1. Diagnostic capability of FG/SP Kiyoshi Ichimoto NAOJ Hinode workshop, 2007.12.8-10, Beijing

2. Contents: - Spectral windows of SOT - Available spectral lines and their Zeeman properties - Detection limit for the magnetic field w/ polarization sensitivity of SOT - Retrievability of magnetic field from NFI observables

3. SOT broadband filters Field of view218" × 109" (full FOV) CCD4k × 2k pixel (full FOV), shared with the NFI Spatial Sampling0.0541 arcsec/pixel (full resolution) Spectral coverage Center (nm)Width (nm)Line of interestPurpose 388.350.7CN IMagnetic network imaging 396.850.3Ca II HChromospheric heating 430.500.8CH IMagnetic elements 450.450.4Blue continuumTemperature 555.050.4Green continuumTemperature 668.400.4Red continuumTemperature Exposure time0.03 - 0.8 sec (typical)

4. BFI

7. Contribution function of BFI continuum log(  5000 )

8. Response function of BFI intensity from  T/T courtesy Dr. Mats Carlsson

9. CH3883, CN4305 (G-band) formation height S. V. Berdyugina etal., 2003, A&A 412, 513–527 Quiet region sunspot

10. SOT narrowband filter Field of view328"×164" (unvignetted 264"×164") CCD4k×2k pixel (full FOV), shared with BFI Spatial sampling0.08 arcsec/pixel (full resolution) Spectral resolution0.009nm (90mÅ) at 630nm Spectral windows (nm) and lines of interest Center -range Linesg eff Purpose 517.20.6Mg I b 517.271.75Dopplergrams and magnetograms 525.00.6Fe I 524.712.00Photospheric magnetograms Fe I 525.023.00 Fe I 525.061.50 557.60.6Fe I 557.610.00Photospheric Dopplergrams 589.60.6Na I D 589.61.33Very weak fields (scattering polarization) Chromospheric fields 630.00.6Fe I 630.151.67Photospheric magnetograms Fe I 630.252.50 Ti I 630.380.92Umbral magnetograms 656.30.6H I 656.28~1.3?Chromosphreic structure Exposure time0.1 - 1.6 sec (typical)

11. NFI 517.27 (Mg b2)

12. NFI 525.02

13. NFI 557.60

14. NFI 589.60 Na D1 D1D2

15. NFI 630.25

16. NFI 656.27 H 

17. MG1 5172.680 3P1 - 3S1 2.700 -.3800WI 1259.0 b2 NA1 5895.920 2S0.5 - 2P0.5.000 -.1840MS 564.0* H 1 6562.740 1 2S 0.5 2P 0.5 10.199 -.0606WI 4020.0 FE1 6302.503 5P1 - 5D0 3.686 -.6100CW 83.0 FE1 5250.207 5D0 - 7D1.121 -4.4600CW 62.0 Zeeman patterns of NFI lines

18. 10” 100”1000” FOV Time res. 1” 0.1” Spatial res. 1sec 1min Time span 1hr 1day 1week 10sec 1 # of wavelength (reliability) Random noise (detection limit) 1min 1hr 1day 10min 4 2 64 16 0.01% 0.1% 1% 0.2” 0.4” SOT/NFI full image Ground SP Ground FG magnetograph SOT/SP full scan SOT performance Resolution for energy element ～  (  x) 2

19. SOT セミナー＠花山 2004.12.7 dx=0.2 ” (SOT) dx=1 ” (ground)  n = 0.5%  n = 0.1% Detection limit  B l (G) 8.51.7  B t (G) 14163  j (A) 1.2 x 10 9 5.2 x 10 8 2.6 x 10 9  (erg, l=10 4 km ) 1.3 x 10 28 6.6 x 10 27 1.3 x 10 29 Accuracy  B t (G, B t =500G)  (deg., ” ) 2044 2.30.45  j (A, ” ) 1.6 x 10 8 3.3 x 10 7 3.3 x 10 8  erg) 2.4 x 10 30 (N=1000) 4.8 x 10 29 (N=1000) 1.5 x 10 31 (N=500) Detection limit and accuracy of magnetic field measurements -- rough comparison with ground-based observations -- Photon noise limited, FeI6302A line

20. S ’ = XS X : polarimeter response matrix Ground calibration X r -1 S ’  S ” on-board demodulatio n S Incident Stokes vector I ’ modulated intensity S T Incident to polarimeter Telescop e S T = TS S ” reduced Stokes vector I ” CCD output S ’ SOT product CCD gain/dark I’’ =  I’+  Polarization modulation Measuremen t error:  S I ’ = W S T dark/gain correction S raw SOT raw data Polarimeter response matrix X : true matrix X r : matrix used in calibration polarimeter response matrix

21. Sheet polarizer window (I,Q,U,V) mask FPP Heliostat ＳＯＴ polarization calibration before launch 2005.6 @Mitaka Using well-calibrated sheet polarizers (linear & circular), the polarimeter response matrices, X, of SP and all wavelength of NFI were determined with an accuracy below. Accuracy:  0.3333 0.3333 0.2500 0.0010 0.0500 0.0067 0.0050 0.0010 0.0067 0.0500 0.0050 0.0010 0.0067 0.0067 0.0500  X < SOT is cross-talk free at  ~ 10 -3 level Diagonal elements tell about the sensitivity of the SOT to Q,U,V

22. Left 1.0000 0.2205 0.0187 -0.0047 0.0012 0.4813 0.0652 -0.0014 0.0001 0.0513 -0.4803 -0.0057 -0.0025 0.0032 -0.0046 0.5256 Right 1.0000 -0.2112 -0.0170 -0.0051 -0.0025 -0.4875 -0.0560 0.0022 -0.0001 -0.0426 0.4907 0.0060 0.0027 -0.0008 0.0042 -0.5301 Median Mueller matrix x matrices at scan center; CCD image each element is scaled to median + tolerance, x 00 (=1) is replaced by I-image The x matrix can be regarded as constant in the CCD. SP

23. X matrix over the CCD, 5172 80x1024 Example of FG/NFI left: theta= -1.571deg. 1.0000 -0.2994 -0.0336 -0.0435 0.0009 -0.4544 0.0208 0.0045 -0.0009 0.0287 0.4478 0.0068 -0.0085 0.0318 -0.0134 0.5774 right: theta= -4.441deg. 1.0000 -0.2871 -0.0305 -0.0434 -0.0003 -0.4473 0.0653 0.0038 -0.0007 0.0738 0.4435 0.0061 -0.0077 0.0310 -0.0150 0.5718

24. 1) Detection limit for circular and linear polarizations  is the photometric accuracy x 33 and x 11 are diagonal elements of X 2) Polarization signals by Zeeman effect in a weak field 3) Thus detection limit for magnetic fields are given by Line profile convoluted with the tunable filter profile Detection limit of NFI for weak fields Difference of 2 nd moments of  and  -components

25. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Q U V SOT modulation profiles from the measured PMU retardance Wavelength (nm) Retardation (wave) 517.3 6.682 525.0 6.572 589.6 5.762 630.2 5.344 656.3 5.110

26. Wavelength (nm)g eff Ｇ Pol. Sensitivity (diagonal element of X) Detection limit for B (Gauss) VQUBlBl BtBt MgI 517.2 1.752.880.5770.45237970 FeI 525.0 3.009.000.2660.60915210 FeI 557.6 0.00 ---- NaI 589.6 1.33 0.6330.297211240 FeI 630.2 2.506.250.5260.50310240 HI 656.3 1.33 0.4020.07378>5000 Detection limit of FG for the weak magnetic fields,  = 0.001

27. Line (A) UsageDetec. limit B  = 0.1% (G) BlBl BtBt 5172Active region lower chrom. Vector mag.fields Shutterless mode is preferable 37970 5250Vector mag.field in photosphere Highest sensitivity to linear pol. with higher spatial resolution 15210 5576Photospheric Dopplergram -- 5896Longitudinal meg.field in lower chromosphere Prominence core imaging 211240 6302Vector mag.field in photosphere Umbral mag.field with TiI line 10240 6563Chromosphere/prominence imaging and Dopplergram No sensitivity to linear pol. 78>5000 Choice of a NFI line

28. NFI observables -- I( i ), Q( i ), U( i ), V( i ), i = 1,,, N Physical quantities derived from the observables --B field strength (G),  inclination (deg.),  azimuth (deg), S Doppler shift (mA) fill factor =1 Other quantities responsible for line formation are assumed to be those in typical quiet sun. An algorithm to derive the magnetic field from the NFI observables is tested. The algorithm is based on the least square using model Stokes profiles calculated beforehand How well can we retrieve the magnetic field from the products (IQUV) of the NFI?

29. データ解析ワークショップ 2004.12.20-23 Q peak （  =90 ゜） Polarization degree Peak wavelength I,Q,V Zeeman profiles against B V peak （  =0 ゜） I Q V

30. The method to derive the magnetic field vector from the NFI observables depends on the number of observed wavelength points. N = 1: 1-dimensional LUT for V/I  B l, Q/I  B t individually N = 2: Rotate the frame to make U=0 (ignore MO effect) + search for the best fitting to model observable in (B, , S) space N > 3: Initial guess with cos-fit algorithm + rotate the frame to make U~0 + search for the best fitting to model observable in (B, , S) sub space To test the performance of the algorithm, numerical simulations are made using ‘artificial sample observables’ (1000 sets) calculated with an atmospheric model with random physical parameters in a range of 0 < B < 3000 G 0 <  < 180 deg. -90 <  < +90 deg. -90 < S < +90 mA

31. No Doppler info. N = 1 at dl = -80mA, Simulation result Sample observable, 1000points B < 2000GB >2000G |S| < 60mAblackblue |S| > 60mAgreenred

32. alternative method: - ignoring MO effect - search entire (S, B,  ) space B < 2000GB >2000G |S| < 60mAblackblue |S| > 60mAgreenred N = 2 at d = [-80, 80] mA, simulation result

33. N = 4 at d = [-110, -70, 70,110] mA, simulation result B < 2000GB >2000G |S| < 60mAblackblue |S| > 60mAgreenred Non-uniform wavelength sampling

34. Diagnostics using SP data Zeeman effect produces polarization in spectral lines Obtain magnetic field vectors and motions in solar atmosphere. slit

35. Stokes profiles fitting program - Milen-Eddington fitting for Hinode SP  Data analysis session.. - SIR fitting programs SP data contains much more information on the structures of the solar atmosphere..