A An Overview of O i f Solar Eruption Theories Solar Eruption - - PowerPoint PPT Presentation

2009 Laboratory, Space, and Astrophysical Plasma Workshop

A O i f

20 February 2009

An Overview of Solar Eruption Theories Solar Eruption Theories

• G. S. Choe
• G. S. Choe

School of Space Research i i Kyung Hee University Yongin, Korea

Contents

1 Overview of solar eruptive phenomena 1. Overview of solar eruptive phenomena 2. Current sheets – A necessary condition f i i for magnetic reconnection 3. MHS equilibria with different field 3. S equ b a w t d e e t e d topologies 4 B i f i f d i th i 4. Brief review of dynamic theories 5. On the field opening p g

Solar Activity and Magnetic Field

l i di l h l li f i h

• A longitudianl magnetogram shows only line-of-sight component.
• Polarity inversion line – a border between different polarities

Solar Eruptive Phenomena p

• Solar Flares

– EM radiation in all wavelengths – 1-4 hour duration – 1026-1032 erg of EM energy released

• Prominence Eruption

Prominence Eruption

– Sudden rise (and disappearance) of a prominence Often accompanied b a flare and/or a CME – Often accompanied by a flare and/or a CME

• Coronal Mass Ejections (CMEs)

– Density-enhanced mass motion in the corona – 1014-1017 g, 100-2000 km s-1 g – 1028-1033 erg of kinetic energy

Solar Flare on 2000 July 14 (Bastille day event)

Prominence Eruption Prominence Eruption

Coronal Mass Ejection Coronal Mass Ejection

SOHO LASCO C3 observation of the corona for a month

X-ray Emission of a Flare

• Soft X-ray: along the loop; thermal

H d X

• Hard X-ray:
• Loop-top
• Footpoins: more non-thermal

Standard Eruptive Flare Model − CSHKP Models − CSHKP Models

Shibata et al., 1995

Solar Eruption and Magnetic Shear

• Magnetic Shear — Tilt of a magnetic field vector from the

direction of the corresponding potential field

• Essential condition for solar flares, formation and eruption of

, p prominences and coronal mass ejections

Solar Plasmas Are Highly Conductive! Solar Plasmas Are Highly Conductive!

The plasma is frozen in the magnetic field. Definition of the general magnetic reconnection Definition of the general magnetic reconnection by Schindler and Hesse (1988).

Magnetic Reconnection

A M C ti l Pi t − A More Conventional Picture

• A thin current layer with high current density is a

necessary condition for magnetic reconnection.

• A singular current sheet would be a sufficient

condition for magnetic reconnection.

Why Current Sheets? Why Current Sheets?

in vacuum

• in vacuum
• ideal MHD

plasma magnetic reconnection p

Current Sheet Formation Is Natural for Emerging Fluxes

Emerging flux model of solar flares by Heyvaerts et al. (1977)

Flaring regions are more or less bipolar.

Shibata et al., 1995

Is This Transition Possible?

Sorry! y I adopted a figure of the Earth’s magnetotail.

If the static configuration changes its field topology by a continuous change of a physical boundary condition, the transition is possible.

Solar Eruption and Magnetic Shear

The magnetic field component in the direction of the polarity inversion line (hereafter the toroidal component) polarity inversion line (hereafter the toroidal component) is important!

Force-free Field Approximation pp

Magnetohydrostatic (MHS) Equilibrium

= ∇ − ∇ − ×

g

Φ p ρ B J

Force-free field

= ×B J

Justified in the solar corona by Justified in the solar corona by

plasma plasma

1 1 p p << = = β

2 magnetic

2 1 ) 8 /( . 1 H h B p << << = = π β

corona corona

• e

photospher

. 2 H h <<

2.5D MHS Equilibrium – Grad-Shafranov Equation

⎞ ⎛ B d

2

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − = ∇ = p B d d J

z z

2

2 2

ψ ψ

Problem Setting of 2.5D Equilibrium g q

• I. Generating Function Method

impose y Arbitraril and ( impose y Arbitraril p(ψ B ) ) ψ ) ( for solve and and ( r ψ p(ψ Bz ) ) ψ ). ( for solve and r ψ

An Analytic Solution by B. C. Low (1977)

An Analytic Solution by B. C. Low (1977)

• Increasing the toroidal

current density can create a current density can create a magnetic island.

• The toroidal current density
• The toroidal current density,

however, is not a physically controllable quantity controllable quantity.

• Thus, the solution sequence

i h i ll i is not physically continuous.

Problem Setting of 2.5D Equilibrium g q

• II. Imposing the footpoint displacement

Imposing

1 footpoint displacement

• 1. footpoint displacement
• 2. entropy per flux

N merical Sol tions of BVP2 Numerical Solutions of BVP2

Choe & Lee 1996

Magnetofrictional method:

• Start with any configuration with a desired field topology

y g p gy

• Remove kinetic energy after every time step

Dynamic Resistive MHD Simulations Dynamic Resistive MHD Simulations

Mikic et al 1988

Biskamp (1988) criticizes that the reconnection is initiated

Mikic et al. 1988

p ( ) by squeezing of the adjacent arcades.

Dynamic Resistive MHD Simulations Dynamic Resistive MHD Simulations

A magnetic island is found to form in an found to form in an isolated sheared arcade.

Mikic & Linker 1994

Flux Rope Formation by Reconnection of Looped Field Lines Looped Field Lines

Van Ballegooijen & Martens, 1989

A 2.5D magnetic island is a line-tied flux rope in 3D.

Dynamics of a Line Current in the Corona (Van Tend & Kuperus, SP 59, 115, 1978)

Assumption

• The solar surface is a rigid perfect conductor.

(infinite inductance assumption)

• Thus, the coronal current is closed on the photosphere.

Thi b d l d b i t b l th f

• This can be modeled by an image current below the surface.
• No equilibrium position.
• The current will go to infinity.

The ambient potential field and gravity exert a downward force.

Dynamics of a Line Current in the Corona (Van Tend & Kuperus, SP 59, 115, 1978)

log B log

A, B, D stable

B(G) (I/c)

C unstable

Flux Rope Catastrophe Model

(F b P i t I b Li ) (Forbes, Priest, Isenberg, Lin) A fl ith fi it

• A flux rope with a finite cross-

section replaces the line current. current.

• Photospheric magnetic

reconnection resembling flux g cancellation transfers photospheric flux to the flux rope.

• The equilibrium position of

th fl i ht the flux rope is sought as a function of the poloidal flux in the flux rope the flux rope.

Flux Rope Catastrophe Model p p

b b Forbes & Isenberg, ApJ 373, 294, 1991

Flux Rope Catastrophe Model

Forbes & Isenberg, ApJ 373, 294, 1991 Priest & Forbes, AARv 10, 313, 2002

Tether-Cutting Model

Sturrock, SP 121, 387, 1989 Moore et al., ApJ 552, 833, 2001

Current Driven Instability of Flux Ropes Current Driven Instability of Flux Ropes

(Chen, 1989)

Assumptions

• Coronal current is closed beneath

the solar surface.

• Coronal current is governed by

the subsurface condition.

• The solar surface is not a rigid
• The solar surface is not a rigid

perfect conductor, but it can respond to the coronal evolution. p

For a strong enough toroidal current the flux rope is current, the flux rope is unstable to radial expansion if the photospheric inductance is the photospheric inductance is low enough.

Comparison of Two Flux Rope Models Comparison of Two Flux Rope Models

Forbes Chen

• Photospheric inductance

infinite

• Photospheric inductance

finite

• Poloidal flux of the flux
• Flux rope poloidal flux

rope increased by flux cancellation p p injected from below the surface

• Ignorable photospheric
• Measurable photospheric

motion during eruption motions (horizontal and/or vertical) during eruption

Ejection of Self-closed Field Structures Ejection of Self closed Field Structures

(Gibson and Low 1998)

• A self closed field structure
• A self-closed field structure

similar to a torus is embedded in an open field and pinned in an open field and pinned down at one point.

• It expands in a self-similar

manner manner.

Ejection of Self-closed Field Structures Ejection of Self closed Field Structures

• Inertia-dominant

Inertia dominant solar interior is not considered considered.

• Photospheric field

Photospheric field (both vertical and horizontal components) horizontal components) changes a lot during eruption. eruption.

Kink Instability

• A twisted flux rope tends to

increase the pitch by self- p y braiding.

• The instability threshold

depends on the BC (e.g., line-tying), aspect ratio l/a, t etc.

• The instability by itself does

not seem sufficient to not seem sufficient to account for solar eruption.

) (r lBφ ) ( ) ( r rBz

φ

= Φ Rust & LaBonte, ApJ 622, L69, 2005 ⎪ ⎧ 1996) Kumar, & (Rust 2π L69, 2005 ⎪ ⎩ ⎪ ⎨ ⎧ = Φ 1990) al., et (Mikic 5 1981) Priest, & (Hood 2.5 ) , (

C

π π

Simulations of Kink Instability

π 1 . 2 = Φ

A magnetic loop equilibrium model by Ti & D li π 9 . 4 = Φ

π 5 3

C ≈

Φ

Titov & Demoulin (1999) is used as the initial condition Torok et al., AA 413, L27, 2004

π 5 . 3

C ≈

Φ

initial condition.

Simulations of Kink Instability

π 5 = Φ

A magnetic loop equilibrium model by Ti & D li Titov & Demoulin (1999) is used as the initial condition initial condition. Torok & Kliem, ApJ 630, L97, 2005

Does twisting a flux rope always develop a kink instability?

• Slow twisting of a flux tube does not lead to kinking

Torok & Kliem, AA 406, 1043, 2003

• Slow twisting of a flux tube does not lead to kinking.
• The development of a kink instability depends on the boundary

condition.

• A sudden emergence of a flux rope is likely to lead to kinking.

Paramagnetic and Diamagnetic Islands Paramagnetic and Diamagnetic Islands

Diamagnetic Flux Rope – A Melon Seed g p

• The ambient field exerts an

upward force upward force.

• The overlying field is in the
• pposite direction to the field
• pposite direction to the field

generated by current.

• The magnetic reconnection peels

The magnetic reconnection peels

• ff the magnetic island.

Hyder, SP 2, 49, 1967 Low & Zhang, ApJ 564 L53 ApJ 564, L53, 2002

Simulation of Melon Seed Injection S u

• e o

Seed jec o

Magnetic Breakout – Virtual Opening Magnetic Breakout Virtual Opening

(Antiochos 1998, 1999)

Magnetic Breakout? g

• Contrary to the original
• Contrary to the original

idea, arcade reconnection creating a flux rope creating a flux rope precedes the breakout reconnection reconnection.

• The breakout reconnection

i t ff ti is not so effective.

• Do we ever observe

signatures of the breakout reconnection in the lower

MacNeice et al., ApJ 614, 1028, 2004

atmosphere?

The Linear FFF as a Stationary State

∫

• =

dV H : surface flux a is boundary whose volume, closed a in B A helicity Magnetic

∫

≠

V

: boundary at whose e,

• pen volum

an in

n

B helicity Magnetic

∫

−

• +

=

V

dV H ) ( ) (

p p

B B A A

Under the constraints

• 1. Bn on the boundary is fixed.

n

y

• 2. H is fixed.

The minimum energy state is the LFFF The minimum energy state is the LFFF.

• True in a finite domain.
• False in an infinite domain.

⇒ limited applicability to the solar corona

Conclusion Conclusion

• There are no theories with universal

applicability applicability.

• When applying a theory to an

pp y g y

• bserved phenomenon, check the

applicable conditions carefully applicable conditions carefully.