Comparison on Calculated Helicity Parameters at Different Observing Sites Haiqing Xu (NAOC) Collaborators: Hongqi, Zhang, NAOC Kirill Kuzanyan, IZMIRAN, Russia Takashi Sakurai, NAOJ Guiping, Ruan, Shandong University

Current helicity density observable Force free field: Two methods for calculating α : α best : minimizes the difference between the observed horizontal magnetic field and one that is computed from the observed longitudinal field under the assumption of a linear force-free field (Pevtsov et al.,1995). Definition of helicity (Hagino and Sakurai,,2004) (Bao and Zhang,1998)

The large sample statistical study of helicity Magnetic field of active regions to have negative magnetic helicity in the northern hemisphere and positive helicity in the southern hemisphere. This rule first found by Seehafer (1990)

Comparison of different instruments Individual active region comparison: there is a basic agreement between different data sets and estimated that there was 12°in the azimuth difference between SMFT and HSP contributed by Faraday rotation (Bao et al., 2000; Zhang et al., 2003) Statistical comparison: About 80% of 270 pairs of vector magnetograms obtained by SMFT and HSP from 1997 to 2000 result in the same sign of α best ( Pevtsov, Dun and Zhang, 2006). About 83% of 228 active regioins observed by SMFT and SFT have the same sign of h c (Xu et al., 2007) -- There is a basic agreement between different data sets. However, some notable differences between data sets have also been found.

further investigate the consistency between helicity proxies derived from different data sets Xu, Gao, Zhang, Sakurai, Hagino, Sokoloff, and Pevtsov, 2012, PASJ, 64, ARs observed by SMFT, SFT, HSP to calculate α av and α best. X-ray images from SXT and magnetograms from MDI to determine the value of α c in corona.  Correction of Faraday rotation for SMFT data (Gao et el.,2008 ， MNRAS ） :No change in sign of α  The correlation between filter-type magnetograph is better than that between filter-type magnetograph and Spectro- polarimeter 。  Correlations between photospheric and coronal helicity parameters are lower than the correlations among photospheric helicity parameters derived from the three magnetographs

Factors that may affect the calculation of helicity Time differences: may cause real evolution of magnetic field. Magneto-optical effects: will affect the sign and magnitude of helicity Calibration of magnetic fields. Spatial resolution and data reduction methods

Comparison of SMFT and SFT The Solar Magnetic Field Telescope at Huairou Solar Observing Station (SMFT/HSOS) : Wavelengh: Fe Ⅰ Å longitudinal field: Å transverse field: 0.0Å field view: 5.23′× 3.63′512*512 pixel (before 2001) 3.75′× 2.81′640*480 pixel (after 2001) The Solar Flare Telescope at Mitake (SFT/MTK): Wavelengh: Fe Ⅰ Å Magnetic field: -0.08Å field view: 512*480 pixel, 0.66″/pixel The design of these two instruments is similar. They are all filter-type magnetograph and the observing time is very close. But there are still 10-20% active regions have different helicity sign (Xu et al., 2012).

The main purpose of this study: To analyze the influence of magnetic field and calibration method on the correlation of helicity parameters inferred from SMFT and SFT data. Data sample: 228 active regions observed by SMFT and SFT from

Data reduction  180°azimuth ambiguity: --following Wang et al. (1994) by comparison with a potential field.  Alignment: --linearly interpolate the data onto the same spatial step size (0.6″/pixel), the same region which include the maximized size of sunspots are selected and shifted respect with each other to determine the optimal registration.  Projection effection: longitudes and latitudes of most of active regions are less than 35° and do not correct the data for projection effects.  Cut off:

Influence of magnetic field and azimuth angle on h c The influence of transverse field and azimuth angle on the correlation of h c inferred from SMFT and SFT data is significant.

Influence of magnetic field and azimuth angle on α Similar as h c, the influence of transverse field and azimuth angle on the correlation of h c inferred from SMFT and SFT data is significant.

influence of calibration on helicity parameters  two factors which reflect influence of calibration on magnetic field observed by SMFT and SFT ：

Recalculate helicity parameters as following:  The correlation of h c (α) inferred from SMFT and SFT is better. The influence of calibration method on the correlation of α is larger than h c

The variation of h c with longitudinal field Zhang (2006) found that helicity parameters α and h c for weak (100G 1000G) fields show opposite sign, and the signs of helicity parameters are consistent with the established hemispheric rule for weak field. Gosain et al. (2013) found the opposite sign of current helicity for weak and strong field, but the helicity of strong fields follow the hemispheric rule. Due to the opposite sign of helicity generated by large scale and small scale field or Magneto-optical effects in strong field region?

The variation of h c with longitudinal field (Supplied by Juan Hao) For SMFTand SFT: Southern hemisphere, h c >0. Northern hemisphere, Bz 600G, h >0. For HSP: Northern hemisphere, hc 0; Bz>800G, hc<0 SMFT NS SFT HSP SP/Hinode

Correlation of hc inferred from SMFT and SFT in different Bz interval

Case study: NOAA8085 (S26E14, 11 Sep. 1997)

Case study: (NOAA8299 (N16W10.7, 13 Aug. 1998)

Conclusion and Discussion Ⅰ Observing results ：  There is a good correlation between the longitudinal field and so it has small influence on the correlation of helicity parameters observed by these two instruments.  The influence of azimuthal angle and transverse field on the correlation of h c (α) inferred from SMFT and SFT is significant.  There is a good consistency of h c among different instruments when Bz less than 600G. The discrepancy increases when Bz stronger than 600G  The value of h c is small when Bz less than 200G.

Conclusion and Discussion Ⅱ Possible reasons Calibration method: The influence of calibration method on the correlation of α is larger than h c. Faraday rotation: This is a major problem for calculating helicity parameters for strong field region. When Bz>0 (Bz<0), the helicity contributed by Faraday rotation is positive (negative). Time difference: The observing time is very close for SMFT and SFT, so the influence on the correlatioin of helicity parameters is small. The time difference is larger between SMFT and HSP (SFT and HSP) The relative low correlation may caused a certain extent by this.

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