Sunspots: the interface between dynamos Sunspots: the interface between dynamos and the theory of stellar atmospheresand the theory of stellar atmospheres

Axel Brandenburg (Nordita/Stockholm)

70 yr Guenther

2

Solar dynamo: what’s missing?Solar dynamo: what’s missing?• “We must know, what we don’t know”

• alpha effect?

• Turbulent diffusion?

Mitra et al. (2010)

Importance of nonlocality?Importance of nonlocality?

Early hydro nonlocalityEarly hydro nonlocality

When is nonlocality importantWhen is nonlocality important

How to deal with it?How to deal with it?R

hein

hard

tale

t al.

(20

14)

Some new type of inverse cascade/transfer?

Could stratification be a missing link?Could stratification be a missing link?

8

2s0t / cBgbu

Finite cross helicity:Analogy with A.B?

cross helicity production:Stratification + B-field

Brandenburg et al (2014)

Self-assembly of a magnetic spotSelf-assembly of a magnetic spot• Minimalistic model• 2 ingredients:

– Stratification & turbulence

• Extensions– Coupled to dynamo– Compete with rotation– Radiation/ionization

9

Sunspots simulated realisticallySunspots simulated realistically

• Appearance of sunspot when coupled to radiation and confined by imposed inflows

10

Rempel et al. (2009) Swedish Solar 1-m Telescope

Sunspot decay

11

Examples of self-assemblyExamples of self-assembly

• Can be result of self-assembly when ~1000 G field below surface12

Stein &

Nordlund (2012)

Turbulent sunspot origins?Turbulent sunspot origins?

14

A possible mechanismA possible mechanism

22122

312

212

312

21 BBUBUB

const

ijijijjiji BBUU

Breakdown of quasi-linear theory

ReM here based on forcing kHere 15 eddies per box scaleReM=70 means 70x15x2=7000

based on box scale

Brandenburg et al (2011,ApJ 740, L50)

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Negative effective magnetic pressure instabilityNegative effective magnetic pressure instability

• Gas+turbulent+magnetic pressure; in pressure equil.

• B increases turbulence is suppressed turbulent pressure decreases

• Net effect?

Kleeorin, Rogachevskii, Ruzmaikin (1989, 1990)

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SetupSetup• 3-D box, size (2)3, isothermal MHD

• Random, nonhelical forcing at kf/k1=5, 15 or 30

• Stratified in z, ~exp(-z/H), H=1, =535• Periodic in x and y• stress-free, perfect conductor in z

• Weak imposed field B0 in y

• Run for long times: what happens?

• Turnover time to=(urms kf)-1, turb diff td=(t k12)-1

• Is longer by factor 3(kf/k1)2 = 3 152 = 675

• Average By over y and t=80to

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Basic mechanismBasic mechanism

Huz / 0 uu

u

y

y Bt

B g

c

BBq

t

U

s

yz2

0p1

2

2*

22

2*

p

p

q

2t

rms*

2tp

A 1 kH

ukq

H

v

Anelastic: descending structure Anelastic: descending structure compression compression

BB amplifies amplifies BB amplifies amplifies

Growth rateGrowth rate

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Much stronger with vertical fieldsMuch stronger with vertical fields

• Gas+turb. press equil.

• B increases

• Turb. press. Decreases

• Net effect?

Or, instead, cascade/transfer?Or, instead, cascade/transfer?

19

2s0t / cBgbu

Finite cross helicity:Analogy with A.B?

cross helicity production:Stratification + B-field

Rudiger et al (2011)

Sunspot Sunspot formation formation that sucksthat sucks

20

Typical downflow speedsMa=0.2…0.3

Mean-field simulation:Neg pressure parameterized

Brandenbur et al (2014)

Bi-polar regions in simulations with coronaBi-polar regions in simulations with corona

21

Warnecke et al. (2013, A

pJL 777, L

37)

Coronal loops?Coronal loops?

Warnecke et al. (2013, ApJL 777, L37)

First dynamo-generated bi-polar regionsFirst dynamo-generated bi-polar regions

23

Mitra et al. (2014, arX

iv)

Still negative effective Still negative effective magnetic pressure?magnetic pressure?Or something new?Or something new?

24

Mitra et al. (2014, arXiv)

Parker’s early work on the subjectParker’s early work on the subject

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Equatorward migration

Need for hydraulicsNeed for hydraulics

26

Near-surface concentration deeply roted tubes

Sunspots from downdraftsSunspots from downdrafts

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Clustered Clustered sunspotssunspots

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“spontaneous” “instability”

Parker (1981)

Flux Flux emergenceemergence

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Later times70h, 105h, 140h

Rempel & Cheung (2014)

Early times24h, 28h, 32h

Updraft during emergence,

Downdraft during spot formation

Move to the Move to the bottom of CZbottom of CZ

The thin flux tube paradigmThe thin flux tube paradigm

31

Caligari et al. (1995) Charbonneau & Dikpati (1999)

32

New aspects in mean-field conceptNew aspects in mean-field concept

buBUEJ

...t JBbu

...... 2p2

1s,,t BqBBqUUuu ijjiijjiji

Ohm’s lawOhm’s law

Theory and simulations: Theory and simulations: effect and turbulent diffusivity effect and turbulent diffusivity

Turbulent viscosity and other effects in momentum equationTurbulent viscosity and other effects in momentum equation

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Earlier results for low RmEarlier results for low Rm

• Rädler (1974) computed magnetic suppression (for other reasons)

• Rüdiger (1974) works only for Pm < 8• Rüdiger et al. (1986) Maxwell tension formally

negative for Rm > 1, but invalid• Rüdiger et al. (2011, arXiv), no negative effective

magnetic pressure for Rm < 1.• Kleeorin et a. (1989, 1990, 1996),

Kleeorin & Rogachevskii (1994, 2007)

34

Fit formula and Rm dependenceFit formula and Rm dependence

22

2*

22

p0p

/1

p

p

qq

eq/ BBβ

2p2

1eff 1 qP

Suction with/without ionizationSuction with/without ionization

Fixed/variable ionizationFixed/variable ionization

Suction in actionSuction in action

Temperature profils

Nonstandard Nonstandard convection?convection?

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ConclusionsConclusions• No evidence for deeply rooted spots

• Local confinement of spots required

• Anticipated by Parker (1978, 1979) negative effective magnetic pressure

instability? Other effects?

• Further concentration from downflow