectrum in 

given model atmosphere 

2. perturbation of one atm. 

parameter 

3. synthesis of „perturbed“ Stokes 

spectrum 

4. calculation of ratio between 

both spectra 

5. repeat (2)-(4) (2) (4) for all τ τi, i, λ λi,atm. i, atm. 

parameter, atm. comp. 

The smart way: 

� knowledge of source function, 

evolution operator and 

propagation matrix 

� direct computation of RFs 

possible (all parameters known 

from solution of RTE RTE, simple 

derivatives) 


Response functions 

Linearization: small perturbation in pphysical 

parameters of the model 

atmosphere propagate „linearly“ to ssmall 

changes in the observed 

Stokes spectrum. p 

introduce these modifications into RRTE: 

only take 1st y order terms, , and introduuce 

contribution function to 

perturbations of observed 

Stokes profiles 

response functions 


Response Functions (2) 

RFs have the role of partial derivatives 

of the Stokes profiles 

with respect to the physical quaantities 

of the model 

atmosphere: 

In words: 

If x k is modified by a unit perturb bation in a restricted 

neighborhood around τ0, then thhe 

values of Rk around τ0 give 

us the ensuing variation of the SStokes 

vector. 

Response function units are invverse 

of their corresponding 

quantities (e.g RFs to temperatuure 

have units K-1 ) 


RFs – Example: Fe 6302.5 

model on the left is: 

�� 500 K hotter 

� 500 G stronger 

� 20° more inclined 

�� 50° 50° larger azimuth 

� no VLOS gradient 

(right: linear gradient) 

Temp 

|B| 

VLOS 


SPINOR: complex model atmos atmospheres spheres 


The even more complex case: 


The fluxtube case: 


The complex fluxtube case: 


SPINOR: Versatility 

� Plane-parallel, 1-component models to 

obtain averaged properties of the 

atmosphere 

� Multiple components (e.g. to take caree 

of scattered light, or unresolved 

features on the Sun). Allows for arbitraary 

number of magnetic or field-free 

components (turns out to be important, 

e.g. in flare observations, where we 

have seen 4-5 components). 

� Flux-tubes in total pressure equilibriumm 

with surroundings, at arbitrary 

inclination 

� in field-free (or weak-field surrounddings) 

� embedded in strong fields (e.g. sunnspot 

penumbra, or umbral dots) 

� includes the presence of multiple flux 

tubes along a ray when computing 

away from disk centre 

�� efficient computation of lines acros s jumps in atmospheric quantities 

� Integration over solar or stellar disk, inncluding 

solar/stellar rotation 

� molecular lines (S. ( Berdyugina) y g ) 

� non-LTE (MULTI 2.2, not tested yet, reequires 

brave MULTI expert) 


Penumbral Flux Tubes 

� SPINOR applied to: 

Fe I 6301 + 6302 6302 

Fe I 6303.5 

Ti I 6303.75 

� 1st component: 

tube ray (discontinuity 

at boundary) 

� 22nd d component: t 

surrounding ray 

Borrero et al. 2006 


SPINOR & HINODE 

Hinode SOT: 10-11-2006 



inv_070214.051204_hinode_test.tgz 

I/I c 

Δ(I/I c) [%] 

Q/I c [%] 

Δ(Q/I Δ( c) [%] 

1.00 

0.83 

0.66 

0.49 

0.32 

3.00 

0 

−3.00 

14.80 

7.40 

0.00 

−7.40 

−14.80 

2.90 

0 

−2.90 

6301.5 

6302.5 

−0.17 0.17 

−0.17 0.17 

λ−λ λ−λ0 [Å] λ−λ 0 [Å] 

6301.5 

−0.17 0.17 

λ−λ 0 [Å] 

FINAL ATM IC= 1 WL= 5000.0000 

6302.5 

−0.17 0.17 

λ−λ 0 [Å] 

1 magnetic component, 5 nodes 

V/Ic [%] ] 

Δ(V/I c) [%] 

U/I c [%] 

Δ(U/I Δ( c) [%] 

11.50 

5.75 

0.00 

−5.75 

−11.50 

2.05 

−2.05 


0 

4.50 

2.25 

0.00 

−2.25 

−4.50 

2.25 

0 

−2.25 

6301.5 

6302.5 

−0.17 0.17 

−0.17 0.17 

λ−λ λ−λ0 [Å] λ−λ 0 [Å] 

6301.5 

−0.17 0.17 

λ−λ 0 [Å] 

6302.5 

−0.17 0.17 

λ−λ 0 [Å] 




inv_070214.024925_hinode_test.tgz 

I/I c 

Δ(I/I c) [%] 

Q/I c [%] 

Δ(Q/I Δ( c) [%] 

1.00 

0.83 

0.66 

0.49 

0.32 

3.00 

0 

−3.00 

14.90 

7.45 

0.00 

−7.45 

−14.90 

1.75 

0 

−1.75 

6301.5 

6302.5 

−0.17 0.17 

−0.17 0.17 

λ−λ λ−λ0 [Å] λ−λ 0 [Å] 

6301.5 

−0.17 0.17 

λ−λ 0 [Å] 


9 

6302.5 

−0.17 0.17 

λ−λ 0 [Å] 


2.4 

flux tube model 

V/Ic [%] ] 

Δ(V/I c) [%] 

U/I c [%] 

Δ(U/I Δ( c) [%] 

11.50 

5.75 

0.00 

−5.75 

−11.50 

1.70 

0 

−1.70 

5.00 

3.33 

1.67 

−0.00 

−1.67 

1.90 

0 

−1.90 

6301.5 

6302.5 

−0.17 0.17 

−0.17 0.17 

λ−λ λ−λ0 [Å] λ−λ 0 [Å] 

6301.5 

−0.17 0.17 

λ−λ 0 [Å] 

6302.5 

−0.17 0.17 

λ−λ 0 [Å] 


A. Lagg - Abisko Winter School 26 

4

Penumbral Flux Tubes 

�� confirms uncombed model 

�� flux tube thickness 100 100-300 300 km 

Borrero et al. 2006 


Multi Ray Flux Tube 

multiple utpe rays ays 

�� pressure balance 

�� broadening of flux tube 

Frutiger (2000) 


2-comp comp model Sunspot + molec cular lines 

SPINOR applied to: 

Fe I 15648 / 15652 

1 magn magn. . comp (6 nodes) 

1 straylight comp. 

molecular OH lines 

without OH 

with OH 

Mathew et al. 2003 


Wilson Depression 

SPINOR applied to: 

Fe I 15648 / 15652 

1 magn. comp (4 nodes) 

1 straylight comp. 

molecular OH lines 

investigation of 

thermal thermal-magnetic magnetic 

relation 

Mathew et al. 2003 


Penumbral Oscillations 

oscillations observed in 

Stokes-Q of 

FeI 15662 and 15665 

calc. l phase h diff difference 

between Q-osc. 

� time delay 

22-C Cin inversion ersionwith ith 

straylight: 

� FT-component 

�� magn magn. background 

RF-calc: difference in 

formation height 

(velocity): ~20 20 km 

relate time delay to 

speed of various wave 

modes 

Bloomfield et al. [2007] 




Stokes-Q of 

FeI 15662 and 15665 





straylight: 








modes 





Stokes-Q of 

FeI 15662 and 15665 




RF RF-calc: calc difference in 


(velocity): ~20 km 

22-C C inversion with 

straylight: 


�� magn. background 



modes 





Stokes-Q of 

FeI 15662 and 15665 





straylight: 








modes 


� best agreement for: 

fast-mode waves 

propagating 50° to the vertical 


Analysis of Umbral Dots (1) 

Analysis of 51 umbral dots 

using SPINOR: 

�� 30 peripheral peripheral, 21 central UDs 

� nodes in log(τ): -3,-2,-1,0 

(spline-interpolated) 

� of interest: 

atomspheric stratification 

�� T(τ) T(τ), B(τ), B(τ) VLOS(τ) 

� INC, AZI, V MIC, V MAC const. 

� no straylight (extensive tests 

showed, that inversions did 

not improve significantly) 

Riethmüller et al., 2008 



center of f UD: 




atmospheric stratification 

retrieved in center (red) and the 

diffuse surrounding (blue) 




Vertical V cut through UD 




Conclusions: 


�� inversion results are 

remarkably similar to 

simulations of Schüssler & 

Vögler (2006) 

� UDs differ from their surrounding 

mainly y in lower layers y 

� T higher by ~ 550 K 

� B lower by ~ 500 G 

�� upflow ~ 800 m/s 

� differences to V&S: 

� field strength g of DB is found to be 

depth dependent 

� surrounding downflows are 

present, but not as strong and as 

narrow as in MHD (resolution?) 


Analysis of Hi Hi-Res Res Simulations 

= 200 G; Grid: 576 x 5776 

x 100 (10 km horiz. cell size) 

Brightness 

(forward calc.) 

Vö Vögler l & Schüssler S hü l 

Magnetic field . 


Pore simulation: brightening nea ar the limb R. Cameron et al. 

μ=1 

μ=0.3 

μ=0 μ=0.5 5 

μ=0.7 


SPINOR: GG-band 

band spectrum syn thesis 

G-Band (Fraunhofer): spectral rang ge from 4295 to 4315 Å 

contains many temperature-sensitive 

molecular lines (CH) 

For comparison with observatioons, 

we define as G-band 

intensity the integral of the speectrum 

obtained from the 

simulation data: 

I 

G 

= 

4315 

∫ 

4295 

A 

I ( λ λ ) d dλλ 

A 

241 CH lines + 87 atomic lines 

[Shelyag, 2004] 


SPINOR: Installation and first us sage 

Download from http://www.mps .mpg.de/homes/lagg 

GBSO download-section � spinor 

use invert and IR$soft 


Exercise ecse IV 

SPINOR installation and b basic usage 

� install and run SPINOR 

� atomic data file, wavelength bound 

�� use xinv interface 

� SPINOR in synthesis (STOPRO)-m 

� 1st inversion: 

Hinode dataset of HeLIx + 

Hinode dataset of HeLIx 

� play with noise level / initial values 

� change log(τ) scale 

�� try to get the atmospheric stratifica 

ation of an 

asymmetric profile 

� invert HeLIx + synthetic profiles 

dary file 

mode 

/ parameter range 

Examples: http://www.mpss.mpg.de/homes/lagg 

� Abisko 2009 � spinor � abisko_spinor.tgz 

unpack in spinor/inversion ns: 

cd spinor/inversions ; ttar 

xfz abisko_spinor.tgz

SPINOR

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