CME Erupting Prominence

CME/Flare Ribbons CME/Flare Loops

Different Aspects of Solar Eruptions

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.

flare ribbons

prominence

X-ray loops

cavity

Large Solar Eruptions

. .

0.5

original plage intensity

Ha

chromosphere

101

102

103soft X-rays

0.0

corona(thermal)

Light Curves

UT15 16 17 18 19 20 210

1

2

3 hard X-rays

nonthermal

(hours)

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100

50

0UT (hours)12 16 20 24

1973 July 29

1 2 3123

later onearly on

inertial line-tying at surface 123 1 2 3

loop

ribbon

Apparent Motion of Loops & Ribbons

Inertial Line-Tying

E = –V × B = 0 .

Photospheric boundary condition:

Evolution of the photosphere is slowcompared to time scale of eruptions.

Plasma below the photosphere isboth massive and a good conductor.

Photospheric convection isnegligible

B normal to surface is fixed.

.

ribbon

fast shock

evaporation

Mach 2 outflow

Ha loops (104 K)

isothermal slow shockconductionfront

chromosphere

current sheet

super hot ornonthermal

CME/Flare Loop Structures

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Density Temperature

Flare-Loop Simulations

Yokoyama & Shibata (2001)

volume involved: > (105 km)3~1016 gms

103 km/sshock

loops

ribbons

≈ 1032 ergs

CME/Flare Energetics

< 100 ergs/cm3energy density:

~

kinetic energy of mass motions:

work done against gravity

heating / radiation:≈ 1032 ergs

≈ 1031 ergs

n = 109 cm–3

T = 106 K

B = 100 G

V = 1 km/s

h = 105 km

Required: ≈ 100 ergs/cm3Nature of Energy Source:

kinetic

thermal

gravitational

magnetic

(mpnV2)/2

nkT

B2/8p

mpngh

10–5

0.1

0.5

400

ergs/cm3

ergs/cm3

ergs/cm3

ergs/cm3

Energy DensityObserved ValuesType

Force-free fields: j || B

How is Energy Stored?

b = 10–3

Current sheets:

reconnectionwhen j > jcritical

emerging flux modelsheared magnetic fields

j × B ≈ 0∇p ≈ 0

How Much Energy is Stored?

B = Bphotospheric + Bcoronal

invariantduring CME

source ofCME energy

jcorona

+

–photospheric sources

Ha imageplage

prominence

from Gaizauskas & Mackay (1997)

model with magnetogram

Bfrom corona ≈ Bfrom photosphere

free magnetic energy ≈ 50% of total magnetic energy

currents currents

L = 6 × 104 km

70 Gauss

50 Gauss

WB = 1032 ergs

Magnetic Energy Conversion:

ideal MHD reconnection

inefficient (< 10%) efficient (100%)

currents

.

(a) (b) (c)

impossibletransition

(a)(b)

(c)

time

ideal

resistive

forbidden

Aly - Sturrock Paradox

Flux Injection Models

generator

(e.g. Chen 1989)

photosphere

~

before onset

after onset

area of circuitincreases

surface flows

During injection energy flows through photosphere.

corona

convection zone

Poynting flux: S = c E × B / (4p)(ergs/cm/sec)

E = –(V × B) / c

> 10 km/sec for > 10 minutes

Injection models predict large surface flows which are never observed.

Kosovichev et al. 1998

. .

time

7

6

5

4

3

2

1

00 2 4 6

Flux-Rope Height h

Source Separation 2l

current sheetforms

critical point

8

jump

4–4 0

4–4 0

4–4 0

x

y

8

0

y

8

0

y

8

0

l = 0.96

l = 0.96

l = 2.50time

A Storage Model

. .

loss of equilibrium

0

1

2

3

4

0 1 2 3 4 5

p

p

h

q

h + r

h – r

h

x-line appearshrs

Trajectories

.

loss of equilibrium

0

1

2

3

4

0 1 2 3 4 5 hrs

x-line appears

Power Output

Titov & Démoulin 1999

Three-Dimensional Storage Models

Sturrock et al 2001Amari et al. 2000

(Low & Zhang 2002)

flux rope with normal polaritybreakout model

(Antiochos et al. 1999)

Other Storage Models

Hybrid Storage Models:

"tether cutting" model

Ideal + Non-Ideal Processes

equilibrium manifold

NEF: New Emerging Flux

Basic Principles I

Driving Force:

R

ring withcurrent I

R

ro

inner edge is pinchedby curvature of rope

repulsive force:

F ∝ ln (R / ro)I 2R

ln (R / ro)IoI ≈

Basic Principles II

Flux Conservation:

( Io is initial I )I

I 1/[R ln(R/r0)]

.

How to Achieve Equilibrium

dipole

flux rope 0

1

–1

distancefrom Sun1 2 3 4

flux rope hoop force

dipole attraction(strapping field)

However, such an equilibrium is unstable!

.

line-tiedsurface field

0

1

–1

distancefrom Sun1 2 3 4

hoop force

dipole attraction

effect of line-tying

stableequilibrium

How to Achieve a Stable Equilibrium

flux rope

Line-tying creates a second, stable equilibrium

Key factor: Line-tying

3D Loss-of-Equilibrium Model

3. line-current

1. flux rope

2. magnetic   charges

Titov & Démoulin (1999)

3 field sources

Simulation of “Torus*” Instability

*nonhelical kink(see Bateman 1973)

1. no subsurface line current2. subcritical twist for helical kink3. torus center near surface

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Key Particle Acceleration Parameters

electricfield

distancetraveled

number accelerated

energy gain / particle: q E d

life time

Electric field for reconnectiondriven processes should beof order VA B.

acceleration timeOther parameters are key to determiningefficiency of a particular mechanism.

Ed

turbulence with DB/B ≈ 1

fast-mode shocks with Mfm ≈ 2

flare ribbons

temporary coronal hole

Reconnection Electric Fields

polarityinversion

line

newly reclosed flux:

FB = Bz dxdy

global reconnection rate:

E ⋅dl = dFbdt

s

s

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15 July 2002

19:54 20:06 20:18 20:30 UT

10

6

4

8

2

0

for estimated separator length of 2 × 105 km:

E ≈ 20 Volts / cm

Observed Reconnection Rate for X3 Flare

initial configuration

cross sections during eruption

Roussev et al. (2003)

3D Flux Rope Simulation end-on view

side view

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Summary

1. Sudden onset of solar eruption is suggestive of an ideal-MHD process.

2. Magnetic reconnection accounts for about 90% of total energy release.

3. No consensus exists as to what triggers an the magnetic field to erupt.