1. Study of magnetic helicity in solar active regions: For a better understanding of solar flares Sung-Hong Park Center for Solar-Terrestrial Research New Jersey Institute of Technology

2. Magnetic helicity can be transported across the boundary by two kinds of flows as follows: Berger & Field (1984) Vertical flow transport of helical fluxes Horizontal flow shearing of field lines A practical approach ( Chae et al. 2004 ) based on the analysis of MDI/SOHO magnetograms was employed to determine the rate of magnetic helicity injection in the solar corona. Chae ’ s Method (2001) S : Photospheric surface of the active region B n : From MDI/SOHO magnetograms A p : From Bn (FFT method) V LCT : From temporal variation of Bn ( LCT method ) Helicity Change Rate (a)Horizontal flux rope emergence (b) Vertical flux rope emergence

3. Calculation of Magnetic Helicity

4. Data sets : MDI magnetograms (Example: AR 10696) - Full-disk field of view - 1 & 96-min cadence - Over 12 years (Dec,1995~) of operation with few gaps - 2 ˝ spatial resolution - In the filament server, we already have the corrected 96-min full disk MDI magnetograms (1996-2006).

5. AR 10696 : Normal Component of Magnetic Field, B n B l =B n cosφ φ: heliocentric angle We assume that the magnetic field on the solar photosphere is normal to the solar surface. Projection effect : Near the disk center (within 60% of the solar radius from the apparent disk center)

6. AR 10696 : Calculation of Vector Potential, A p From the FFT method The magnitude of vector potential is the biggest near the polarity inversion line.

7. AR 10696 : Calculation of LCT velocity field, v LCT From the LCT method with two parameters : w = 10 arcsec Δ t = 60 or 96 min Shearing flow near the polarity inversion line

8. AR 10696 : Helicity Change Rate Shearing flow near the polarity inversion line injects negative helicity to the corona during first 3000 minutes after the starting time of measurement.

9. Two kinds of Helicity Study

10. Our Goal Approach Our Goal : To find a possible characteristic helicity evolution pattern that is associated with a flare impending mechanism. Approach : We have investigated long term (a few days) variations of the magnetic helicity around eleven X-class flares which occurred in seven active regions (NOAA 9672, 10030, 10314, 10486, 10564, 10696, and 10720), and compared the results with GOES soft X-ray light curves. 1. Case Study

11. AR 9672 : LCT Velocity Field and Helicity

12. Time variations of helicity accumulation, magnetic flux and GOES X-ray flux for 3 active regions The helicity is shown as cross symbols and the magnetic flux is shown as diamonds. The GOES X-ray flux is shown as the dotted lines. Phase I, the interval over which the helicity accumulation is considered, and phase II, the following phase of relatively constant helicity, are marked.

13. Time variations of helicity accumulation, magnetic flux and GOES X-ray flux for 4 active regions

14. Time variations of helicity accumulation, and magnetic flux for 6 non-flare active regions

15. Our analysis reveals that there were two distinct phases of helicity variation around some major flares (4 among 11 X-class flares). Phase 1 Phase 2 In case where flares occur in phase II, it may imply that solar active regions can wait for major flares after the helicity accumulated to some limiting amount. An active region may evolve to a certain stage where the helicity no longer increases, and the system waits until it unleashes the stored energy by producing flares due to certain mechanism of triggering. flare A phase of linearly increasing helicity A phase of relatively constant helicity

16. Helicity parameters with GOES X-ray flux integrated over the flaring time Correlation coefficient (CC) is specified in each panel. The uncertainties of the average helicity change rate, the amount of helicity accumulation, and the helicity accumulation time are shown as error bars in each panel.

17. Our Goal Approach Our Goal : T o examine if magnetic helicity injection will carry extra weight in predicting flares Approach : We have investigated three magnetic parameters (unsigned magnetic flux, magnetic helicity change rate, and magnetic helicity accumulation) of 117 solar active regions and compared them with the soft X-ray flare index for the three time windows of 0-12 hours, 12-24 hours, and 24-48 hours after the quantities are calculated. 2. Statistical Study

18. Definition of magnetic parameters : Average Helicity Change Rate : Helicity Accumulation Change : Average Unsigned Magnetic Flux : Helicity Accumulation Time

19. We calculate these quantities during a period of 24 hours after an active region appears or rotates to a position within 0.6 of the solar radius from the apparent disk center. We then compare these parameters with the flare index derived from GOES X-ray observation for the three time windows after the magnetic helicity measurement:0-12 hours, 12-24 hours, and 24-48 hours. Method

20. Critical Value: 310x10 20 Mx

21. Critical Value: 5x10 40 Mx 2 hr -1

22. Critical Value: 100x10 40 Mx 2

23. 0 - 12 hours Critical value

24. 12 - 24 hours Critical value

25. 24 - 48 hours Critical value

26. Magnetic parameters with soft X-ray flare index (0-24 hours)

27. 1. Case Study a. A substantial amount of helicity accumulation is found before the flare in all the events. The helicity increases at a nearly constant rate, (4.5-48)x10 40 Mx 2 hr -1, over a period of 0.6 to a few days, resulting in total amount of helicity accumulation in the range of (1.8-16)x10 42 Mx 2. b. There is a strong positive correlation between the average helicity change rate of phase I and the corresponding GOES X-ray flux integrated over the flaring time. c. Monitoring of helicity variation in target active regions may also aid the forecasting of flares. A warning sign of flares can be given by the presence of a phase of linearly increasing helicity, as we found that all the major flares occur after significant helicity accumulation. Summary & Further works

28. 2. Statistical Study a. There seems to be a critical value of magnetic parameters (average helicity change rate, average unsigned magnetic flux, and helicity accumulation change) for a solar active region to produce a flare. b. We could find that the consideration of both critical values of average helicity change rate and average unsigned magnetic flux makes the higher prediction for the probability of occurrence and nonoccurrence of a flare on the active region within 24 hours. It means magnetic helicity injection will carry extra weight in predicting flares. c. The correlation between magnetic parameters and flare index is weak, but we need to investigate more active regions. Summary & Further works

29. 1. More Active Regions a. Case study : To check up whether there is also the characteristic helicity evolution pattern for the more active regions which produced X-class flares b. Statistical study : To investigate the probability for flare occurrence and nonoccurrence with a critical value of the magnetic parameters, and correlation between flare index and magnetic parameters. 2. Different Data a. Hinode filtergram (FG) data: - better spatial resolution (0.08″) - 2 minute cadence b. IRIM : deeper photosphere, weaker magnetic field Summary & Further works