The solar dynamoThe solar dynamo

Axel BrandenburgAxel Brandenburg

2

Importance of solar activityImportance of solar activity

3

Solar 11 year sunspot cycleSolar 11 year sunspot cycle

• Sunspots between +/- 30 degrees around equator• New cycle begins at high latitude• Ends at low latitudes

– equatorward migration

butterfly diagram

4

SunspotsSunspots

5

SunspotsSunspots

6

Large scale coherenceLarge scale coherence

Active regions, bi-polaritysystematic east-west orientationopposite in the south

7

22 year magnetic cycle22 year magnetic cycle• Longitudinally averaged radial field

• Spatio-temporal coherence– 22 yr cycle, equatorward migration

Poleward branch orpoleward drift?

butterfly diagram

8

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

Differential rotation(faster inside) Cyclonic convection;

Buoyant flux tubesEquatorward

migration

New loop

-effect

9

The Sun today and 9 years agoThe Sun today and 9 years ago

Solar magnetograms:Solar magnetograms:Line of sight B-field fromLine of sight B-field fromcircularly polarized lightcircularly polarized light

10

Sunspot predictionsSunspot predictions

11

Grand minima/maxima?Grand minima/maxima?

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Cycic Maunder mininum: Cycic Maunder mininum: 1010Be recordBe record

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Long time scales: different Long time scales: different oscillators instead of chaos?oscillators instead of chaos?

Saar & Brandenburg (1999, ApJ 524, 295)

14

News from the 5 min oscillationsNews from the 5 min oscillationsD

isco

vere

d in

196

0 (L

eigh

ton

et a

l. 19

62)

Was thought to be response of upper atmosphere to convection

15

Solar granulationSolar granulation

Horizontal size L=1 Mm, sound speed 6 km/s

Correlation time 5 min = sound travel time

16

Degree Degree ll, order , order mm

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5 min osc are 5 min osc are globalglobal

Roger Ulrich (1970)

Franz-Ludwig Deubner (1974)

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GONGGONGglobal global

oscillation oscillation network network groupgroup

Since late 1980ties

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Current Current state of state of the artthe art

SOHOSpace craft1993 – nowlost in 1998

20

Only p-modes observedOnly p-modes observed

0..;24

21

g-modes g-modes

• Would probe the center

• Are evanescent in the convection zone

22

RefractionRefractionReflectionReflection

Top: reflectionwhen wavenlength~ density scale height

Deeper down:Sound speed large

RT

cs 2

23

Inversion: input/outputInversion: input/output

Duval law Sound speed

uuFu

G

GuuFu

0

0

d )(' 1

)(

d )(' )(

2

rknR

r

r d 0

0

22

2 )1(

r

ll

ck

sr

2

2

2

)1(

llu

c

r

s

24

Internal angular velocityInternal angular velocity

R

nlnlm rrrm00

0 d d ,

25

Internal angular velocityInternal angular velocityfrom helioseismologyfrom helioseismology

spoke-like at equ.d/dr>0 at bottom

? d/dr<0 at top

26

Cycle Cycle dependencedependence

of of (r,(r,))

27

In the days before In the days before helioseismologyhelioseismology

• Angular velocity (at 4o latitude): – very young spots: 473 nHz

– oldest spots: 462 nHz

– Surface plasma: 452 nHz

• Conclusion back then:– Sun spins faster in deaper convection zone

– Solar dynamo works with d/dr<0: equatorward migr

28

Activity from the dynamoActivity from the dynamo

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Buoyant rise of flux tubesBuoyant rise of flux tubes

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A long path toward the A long path toward the overshoot dynamo scenarioovershoot dynamo scenario• Since 1980: dynamo at bottom of CZ

– Flux tube’s buoyancy neutralized– Slow motions, long time scales

• Since 1984: diff rot spoke-like– d/dr strongest at bottom of CZ

• Since 1991: field must be 100 kG– To get the tilt angle right

Spiegel & Weiss (1980)

Golub, Rosner, Vaiana, & Weiss (1981)

31

The 4 dynamo scenariosThe 4 dynamo scenarios• Distributed dynamo (Roberts & Stix 1972)

– Positive alpha, negative shear• Overshoot dynamo (e.g. Rüdiger & Brandenburg 1995)

– Negative alpha, positive shear• Interface dynamo (Markiel & Thomas 1999)

– Negative alpha in CZ, positive radial shear beneath– Low magnetic diffusivity beneath CZ

• Flux transport dynamo (Dikpati & Charbonneau 1999)

– Positive alpha, positive shear– Migration from meridional circulation

32

Paradigm shiftsParadigm shiftsi) 1980: magnetic buoyancy (Spiegel & Weiss)

overshoot layer dynamos

ii) 1985: helioseismology: d/dr > 0 dynamo dilema, flux transport dynamos

iii) 1992: catastrophic -quenching Rm-1 (Vainshtein & Cattaneo) Parker’s interface dynamo Backcock-Leighton mechanism

April 21, 2023

(i) Is magnetic buoyancy a problem?(i) Is magnetic buoyancy a problem?

Stratified dynamo simulation in 1990Expected strong buoyancy losses,but no: downward pumping Tobias et al. (2001)

April 21, 2023

(ii) Before helioseismology(ii) Before helioseismology• Angular velocity (at 4o latitude):

– very young spots: 473 nHz– oldest spots: 462 nHz– Surface plasma: 452 nHz

• Conclusion back then:– Sun spins faster in deaper convection zone– Solar dynamo works with d/dr<0: equatorward migr

Yoshimura (1975) Thompson et al. (1975)Brandenburg et al. (1992)

35

Near-surface shear layer:Near-surface shear layer:spots rooted at spots rooted at r/Rr/R=0.95?=0.95?

Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) Pulkkinen & Tuominen (1998)

nHz 473/360024360

/7.14

ds

do

o

=AZ=(180/) (1.5x107) (210-8)

=360 x 0.15 = 54 degrees!

36

(iii) Problems with mean-field theory?(iii) Problems with mean-field theory?

• 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?

37

Revisit paradigm shiftsRevisit paradigm shiftsi) 1980: magnetic buoyancy

counteracted by pumping

ii) 1985: helioseismology: d/dr > 0 negative gradient in near-surface shear layer

iii) 1992: catastrophic -quenching overcome by helicity fluxes in the Sun: by coronal mass ejections

38

Arguments against and in favor?Arguments against and in favor?

• Flux storage• Distortions weak• Problems solved with

meridional circulation• Size of active regions

• Neg surface shear: equatorward migr.• Max radial shear in low latitudes• Youngest sunspots: 473 nHz• Correct phase relation• Strong pumping (Thomas et al.)

• 100 kG hard to explain

• Tube integrity

• Single circulation cell

• Too many flux belts*

• Max shear at poles*

• Phase relation*

• 1.3 yr instead of 11 yr at bot

• Rapid buoyant loss*

• Strong distortions* (Hale’s polarity)

• Long term stability of active regions*

• No anisotropy of supergranulation

in favor

against

Tachocline dynamos Distributed/near-surface dynamo

Brandenburg (2005, ApJ 625, 539)

39

Application to the sun:Application to the sun:spots rooted at spots rooted at r/Rr/R=0.95=0.95

Ben

evol

ensk

a ya,

Hoe

kse m

a,K

o sov

iche

v, S

c her

rer

(199

9)

nHz 473/360024360

/7.14

ds

do

o

–Overshoot dynamo cannot catch up

=AZ=(180/) (1.5x107) (210-8)

=360 x 0.15 = 54 degrees!

40

Simulating solar-like differential rotation Simulating solar-like differential rotation

• Still helically forced turbulence

• Shear driven by a friction term

• Normal field boundary condition

41

Simulating solar-like differential rotation Simulating solar-like differential rotation

• Still helically forced turbulence

• Shear driven by a friction term

• Normal field boundary condition

42

Cartesian box MHD equationsCartesian box MHD equations

JBuA

t

visc2 ln

D

DFf

BJu

sc

t

utD

lnD

AB

BJ

Induction

Equation:

Magn.Vectorpotential

Momentum andContinuity eqns

ln2312

visc SuuF

Viscous force

forcing function kk hf 0f (eigenfunction of curl)

43

Tendency away from filamentary fieldTendency away from filamentary field

Cross-sections at different times

Mean field

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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)

45

Magnetic HelicityMagnetic Helicity V

- VH d curl 1 BB

1

2

212 H

J. Chae (2000, ApJ)

+

+

- -

11

d d1

SL

H SBA

2 d2

S

SA 1

AB

46

Helicity fluxes at large and small scalesHelicity fluxes at large and small scales

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)

47

Simulations showing large-scale fieldsSimulations showing large-scale fieldsHelical turbulence (By) Helical shear flow turb.

Convection with shear Magneto-rotational Inst.

1t

21t

kc

k

Käp

yla

et a

l (20

08)

48

Origin of sunspotOrigin of sunspot

Theories for shallow spots:Theories for shallow spots:(i) Collapse by suppression(i) Collapse by suppression

of turbulent heat fluxof turbulent heat flux(ii) Negative pressure effects(ii) Negative pressure effects

from <from <bbiibbjj>-<>-<uuiiuujj> vs > vs BBiiBBjj

49

clockwise tilt(right handed)

left handedinternal twist

Build-up & release of magnetic twistBuild-up & release of magnetic twist

New hirings:New hirings:• 4 PhD students4 PhD students• 4 post-docs (2yr)4 post-docs (2yr)• 1 assistant professor1 assistant professor• 2 Long-term visitors2 Long-term visitors

Upcoming work:Upcoming work:• Global modelsGlobal models• Helicity transportHelicity transport• coronal mass ejectionscoronal mass ejections• Cycle forecastsCycle forecasts

Coronal mass ejectionsCoronal mass ejections