Self-assembly of shallow magnetic spots Self-assembly of shallow magnetic spots through strongly stratified turbulencethrough strongly stratified turbulence

Axel Brandenburg (Nordita/Stockholm)

Kemel+12Kemel+12

Brandenburg+13Brandenburg+13Warnecke+11Warnecke+11KKäpylääpylä+12+12

The thin flux tube paradigmThe thin flux tube paradigm

2

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

Helioseismology vs current thinkingHelioseismology vs current thinking

3

Zhao, K

osovichev, et al (2010)

B05B05

4

Sunspots simulated realisticallySunspots simulated realistically

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

5

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

Examples of self-assemblyExamples of self-assembly

• Can be result of self-assembly when ~1000 G field below surface6

Stein &

Nordlund (2012)

Turbulent sunspot origins?Turbulent sunspot origins?

8

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 (2011,ApJ 740, L50)

9

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)

10

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

11

Basic mechanismBasic mechanism

Huz / 0 uu

u

yy B

t

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

12

Magnetic helicity spectraMagnetic helicity spectra

)(

)(ˆˆ)(

kHki

kEkkkM

kijk

jiijij

13

Much stronger with vertical fieldsMuch stronger with vertical fields

• Gas+turb. press equil.

• B increases

• Turb. press. Decreases

• Net effect?

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

14

Sunspot decay

15

Some new type of inverse cascade/transfer?Some new type of inverse cascade/transfer?

16

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

17

Typical downflow speedsMa=0.2…0.3

Mean-field simulation:Neg pressure parameterized

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

18

Warnecke et al. (2013, A

pJL 777, L

37)

Coronal loops?Coronal loops?

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

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

20

Warnecke et al. (2013, 777, L

37)

21

Next level in mean-field conceptNext level in mean-field concept

WUJBbu ...t

.........

...

(1975) Soward & Roberts (1974),Rüdiger (1974),Rädler

2p2

1s

(2010) gBrandenbur & Rheinhardt

,

,,t

BqBBqBB

UUUuu

ijjilkijklkijk

ijjikijkkijkji

effect, turbulent diffusivity, Yoshizawa effect, etceffect, turbulent diffusivity, Yoshizawa effect, etc

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

22

How about tilt angles?How about tilt angles?

Hindman et al. (2009, ApJ)Brandenburg (2005, ApJ)

Tilt here from latitudinal shearTilt here from latitudinal shear

23

Thanks to Astrophysics Thanks to Astrophysics group at Nordita and …group at Nordita and …

24

ConclusionsConclusions

• No evidence for deeply rooted spots

• Local confinement of spots required negative effective magnetic pressure

instability

• Further concentration from downflow

25

Dynamo wave from simulations Kap

yla et al (2012)

Type of Type of dynamo?dynamo?

26

• Use phase relation

• Closer to 2 dynamo

• Wrong for dyn.

Mitra et al. (2010)

Oscillatory 2 dynamo

# of cells# of cells

27

• Multi-cellular

Kapyla et al. (2012)

28

How deep are sunspots rooted?How deep are sunspots rooted?

• Solar activity may not be so deeply rooted• The dynamo may be a distributed one• Near-surface shear important

Hindm

an et al. (2009, ApJ)

29

Larger scale separation: 30 instead of 15

30

Alternative sunspot originsAlternative sunspot origins

Theories for shallow spots:Theories for shallow spots:

(i) Collapse by suppression(i) Collapse by suppressionof turbulent heat fluxof turbulent heat flux

(ii) Negative pressure effects(ii) Negative pressure effectsfrom <from <uuiiuujj> vs > vs BBiiBBjj

Kosovichev et al. (2000)

Kosovichev et al. (2000)

PencilPencilcodecode

• Started in Sept. 2001 with Wolfgang Dobler• High order (6th order in space, 3rd order in time)• Cache & memory efficient• MPI, can run PacxMPI (across countries!)• Maintained/developed by ~80 people (SVN)• Automatic validation (over night or any time)• 0.0013 s/pt/step at 10243 , 2048 procs• http://pencil-code.googlecode.com

• Isotropic turbulence– MHD, passive scl, CR

• Stratified layers– Convection, radiation

• Shearing box– MRI, dust, interstellar– Self-gravity

• Sphere embedded in box– Fully convective stars– geodynamo

• Other applications– Chemistry, combustion– Spherical coordinates