Calibration of Solar Magnetograms and 180 degree ambiguity resolution

Moon, Yong-Jae ( 文 鎔 梓 )

(Korea Astronomy and Space Science Institute)

Acknowledgement

• 1994 : Huairou, Dr. Ai, Dr. J. Wang, Dr. Zhang

• 1997 : Mitaka, Dr. Ichimoto, Dr. Sakurai

• 1999 : MEES, HSP, Dr. Mickey

• 2001 : BBSO, Dr. H. Wang

• 2002 : ASP, Dr. Pevtsov, Dr. Skumanich

• 2005 : talk2.ppt from WWW by Dr. J. Wang

(srg.bao.ac.cn/weihailect/wangjx/TALK2.PPT )

Outline • Introduction• Calibration of filter-based magnetograms : non-linear calibration, k-factor problem• Calibration of spectrometer-based magnetograms : Stokes V signal anomaly• Comparison of magnetograms • A new 180 ambiguity resolution method : Uniform Shear Method• Conclusions

Introduction • Magnetic field is the source of solar explosions• Routine observations available at the photosphere • We need 4 dimensional data (x,y,wavelength, Stokes

Vector) at a given time• Two types of solar magnetographs 1) filter-based : MSFC, BBSO, Huairou, Mitaka, IVM - narrow band filtergram (2D spatial, Stokes) - high time res., wide field of view 2) Spectrometer-based : ASP, HSP …… - Spectrometer (1D spatial +Stokes, spatial scan) - accurate field measurements with fill fraction

Radiative Transfer of Stokes Parameters(Weak Field Approximation, Jefferies et al. 1989)

21

41221

22122

22

)()()(

sincos

),(2tan)2

sin()(

2sin)2

sin(2cos)

2

sin(

),(cos

IUQB

IVB

BB

AzimuthQ

UIUQ

IU

IQ

nInclinatioI

V

l

blb

b

bb

d

bbb

where are calibration coefficients for line-of-sight and transverse components, respectively, and

41

2

2

2

2

////

I

Q

I

UCB

I

VCB

//

arctanarctan2

1

B

B

Q

U

CandC//

2. Calibration of Filter-based Magnetograms

Hagyard and Kineke(1995) developed an iterative procedure to improve the calibration using analytic solution of Stokes radiative equations

Fe 5250 line

Moon et al.(1999) : Fe I 6302.5 line

k-factor problem : Underestimation of magnetic field strength Gary et al(1987) : 8.1 to match Mount Wilson data Gary et al.(1991) : instrumental depolarization MSFC usually adopt k=4. Chae(1996) : seeing corrected fields still require a k-factor (k=2.2 ) Mitaka : to match both Bot and Bpt Huairou : non-linear calibration curves

kI

Q

I

UCB

kI

VCB

41

2

2

2

2

////

Lites et al.(1994)

The k-factor seems to be due to magnetic fill fraction: k=1/f

Non-linear Least square method (Skumanich and Lites 1987) :

ijii

ijii

jiii

jiii

fitaIobsIfitaVobsV

fitaUobsUfitaQobsQ

iIiV

iUiQ

2121

21212

)];()([)];()([

)];()([)];()([

22

22

Magnetic fields vectors and thermodynamical parameters are simultaneously determined.Basic assumption : Milne Eddington Atmosphere (All parameters do not depend on optical depth)

3. Calibration of Spectrometer -based Magnetograms

ASP data, Bt=688 G, Bl= 971 G, i=35 degree

Bt=436 G, Bl= -10 G, i=89 degree

Community Inversion Code http://www.hao.ucar.edu/public/research/cic/

1. Melanie : Milne Eddington line analysis

2. Lilia : LTE inversion, stratification, individual lines

3. Dianne (beta) : Direct inversion using Neural Network

4. Comparison of different magnetograms

Wang et al.(1992)

Ronan et al.(1992)

Two anti-parallel polarization signals of the transverse fields are identical.

The only way to remove the ambiguity is to employ a new constraint from other physical or observational assumptions which are independent from Zeeman effect.

Importance : for a meaningful understanding of several important physical parameters such as vertical current density, shear angle etc.

5. A new 180 ambiguity resolution method

- Potential field assumption Best assumption : Minimize the difference betw

een observation and extrapolation - Magnetic charge method : Wang (1993)- Synthesized Method : Wang and Lin (1993) - Multi-step method : Canfield et al.(1993)- Functional Minimization (J or ): Metcalf(1994), Gary and Demoulin (1995) Georgoulis et al.(2004)-H observations : fibril alignment and/or chirality

00 ptot BBB

0 B

1) Potential Field Method

2) : vector with most probable shear

0 stot BB

Uniform Shear Method (Moon et al. 2003, Solar Physics, 217, 79)

0 mtot BB

3)

: mean neighboring

transverse vector

Shear Angle Distribution

Potential Field

Uniform Shear

Canfield et al.(1993)

Moon et al.(2003)

AR5747

Uniform Shear

Canfield et al.(1993)

Moon et al.(2003)

Canfield et al.(1993)

AR6233

Shear Angle DistributionAR5747

AR6233

1. Filter-based and Spectrometer-based magnetographs are complementary each other : Imaging Vector Magnetograph (MEES, BBSO)

2. Cross-comparison is recommended :

ASP data for quantitative measurements

MDI data for seeing effect

3. New missions : NST, SDO, Solar-B, ATST ….

4. What is a reasonable criterion to determine which ambiguity resolution method is correct.

: current minimization, Jz comparison

6. Concluding Remarks