Self-assembly of shallow magnetic spots through strongly stratified turbulence
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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)
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)
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
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
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)
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
24
ConclusionsConclusions
• No evidence for deeply rooted spots
• Local confinement of spots required negative effective magnetic pressure
instability
• Further concentration from downflow
Type of Type of dynamo?dynamo?
26
• Use phase relation
• Closer to 2 dynamo
• Wrong for dyn.
Mitra et al. (2010)
Oscillatory 2 dynamo
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)
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