Coronal Mass Ejections - the Coronal Mass Ejections - the exhaust of modern dynamosexhaust of modern dynamos

Examples: systematic swirl (helicity)Examples: systematic swirl (helicity)

Measuring it quantitativelyMeasuring it quantitatively

Connection with the dynamoConnection with the dynamo

Axel Brandenburg (Axel Brandenburg (Nordita, StockholmNordita, Stockholm))

2

Examples ofExamples ofhelical exhaust helical exhaust

3

Sigmoidal structures:Sigmoidal structures:

North/SouthNorth/Southdependence dependence

south

4

Sigmoidal filamentsSigmoidal filaments

(from S. Gibson)

5

6

Magnetic helicityMagnetic helicity V

VH d BA

1

2

212 H

11

d d1

SL

H SBA

2 d2

S

SA

1S

1

AB

7

Flux crossingsFlux crossings V

VH d BA

1

2

212 H

J. Chae (2000, ApJ)

+

+

++ - -

8

It’s a popular logo too…It’s a popular logo too…

9

Magnetic helicity from crossingsMagnetic helicity from crossingsJ. Chae (2000, ApJ)

++ - -

10

Current helicity and Current helicity and magn. hel. Fluxmagn. hel. Flux

Bao & Zhang (1998),neg. in north, plus in south

(also Seehafer 1990)

Berger & Ruzmaikin (2000)

cycle/Mx104 246S

NDeVore (2000)

cycle/Mx10 246

(for BR & CME)

11

Helicity in Magnetic CloudsHelicity in Magnetic Clouds

From fits to a linear force-free field Lynch et al. (2005)

2)()( xBxBM jiij

12

Helicity from time seriesHelicity from time series

)()( xBxBM jiij

)(

)()(

kHki

kEkkkM

kijk

jiijij

)()( xBxBM jiij

)()()( rxxr jiij BBM

Matthaeus et al. (1982)

13

14

Nindos et al. (2003)

15

Nindos &Andrews (2004)

16

Magnetic helicity conservationMagnetic helicity conservation

2221

d

dJBJuB

t

0d

d 2/12/121 BJBBuBA

t

kkBJ 2/1How J diverges as 0

Ideal limit and ideal case similar!

2/112/1221

d

d uωωfuωt

17

No helicity production by flowsbut segragation in space:

H<0

H>0

Generates toroidalfrom poloidal field

Poloidal field regenerated bytilting (Coriolis force)

18

Twisting an existing tube:Twisting an existing tube:segragation in spectral spacesegragation in spectral space

19

Cancelling magn helicityCancelling magn helicityintroduced in single tubeintroduced in single tube

20

-effect dynamos (large scale)-effect dynamos (large scale)

Differential rotation(prehelioseism: faster inside)

Cyclonic convection;Buoyant flux tubes Equatorward

migration

New loop

-effect?need meridional circulation

21

Tilt Tilt pol. field regeneration pol. field regeneration

N-shaped (north)S-shaped (south)

standarddynamo picture

internal twistas dynamo feedback

22

Production of LS helicityProduction of LS helicity

0 baBABA

bjforcing produces uω baand

bBB jJJ aAA

Yousef & BrandenburgA&A 407, 7 (2003)

But no net helicity production

baBA therefore:

alpha effect

23

Problems with Problems with -effect -effect • Catastrophic quenching??

– ~ Rm-1, t ~ Rm

-1

– Field strength vanishingly small!?!

• Something wrong with simulations– so let’s ignore the problem

• Possible reasons:– Suppression of lagrangian chaos?– Suffocation from small scale magnetic helicity?

24

Connection with Connection with effect: effect: writhe with writhe with internalinternal twist as by-product twist as by-product

clockwise tilt(right handed)

left handedinternal twist

031 / bjuω both for thermal/magnetic

buoyancy

JBB

T dt

d2

T

BBJ

effect produces

helical field

25

Simulations: forced turbulence w/shearSimulations: forced turbulence w/shear

Negative current helicity:net production in northern hemisphere

SJE d2 Sje d21046 Mx2/cycle

Brandenburg & Sandin (2004, A&A 427, 13)

Helicity fluxes from shear: Vishniac & Cho (2001, ApJ 550, 752)Subramanian & Brandenburg (2004, PRL 93, 20500)

26

Saturation: 50% energy in large scalesSaturation: 50% energy in large scales

geometryhere relevantto the sun

no helicity, e.g.

azimuthallyaveraged

neg helicity(northern hem.)

...21

JWBB

a

t

Rogachevskii & Kleeorin (2003, 2004)

27

ConclusionConclusion • 11 yr cycle• Dyamo (SS vs LS)• Problems

– -quenching– slow saturation

• Solution– Modern -effect theory– j.b contribution– Magnetic helicity fluxes

• Location of dynamo– Distrubtion, shaped by– near-surface shear

1046 Mx2/cycle