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Paradigm shifts in solar dynamo modelling. Magn. buoyancy, radial diff rot, & quenching dynamo at the bottom of CZ Simulations: strong downward pumping Radial diff rot negative near surface! Quenching alleviated by shear-mediated helicity fluxes - PowerPoint PPT Presentation
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Paradigm shifts in solar Paradigm shifts in solar dynamo modellingdynamo modelling
(i)(i) Magn. buoyancy, radial diff rot, & quenching Magn. buoyancy, radial diff rot, & quenching dynamo at the bottom of CZ dynamo at the bottom of CZ
(ii)(ii) Simulations: strong downward pumpingSimulations: strong downward pumping
(iii)(iii) Radial diff rot negative near surface!Radial diff rot negative near surface!
(iv)(iv) Quenching alleviated by shear-mediated helicity fluxesQuenching alleviated by shear-mediated helicity fluxes
Axel Brandenburg (Axel Brandenburg (Nordita, StockholmNordita, Stockholm))
2
Solar dynamos in the 1970sSolar dynamos in the 1970s
• Distributed dynamo (Roberts & Stix 1972)
– Positive alpha, negative shear– Well-defined profiles from mixing length theory
Yoshimura (1975)
3
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
(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)
5
(ii) Positive or negative radial shear?(ii) Positive or negative radial shear?
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!
Before helioseismologyBefore 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. (2003)Brandenburg et al. (1992)
7
(iii) Quenching in mean-field theory?(iii) Quenching in 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?
8
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
ylä
et a
l (20
08)
9
Upcoming dynamo effort in Upcoming dynamo effort in StockholmStockholm
Soon hiring:Soon hiring:• 4 students4 students• 4 post-docs (2 now)4 post-docs (2 now)• 1 assistant professor1 assistant professor• Long-term visitorsLong-term visitors
10
Built-in feedback in Parker loopBuilt-in feedback in Parker loop
031 / bjuω both for thermal/magnetic
buoyancy
JBB
T dt
d2
T
BBJ
effect produces
helical field
clockwise tilt(right handed)
left handedinternal twist
11
Interpretations and predictionsInterpretations and predictions
• In closed domain: resistively slow saturation• Open domain w/o shear: low saturation
– Due to loss of LS field
– Would need loss of SS field
• Open domain with shear– Helicity is driven out of domain (Vishniac & Cho)
– Mean flow contours perpendicular to surface!
B
12
Nonlinear stage: consistent with …Nonlinear stage: consistent with …
SSCF need
22
2ft
2SSC
2f2
1t
/1
2/
/
eqm
eqmK
BR
kt
BkR
B
FBJ
Brandenburg (2005, A
pJ)
ijjiVC UUC ,,21
ijSS
C S , BBSF
13
Forced large scale dynamo with fluxesForced large scale dynamo with fluxes
geometryhere relevantto the sun
Negative current helicity:net production in northern hemisphere
SJE d2 Sje d2
1046 Mx2/cycle
14
Best if Best if contours contours to surface to surfaceExample: convection with shear
Käpylä et al. (2008, A&A) Tobias et al. (2008, ApJ)
need small-scale helicalexhaust out of the domain,not back in on the other side
MagneticBuoyancy?
15
To prove the point: convection with To prove the point: convection with vertical shear and open b.c.svertical shear and open b.c.s
Käpylä et al.(2008, A&A 491, 353)
Magnetic helicity flux
Effects of b.c.s only in nonlinear regime
16
Lack of LS dynamos in some casesLack of LS dynamos in some cases
• LS dynamo must be excited
• SS dynamo too dominant, swamps LS field
• Dominant SS dynamo: artifact of large PrM=
1
f
rms1t
1
ff
12
31
31
1t
k
k
u
U
k
UC
k
k
kkC
CCD
u
uω
Brun, Miesch, & ToomreBrun, Miesch, & Toomre(2004, ApJ 614, 1073)(2004, ApJ 614, 1073)
17
Low PrLow PrMM dynamos dynamos
with helicity do workwith helicity do work• Energy dissipation via Joule• Viscous dissipation weak• Can increase Re substantially!
18
and and cyccyc in quenched state in quenched state
22
2ft
2SSC
2f2
1t
/1
2/
/
eqm
eqmK
BR
kt
BkR
B
FBJ
SSC
2f2
1mt F kk
2m´ /BBJk
21tcyc k
19
tt((RRmm) dependence for B~B) dependence for B~Beqeq
(i) is small consistency(ii) 1 and 2 tend to cancel(iii) to decrease (iv) 2 is small
021t1 kk
20
Calculate full Calculate full ijij and and ijij tensors tensors
pqpqpqpqpqpq
tbbubuBubU
b 2
Response to arbitrary mean fields
... ,
0
0
sin
,
0
0
cos2111
kzkz
BB
pqkjijk
pqjij
pqj BB ,
kzkkz
kzkkz
cossin
sincos
1131121
1
1131111
1
21
1
111
113
11
cossin
sincos
kzkz
kzkz
k
213223
113123
*22
*21
*12
*11
Example:
pqpq buCalculate
21
Kinematic Kinematic and and tt
independent of Rm (2…200)independent of Rm (2…200)
1frms3
10
rms31
0
ku
u
Sur et al. (2008, MNRAS)
1frms
231
0
31
0
ku
u
uω
22
Time-dependent caseTime-dependent case
21t1 )()()( kskss
0d )(ˆ)( ttes st
'd )'()'(ˆ tttt BB
23
From linear to nonlinearFrom linear to nonlinear
pqpq ab
AB
uUU
Mean and fluctuating U enter separately
Use vector potential
24
Nonlinear Nonlinear ijij and and ijij tensors tensors
jiijij
jiijij
BB
BB
ˆˆ
ˆˆ
21
21
Consistency check: consider steady state to avoid d/dt terms
0
2121121
21t1
kk
kk
Expect:
=0 (within error bars) consistency check!
25
Application to passive vector eqnApplication to passive vector eqn
ijij
ijij
jiijij
BB
BB
BB
~~
ˆˆ
1
21
21
0
cos
sin~
,
0
sin
cos
kz
kz
kz
kz
BB
BBuB ~~~
2
t
Verified by test-field method
000
0sinsincos
0sincoscosˆˆ 2
2
kzkzkz
kzkzkz
BB ji
Tilgner & Brandenburg (2008)
26
Shear turbulenceShear turbulence
JJμJδε t
0
0
μ
*21
*12
t
*12
21tt
*21
21t
1
k
S
k
Growth rate
Use S<0, so need negative *21 for dynamo
27
Dependence on Sh and RmDependence on Sh and Rm
28
Direct simulationsDirect simulations
29
Fluctuations of Fluctuations of ijij and and ijij
Incoherent effect(Vishniac & Brandenburg 1997,Sokoloff 1997, Silantev 2000,Proctor 2007)
30
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
31
The FutureThe Future• Models in global geometry• Realistic boundaries:
– allowing for CMEs– magnetic helicity losses
• Sunspot formation– Local conctrations– Turbulent flux collapse– Negative turbulent mag presure
• Location of dynamo– Near surface shear layer– Tachocline
1046 Mx2/cycle
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