1. Study of Magnetic Helicity Injection in the Active Region NOAA 11158 Associated with the X-class Flare of 2011 February 15 Sung-Hong Park 1, K. Cho 1, Y. Kim 1, S. Bong 1, D. E. Gary 2, Y. Park 1 1 Korea Astronomy and Space Science Institute 2 New Jersey Institute of Technology

2. 1. Aims The main objective of this study is to examine a long-term (a few days) precondition and a trigger mechanism for an X2.2 flare peaking at 01:56 UT on 2011-Feb-15 in GOES soft X-ray flux. For this, we investigate the variation of magnetic helicity injection through the photospheric surface of the flare- productive active region NOAA 11158 during (1) the long- term period of February 11-15 with a 1-hour cadence and (2) the short-term period of 01:26-02:10 UT on February 15 with a 45-second cadence

3. 2. Magnetic Helicity Magnetic helicity is a useful parameter to quantitatively measure the global complexity and non-potentiality of a magnetic field system (Démoulin & Pariat 2009). Magnetic helicity consists of: (a) twists of magnetic field lines inside a flux tube and kinks of flux tube axes, and (b) inter-linkages between flux tubes.

4. (1) Method -Helicity Flux Density (Pariat et al. 2005) where B n is the normal magnetic field component, x is the position vector, and u is the apparent horizontal velocity of the photospheric field line footpoints. u is measured with the differential affine velocity estimator (DAVE) method developed by Schuck (2006). 3. Helicity Calculation -Helicity Injection Rate & Helicity Accumulation

5. (2) Data The helicity injection was determined using line-of-sight magnetograms with high spatial and temporal resolution taken by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). 2011-02-12 19:00 UT 2011-02-11 08:00 UT 2011-02-12 08:00 UT 2011-02-13 08:00 UT2011-02-14 08:00 UT2011-02-15 08:00 UT

6. (3) Example: Velocity Map

7. (3) Example: Helicy Flux Density Map

8. (1) Long-term Profile of Helicity Injection 4. Results X2.2

9. (2) Short-term Profile of Helicity Injection 01:48 UT Note that when the total injection rate of helicity in the flaring active region changed its sign from positive (right-handed) to negative (left- handed), the X2.2 flare occurred simultaneously. 01:48 UT Note that when the total injection rate of helicity in the flaring active region changed its sign from positive (right-handed) to negative (left- handed), the X2.2 flare occurred simultaneously.

10. (3) Helicity Injection Rate vs. KSRBL Radio Flux The Korean Solar Radio Burst Locator (KSRBL) is a radio spectrometer designed to observe solar decimeter and microwave bursts over a wide band (0.245-18 GHz).

11. (4) Helicity Flux Density Maps 2011-02-15 01:40:24 UT2011-02-15 01:49:24 UT 2011-02-15 01:51:39 UT 2011-02-15 01:53:09 UT

12. 2011-02-15 01:56:09 UT 2011-02-15 02:06:39 UT (5) Potential Field Extrapolation Red (Blue) lines indicate the field lines of which foot points have positive (negative) magnetic helicity.

13. 2011-02-15 01:44:09 UT

14. 2011-02-15 01:49:24 UT

15. 2011-02-15 01:51:39 UT

16. 5. Summary & Conclusions We found two characteristic phases of helicity injection related to the X2.2 flare. (1)A large amount of positive helicity was first injected over ~2 days with a phase of monotonically increasing helicity. (2)Then the flare started simultaneously with a significant injection of the opposite (negative) sign of helicity around the flaring magnetic polarity inversion line. Injection of helicity of opposite sign Phase 1 flare Monotonically increasing helicity Phase 2

17. This observational finding clearly supports the previous studies that (1) there is a continuous injection of helicity a few days before flares (Park et al. 2008, 2010) and (2) a rapid injection of the helicity in the opposite sign into an existing helicity system triggers flares (Kusano et al. 2003). Formation of helicity inversion layers by the injection of the countersigned helicity by shear motion and/or by emergence (Kusano et al. 2003)

18. References Démoulin, P., & Pariat, E. 2009, Adv. Space Res., 43, 1013 Kusano, K., et al. 2003, Adv. Space Res., 32, 1931 Pariat, E., et al. 2005, A&A, 439, 1191 Park, S.-H., et al. 2008, ApJ, 686, 1397 Park, S.-H., et al. 2010, ApJ, 718, 43 Schuck, P. W. 2006, ApJ, 646, 1358 Démoulin, P., & Pariat, E. 2009, Adv. Space Res., 43, 1013 Kusano, K., et al. 2003, Adv. Space Res., 32, 1931 Pariat, E., et al. 2005, A&A, 439, 1191 Park, S.-H., et al. 2008, ApJ, 686, 1397 Park, S.-H., et al. 2010, ApJ, 718, 43 Schuck, P. W. 2006, ApJ, 646, 1358 Acknowledgments The authors thank the SDO/HMI team for providing the full- disk photospheric magnetogram data with high spatial and temporal resolution via the Joint Science Operations Center (JSOC).