Diagnostic capability of FG/SP Kiyoshi Ichimoto NAOJ Hinode workshop, , Beijing

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

SOT broadband filters Field of view218" × 109" (full FOV) CCD4k × 2k pixel (full FOV), shared with the NFI Spatial Sampling arcsec/pixel (full resolution) Spectral coverage Center (nm)Width (nm)Line of interestPurpose CN IMagnetic network imaging Ca II HChromospheric heating CH IMagnetic elements Blue continuumTemperature Green continuumTemperature Red continuumTemperature Exposure time sec (typical)

BFI

Contribution function of BFI continuum log(  5000 )

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

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

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 Mg I b Dopplergrams and magnetograms Fe I Photospheric magnetograms Fe I Fe I Fe I Photospheric Dopplergrams Na I D Very weak fields (scattering polarization) Chromospheric fields Fe I Photospheric magnetograms Fe I Ti I Umbral magnetograms H I ~1.3?Chromosphreic structure Exposure time sec (typical)

NFI (Mg b2)

NFI

NFI

NFI Na D1 D1D2

NFI

NFI H 

MG P1 - 3S WI b2 NA S P MS 564.0* H S 0.5 2P WI FE P1 - 5D CW 83.0 FE D0 - 7D CW 62.0 Zeeman patterns of NFI lines

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 % 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

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

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

Sheet polarizer window (I,Q,U,V) mask FPP Heliostat ＳＯＴ polarization calibration before launch 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:   X < SOT is cross-talk free at  ~ level Diagonal elements tell about the sensitivity of the SOT to Q,U,V

Left Right 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

X matrix over the CCD, x1024 Example of FG/NFI left: theta= deg right: theta= deg

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

Q U V SOT modulation profiles from the measured PMU retardance Wavelength (nm) Retardation (wave)

Wavelength (nm)g eff Ｇ Pol. Sensitivity (diagonal element of X) Detection limit for B (Gauss) VQUBlBl BtBt MgI FeI FeI NaI FeI HI >5000 Detection limit of FG for the weak magnetic fields,  = 0.001

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

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?

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

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

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

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

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

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

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..