1. 1 A New Model of Solar Flare Trigger Mechanism Kanya Kusano (Hiroshima University) Collaboration with T.Maeshiro (Hiroshima Univ.) T.Yokoyama (Univ. of Tokyo) T.Sakurai (NOAJ) Plasma Theory Group, Hiroshima University

2. 2 Objective To understand the trigger mechanism of solar flares. Where, When, How, & Why are solar flares triggered explosively?

3. 3 Trigger Problem of Solar Flares reconnection flare loop We have to explain 1.Sudden onset 2.Current sheet formation 3.Precursor phenomena (e.g. sigmoid) Magnetic Helicity & Energy Solar Flare causality? Sigmoid slow fast

4. 4 Trigger Models Loss of Equilibrium (Forbes & Priest 1995) Loss of Stability Ideal MHD instability: kink mode (Kliem et al. 2004) Sheared field driven Moore et al. 1997 Magnetic neutral line

5. 5 Sheared Field Driven Model Mikic et al 1988, 1994 Kusano et al. 1995, 2002(3D) t=65 t=74 t=82 Shearing motionConverging motion Inhester, Birn, Hesse 1992 Birn, Forbes, et al. 2003 (3D) Amari et al. 2003 (3D)

6. 6 Strategies Observation Magnetic Helicity Injection Numerical Simulation 3D MHD large-scale simulation

7. 7 Magnetic Helicity Measurement SOHO/MDI Vector magnetograph (NAOJ, Tokyo) solution Correlation tracking n t MDI image Magnetic helicity flux Cha 2001 LCT Kusano et al. 2002 LCT+ induction eq. Demouline & Berger 2003 LCT Welsh et al. 2003 ILCT Longcope 2004 minimum velocity

8. 8 Measurement of Helicity Flux X-ray flux Helicity flux emerging shear Helicity emerging total X-ray energy Energy flux shear emerging Energy total Potential field (Kusano et al. ApJ, 2002)

9. 9 Helicity Injection & Soft X-ray Soft X-ray flux statistically well correlates with magnetic helicity flux. Magnetic Helicity Flux Soft-X Ray Flux (Maeshiro et al. 2004) Soft-X Ray Flux (Magnetic Helicity Flux) x (Shear Inversion Length)

10. 10 Helicity Injection & Solar Flare Amplitude of helicity flux does NOT directly correlate with flare onset. Helicity flux changes the sign within an active region. Flare Helicity Injection AR (time)  H (Mx 2 )  H/  2 8100 (120hr)4.0x10 42 0.02

11. 11 A Hypothesis of Shear Reversal Ba<0 Ba>0 Annihilation of the right-handed and left-handed magnetic shear may lead to an energy release. reversed shear shear-free field liberation of free enegy shear inversion (Kusano et al. 2003 Advances in Space Research) reconnection current sheet

12. 12 Simulation Model (3D MHD) Finite difference: 256 X 256 X 1024 (  ~10 -3 ) Initial state ： linear force-free (2D arcade) Boundary Condition: shear motion reversing magnetic shear (0.05V A ) Anomalous resistivity x y z

13. 13 MHD Simulation of Shear Reversal 2D 3D x y z magnetic field lines

14. 14 Evolution (Model 1) time kinetic energy (total) magnetic energy (Fourier mode) magnetic energy (total) turbulenteruptive x z t=8.5 t=24.5 t=33.0 z z current sheet 1 Bx current sheet 2 x yz t

15. 15 3D MHD Simulation of Shear Reversal 1 st reconnection 2 nd reconnection eruption 1 st reconnection 2 nd reconnection explosive growth tearing instability internal collapse

16. 16 T-shape 3D reconnection 1 2 3 CS1 CS2 CS1 Reconnection 2 B Reconnection 1 B Interaction of reconnections

17. 17 Current Sheet Evolution Spontaneous to Driven time resistivity enhanced

18. 18 Nonlinear Instability of Double Tearing Mode Instability in Tokamak Ishii, Azumi, Kishimoto (2002, PRL) Explosive Growth Rutherford phase current sheet

19. 19 ‘ Reversed-Shear Model ’ feedback Reversing shear Tearing Instability Reconnection 1 Flux Annihilation Collapse of Arcade Reconnection 2 Eruption Explosive Growth → trigger of flare 2004 APJ

20. 20 time Kinetic Energy relaxation phase (model 2) Strong Reversal

21. 21 time Kinetic Energy “ Sigmoid ”

22. 22 x-z 面における Bx と電流密度の等高線（白線） Kinetic Energy

23. 23 Taylor-type Relaxation Almost uniform  in sigmoid.  is limited by 2  /h. z α h 2  /h t=0 t=30 z shear reversal consistent with Taylor’s relaxation theory

24. 24 Dependency on Shear Reversal Linear growth rate is not important Sufficient flux should be reversed. AB CD AB C D Casetearingexplosion A  × B  × C  ○ D  ○ time Kinetic energy

25. 25 Predictions Solar flares should be triggered from a point on magnetic shear inversion. Down-flow should exist even prior to the onset of flares. The first flaring point should be located above sigmoid. 1 2 1 2

26. 26 Ba<0 left-handed Ba>0 right-handed axial field Trace 1600A Flaring from shear reversal (Maeshiro et al. 2004)

27. 27 Correlation with Flares Yamamoto et al. (2004) 相関値、 0.73 、 棄却率、 2.9e-4 。 相関値、 0.89 、 棄却率、 1.8e-7 。 Max X-ray Flux  (Magnetic flux)

28. 28 Summary A new model of the flare triggering mechanism was proposed. Resistive tearing instability on the magnetic shear inversion surface. Sigmoid as the Taylor-type relaxed (quasi- linear force free) state. Internal collapse of magnetic arcade. T-shape reconnection “ reconnection driven reconnection ” Measurement of magnetic helicity injection is now possible.