The Kink Instability in Solar Eruptions

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The Kink Instability in Solar Eruptions
Tibor Török (Mullard Space Science Laboratory)
in collaboration with
Bernhard Kliem (Astrophysical Institute
Potsdam) Slava Titov (Ruhr-University
Bochum) Thomas Neukirch (University of St.
Andrews)

• solar eruptions and their modeling

• kink instability of a coronal loop

• comparison to observations

• summary and conclusions

talk given at MSSL solar group seminar
(16.08.2004)
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manifestations of solar eruptions
flare
eruptive prominence
CME
Flare sudden explosion on the Sun
Prominence dense and cool structure in corona
Coronal Mass Ejection ejected plasma-cloud
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large solar eruption
2D sketch
main phase
initiation phase
(Forbes, 2000)

• main phase quiete well understood (standard
  model)

• initiation process remains unclear

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large solar eruption
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solar eruption models

• eruptions mainly magnetically driven

• storage and release models

• arcade-like or flux-rope-like topologies
  considered

Tether Cutting
Magnetic Breakout
flux rope models
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model motivation
often observed

• one dominant loop-shaped flux system

• signatures of twisted flux

• signatures of kink instability (helical shape)

? consider model with single twisted flux tube
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twisted magnetic flux tubes

• stability mainly controlled by twist

• model of a coronal loop for

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kink instability

• perturb kink-unstable flux tube
• ? growing helical distortion (kink)
• ? helical current sheet

• instability occurs if

• straight flux tubes

• curved flux tubes not yet studied

(Gerrard et al., 2001)
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model of a coronal loop
Titov and Démoulin, AA 351, 707 (1999)

• approximate analytical force-free equilibrium

• model of a coronal loop for

• 3D ideal MHD simulations with

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magnetohydrodynamic description

• Magnetic Reynolds Number

ideal MHD (field lines frozen into plasma)

• Plasma Beta

vanishing pressure ??? magnetic field force-free
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numerics

• 3D numerical simulations

• compressible ideal MHD

• pressure and gravity neglected

• equations discretized on non-uniform cartesian
  grid

• two-step Lax-Wendroff scheme for integration

• finite differencing

• explicit scheme

• 2nd order in space and time

• viscosity and artificial smoothing for
  stabilization

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stable equilibrium

• initial perturbations damped away

• existence of equilibrium proven

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unstable equilibrium

• spontaneous development of kink instability

• new feature vertical current sheet

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kink instability
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growth rates

• exponential growth ? instability

• growth rates and threshold similar to
  cylindrical case

• instability saturates ? no eruption

(due to the strong overlying field in the TD
model)
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failed filament eruption
simulation ( )
TRACE (195 Å)
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failed filament eruption
(Ji et al., 2003)
rise characteristics and evolution of helical
shape reproduced
? filament is twisted flux tube
? destabilization due to kink instability
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another example
? ? 9?
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full eruption
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modified model

• eruption prevented by strong overlying field

• replace line current by a pair of dipoles

? flux rope erupts
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modified model
Gallagher et al., ApJ 588, L53 (2003)
simulation

• qualitative agreement with rise characteristics
  of CME

• reconnected field lines form cusp structure

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summary conclusions

• TD equilibrium is kink-unstable for

• first systematic study of the kink instability
• of a line-tied curved flux rope performed

• essential features of solar eruptions reproduced

• kink instability of a twisted flux rope
  identified as
• the initiation mechanism of a substantial
  fraction
• of solar eruptions

• overlying field important for success of
  eruption