. .

0.5

original plage intensity

Hα

chromosphere

101

102

103 -soft X rays

0.0

corona( )thermal

& Eruptive Solar Flares Reconnection

UT15 16 17 18 19 20 210

1

2

3 -hard X rays

nonthermal

( )hours

.

Hα ribbons

prominence

- X ray loops

cavity

Eruptive Solar Flares

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.

ribbon

fast shock

evaporation

Mach 2 outflow

Hα (10loops 4 )K

isothermal slow shock

conductionfront

chromosphere

current sheet

super hot ornonthermal

/ CME Flare Loop Structures

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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 surface123 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 slow .compared to time scale of eruptions

Plasma below the photosphere is .both massive and a good conductor

No photospheric convection

B normal .to surface is fixed

volume involved: > (105 )km3~1016 gms

103 /km sshock

loops

ribbons

≈ 1032 ergs

/ CME Flare Energetics

< 100 /ergs cm3 :energy 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 cm3 :Nature of Energy Source

kinetic

thermal

gravitational

magnetic

(mpnV2)/2

nkT

B2/8π

mpngh

10–5

0.1

0.5

400

/ergs cm3

/ergs cm3

/ergs cm3

/ergs cm3

Energy Density Observed ValuesType

Force-free fields: j || B

How is Energy Stored?

β = 10–3

:Current sheets

reconnection whenj > jcritical

emerging flux model sheared magnetic fields

j × B ≈ 0∇p ≈ 0

How Much Energy is Stored?

B = Bphotospheric + Bcoronal

invariantduring CME

source ofCME energy

jcorona

+

–

photospheric sources

Hα imageplage

prominence

& (1997)from Gaizauskas Mackay

model with magnetogram

B from corona ≈ B from photosphere

free magnetic energy≈ 50% of total magnetic energy

currents currents

flare ribbons

temporary coronal hole

Reconnection Rates Inferred from Observations

polarityinversion

line

newly reclosed flux:

ΦB = Bz dxdy

σ

:global reconnection rate E ⋅dl = dΦbdt

σ

y

x

l along separator

.

Observed Reconnection Rate for X3 Flare

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

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

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 2

R

ln (R / ro)IoI ≈

Basic Principles II

:Flux Conservation

( Io is initial I )I

.

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

.

(a) (b) (c)

impossible transition

(a)

(b)

(c)

time

ideal

resistive

Aly - Sturrock Conjecture

. .

time

7

6

5

4

3

2

1

00 2 4 6

Flux-Rope Height h

Source Separation 2λ

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

λ = 0.96

λ = 0.96

λ = 2.50time

Catastrophe 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 appears

hrs

Trajectories

.

0

1

2

3

4

0 1 2 3 4 5 hrs

total magnetic power output

current sheet poynting flux

loss of equilibrium x-line appears

Power Output

for MA = 0.1

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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.