1. 1 Yongliang Song & Mei Zhang (National Astronomical Observatory of China) The effect of non-radial magnetic field on measuring helicity transfer rate

2. Our previous studies (Zhang & Low 2005; Zhang et al. 2006; Zhang & Flyer 2008; Zhang et al. 2012) have suggested that: (1) Magnetic helicity is accumulating in the corona; (2) There is an upper bound on the total magnetic helicity that force-free magnetic field can contain; (3) Once the accumulated helicity has reached the upper bound, an expulsion such as CMEs become unavoidable. Motivation

3. 3 We can monitor the evolution of magnetic helicity and use it to predict the eruption of CMEs. --- We can calculate the helicity transfer rate on the photosphere to monitor the helicity accumulation in the corona. --- We can estimate the helicity upper bound corresponding to current boundary flux distribution. Based on this model,  This requests an accurate measurement of magnetic helicity transfer rate.

4. First term: emergence term; Second term: shearing term Before SDO, previous studies have used MDI data and have put into the calculation two assumptions. (1) if U is from tracking footpoints. Helicity transfer rate

5. They calculated the helicity transfer rate in two active regions (AR11072 & AR11158) using HMI/SDO vector magnetograms and DAVE4VM code, and found that (1) apparent tangential velocity derived by tracking field- line footpoints is more consistent with tangential plasma velocity than with the flux transport velocity; (2) relative magnetic helicity in the active-region corona is mainly contributed by the shearing term (88%, 66%). Liu & Schuck (2012) checked the first assumption.

6. In previous studies, they have also assumed that the magnetic field being no-radial will NOT influence the calculation of helicity transfer rate. However, there is another assumption. Our purpose is to check this assumption.

7. There are a good fraction of the sunspot area where the horizontal magnetic field is larger than the vertical field. Histogram of Bt/Bz in a magnetogram of a sunspot

8. We study two active regions observed by HMI/SDO as in Liu & Schuck (2012) NOAA 11072: 2010.5.20 emerge at S15E48 bipolar AR 144 hours ob. 720 magnetograms NOAA 11158: 2011.1.10 emerge at S20E60 multipolar AR produce an X-class flare 120 hours ob. 600 magnetograms

9. NOAA11072 as an example : from the disk center to the limb 2010-05-23 07:00:00 UT 2010-05-26 08:00:00 UT

10. Bn Near disk center: HMI Limb: MDI-like Near disk center: MDI-like Limb: HMI

11. dH/dt Near disk center ： MDI-like Near disk center ： HMI Limb ： MDI-likeLimb ： HMI MDI-like ： LCT HMI ： DAVE4VM

12. dH/dt (shearing term, after a recalibration) NOAA 11158 NOAA 11072 Blue: MDI-like Red: MDI-like, DAVE Black: HMI, DAVE4VM

13. NOAA 11158 NOAA 11072 H m (accumulated helicity, shearing term, after a recalibration) Blue: MDI-like Red: MDI-like, DAVE Black: HMI, DAVE4VM

14. Summary We checked the effect of non-radial magnetic field on measuring helicity transfer rate by comparing the results using vector magnetograms taken by HMI/SDO with those using only line-of-sight magnetograms. We find that: 1) The effect of the non-radial magnetic field on the calculation of magnetic helicity transfer rate is strong when the active region is observed near the limb and is relatively small when the active region is close to the disk center; 2) If only considering the accumulation of magnetic helicity from the shearing term, the effect of non-radial magnetic field then becomes minor.

15. Implication Since the shearing term is the dominant component in the helicity transport and the effect of non-radial field is minor for the calculation of accumulated magnetic helicity, we could still use MDI data to study the solar- cycle variation of helicity transport and accumulation, and investigate their possible relation with the solar-cycle variation of CME production.

16. 16 Thank you for your attention! Huairou Solar Observing Station, NAOC