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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

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

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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

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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 Magnetic neutral line

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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 (3D) Amari et al (3D)

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

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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 LCT+ induction eq. Demouline & Berger 2003 LCT Welsh et al ILCT Longcope 2004 minimum velocity

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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)

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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)

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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/ (120hr)4.0x

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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 Advances in Space Research) reconnection current sheet

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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

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

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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

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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

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

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17 Current Sheet Evolution Spontaneous to Driven time resistivity enhanced

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

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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

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

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21 time Kinetic Energy “ Sigmoid ”

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

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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

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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

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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

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

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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)

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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.

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