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A New Model of Solar A New Model of Solar Flare Trigger Flare Trigger MechanismMechanism

Kanya Kusano(Hiroshima University)

Collaboration withT.Maeshiro (Hiroshima Univ.)T.Yokoyama (Univ. of Tokyo)

T.Sakurai (NOAJ)

Plasma Theory Group, Hiroshima University

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Objective To understand the trigger

mechanism of solar flares.

Where, When, How, & Whyare solar flares triggered

explosively?

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Trigger Problem of Solar Flares

reconnection

flare loop

We have to explain 1. Sudden onset2. Current sheet

formation3. Precursor phenomena

(e.g. sigmoid)

Magnetic Helicity & Energy

Solar Flare

causality?

Sigmoid

slow

fast

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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

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Sheared Field Driven Model

Mikic et al 1988, 1994Kusano et al. 1995, 2002(3D)

t=65

t=74 t=82

Shearing motion Converging motion

Inhester, Birn, Hesse 1992Birn, Forbes, et al. 2003 (3D)Amari et al. 2003 (3D)

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Strategies Observation

Magnetic Helicity Injection

Numerical Simulation3D MHD large-scale simulation

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Magnetic Helicity Measurement

SOHO/MDI Vector magnetograph(NAOJ, Tokyo)solution

Correlationtracking

ntnntnt

)( BVBVB

n

t

MDI image

BVESAE ,dH p

Magnetic helicity flux

Cha 2001 LCTKusano et al. 2002 LCT+ induction eq.Demouline & Berger 2003 LCTWelsh et al. 2003 ILCTLongcope 2004 minimum velocity

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Measurement of Helicity FluxX-ray flux

Helicity flux emerging

shear

Helicity emerging

total

X-ray energy

Energy flux

shear

emerging

Energytotal

Potentialfield

(Kusano et al. ApJ, 2002)

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Helicity Injection & Soft X-ray Soft X-ray flux statistically well correlate

s with magnetic helicity flux.

Magnetic Helicity Flux

Soft-

X Ra

y F

lux

(Maeshiro et al. 2004)So

ft-X

Ray

Flu

x

(Magnetic Helicity Flux) x (Shear Inversion Length)

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Helicity Injection & Solar Flare Amplitude of helicity flux does NOT direc

tly correlate with flare onset. Helicity flux changes the sign within an a

ctive region.Flare

Helicity Injection pAE

AR (time) H (Mx2)

H/2

8100 (120hr)

4.0x1042 0.02

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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

shearinversion

(Kusano et al. 2003 Advances in Space Research)

reconnectioncurrent sheet

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Simulation Model (3D MHD)

)(,2 JBVB

VBJVVV

tt

541

50

00

010

00

10,105,10

)(

)(

mR

JJJ

JJJJ

Finite difference: 256 X 256 X 1024 (~10-3) Initial state ： linear force-free (2D arcade) Boundary Condition:

shear motion reversingmagnetic shear (0.05VA)

Anomalous resistivity

x

y

z

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MHD Simulation of Shear Reversal

2D 3D

x

y

z

0/ x

magnetic field lines

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Evolution (Model 1)

time

kinet

ic en

ergy

(tota

l)m

agne

tic e

nerg

y(F

ourie

r mod

e)m

agne

tic e

nerg

y(to

tal)

turbulent eruptive

x

z

t=8.5

t=24.5

t=33.0

z

z current sheet 1Bx

current sheet 2

x

yz

t

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3D MHD Simulation of Shear Reversal

1st reconnection 2nd reconnection

eruption

1st reconnection

2nd reconnection

explosive growth

tearing instability internal collapse

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T-shape 3D reconnection1

2

3CS1

CS1 CS2

CS2

CS1

Reconnection 2

B

Reconnection 1

B

Interaction of reconnections

30/ L

21/ L

12/ L

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Current Sheet Evolution Spontaneous to Driven

time

/// LVVVV inAinout

resistivity enhanced

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Nonlinear Instability of Double Tearing Mode Instability in Tokamak Ishii, Azumi, Kishimoto (2002, PRL)

1600

105 5

r

m

N

RExplosive Growth

Rutherford phasecurrent sheet

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‘Reversed-Shear Model’

feedback

Reversing shear Tearing

Instability Reconnection 1 Flux Annihilation Collapse of

Arcade Reconnection 2 EruptionExplosive Growth → trigger of flare

2004 APJ

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time

Kine

tic E

nerg

y

relaxation phase (model 2)

Strong Reversal

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time

Kine

tic E

nerg

y

“Sigmoid”

22x-z 面における Bx と電流密度の等高線（白線）

Kine

tic E

nerg

y

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Taylor-type Relaxation Almost uniform in sigmoid. is limited by 2/h.

z

α

h

2/ht=0

t=30 z

shear reversal

consistent with Taylor’s relaxation theory

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Dependency on Shear Reversal

Linear growth rate isnot important

Sufficient flux should bereversed.

A B

C D

A BC D

Case

tearing explosion

A ×

B ×

C ○

D ○time

Kine

tic e

nerg

y

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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 21 2

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Ba<0

left-handed

Ba>0

right-handed

axial field||/)]([ PppaB ABBA

Trace 1600A

Flaring from shear reversal

(Maeshiro et al. 2004)

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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 Max X-ray Flux

(Magnetic flux) 200 |)]([| BBA

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Summary A new model of the flare triggering mech

anism was proposed. Resistive tearing instability on the magnetic

shear inversion surface. Sigmoid as the Taylor-type relaxed (quasi-lin

ear force free) state. Internal collapse of magnetic arcade. T-shape reconnection

“reconnection driven reconnection” Measurement of magnetic helicity injecti

on is now possible.