Paradigm shifts in solar dynamo modelling
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Transcript of Paradigm shifts in solar dynamo modelling
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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))
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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)
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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
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(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)
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(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!
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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)
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(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?
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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)
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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
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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
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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
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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
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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
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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?
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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
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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)
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Low PrLow PrMM dynamos dynamos
with helicity do workwith helicity do work• Energy dissipation via Joule• Viscous dissipation weak• Can increase Re substantially!
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and and cyccyc in quenched state in quenched state
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2ft
2SSC
2f2
1t
/1
2/
/
eqm
eqmK
BR
kt
BkR
B
FBJ
SSC
2f2
1mt F kk
2m´ /BBJk
21tcyc k
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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
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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
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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
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Time-dependent caseTime-dependent case
21t1 )()()( kskss
0d )(ˆ)( ttes st
'd )'()'(ˆ tttt BB
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From linear to nonlinearFrom linear to nonlinear
pqpq ab
AB
uUU
Mean and fluctuating U enter separately
Use vector potential
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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!
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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)
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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
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Dependence on Sh and RmDependence on Sh and Rm
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Direct simulationsDirect simulations
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Fluctuations of Fluctuations of ijij and and ijij
Incoherent effect(Vishniac & Brandenburg 1997,Sokoloff 1997, Silantev 2000,Proctor 2007)
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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
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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