A Method for Solving 180 Degree Ambiguity in Observed Solar Transverse Magnetic Field Huaning Wang National Astronomical Observatories Chinese Academy Of Sciencies

Contents 1. Introduction 1. Introduction 2. The best fit force-free factor 2. The best fit force-free factor 3. Examples 3. Examples

1. Introduction (1) It is an intrinsic problem (figure 1) arising from the linear polarized component in Zeeman’s splitting. (2)Theoretical criteria are needed to determine the direction of the azimuth of observed transverse field the direction of the azimuth of observed transverse field Potential field Potential field Linear force-free field Linear force-free field Zero-divergence Zero-divergence Minimum energy solution Minimum energy solution All of these criteria have their limitations. All of these criteria have their limitations.

Figure 1 Observed field with 180 Degree Ambiguity

(3) Observed coronal loops can be taken as references Coronal loops -- Inferred coronal magnetic field Coronal loops -- Inferred coronal magnetic field -- Observed photospheric magnetic field -- Observed photospheric magnetic field Inferred field lines from observed photospheric field should Inferred field lines from observed photospheric field should be in agreement with coronal loops (figure 2) be in agreement with coronal loops (figure 2) (4) The force-free factor determines the global configuration of the inferred field configuration of the inferred field Try to find the best fit force-free factor in an active region! Try to find the best fit force-free factor in an active region!

Figure 2 Trace Observation Figure 2 Trace Observation

（ 1 ） Bo(x,y) -- observed transverse field Bi (x,y) -- inferred transverse field Bi (x,y) -- inferred transverse field P(x,y)= P(x,y)= S= S= （ 2 ） Bi is determined with linear force- free model by taking observed longitudinal field as by taking observed longitudinal field as boundary condition boundary condition 2. The best fit force-free factor

（ 3 ） Select suitable value of force-free factor (α_best ) to obtain maximum value of S (α_best ) to obtain maximum value of S (4) Bo is calibrated with Bi, which is inferred (4) Bo is calibrated with Bi, which is inferred field based on linear force-free model field based on linear force-free model (αα_best) (α=α_best ) (5) Note: The noise level of observed transverse (5) Note: The noise level of observed transverse magnetic field should be determine. The field magnetic field should be determine. The field in the noisy area cannot be included in the in the noisy area cannot be included in the integration. integration.

（ 1 ） Comparison between inferred field lines and coronal loops observed by TRACE. The field lines are inferred with Yan’s model by taking Huairou data as boundary condition. 3. Examples

(2) Comparison between inferred field lines and coronal loops observed by Yohkoh. The field lines are inferred with Yan ’ s model by taking Huairou and Mitaka data as boundary condition. (figure 3) (3) Observed vector magnetogram in AR9077 July , 01:19UT (figure 4). The 180 degree ambiguity has been removed.

Figure 3 Inferred field line and X-ray image

Figure 4 Calibrated field

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