The solar dynamo
Axel Brandenburg (Nordita/Stockholm)
Käpylä+11
Kemel+11
Ilonidis+11
Warnecke+11
Brandenburg+11
White light
image of
yesterday
Tips of
icebergs:
Magnetic flux
concentrations
in
magnetogram!
2
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Standard dynamo wave
New loop
Differential rotation
(faster inside)
Cyclonic convection;
Buoyant flux tubes

a-effect
Equatorward
migration
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Alternative proposal:
Conveyor belt model
Dikpati et al. (2006)
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Simulations of the solar dynamo?
• Tremendous stratification
– Not only density, also scale height change
• Near-surface shear layer (NSSL) not resolved
• Contours of W cylindrical, not spoke-like
• (i) Rm dependence (catastrophic quenching)
– Field is bi-helical: to confirm for solar wind
• (ii) Location: bottom of CZ or distributed
– Shaped by NSSL (Brandenburg 2005, ApJ 625, 539)
– Formation of active regions near surface
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Brun, Brown, Browning, Miesch, Toomre
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Parameter space
• Solar-like models currently faster than Sun
• Artifacts? Limited scale separation  too
much turbulent diffusion ~ l
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Ghizaru,
Charbonneau,
Racine, …
• Cycle now
common!
• Activity
from bottom
of CZ
• but at high
latitudes
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Pencil
code
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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 ms/pt/step at 10243 , 2048 procs
http://pencil-code.googlecode.com
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Isotropic turbulence
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Stratified layers
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MRI, dust, interstellar
Self-gravity
Sphere embedded in box
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Convection, radiation
Shearing box
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MHD, passive scl, CR
Fully convective stars
geodynamo
Other applications
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Chemistry, combustion
Spherical coordinates
Kapyla et al (2012)
Dynamo wave from simulations
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Remaining aspects
(i) Bi-helical fields  inverse cascade
(ii) Solar wind also bi-helical field
(iii) Formation of active regions at solar surface
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(i) Dynamo produces bi-helical field
Magnetic helicity spectrum
 H (k )dk 
Pouquet, Frisch,
& Leorat (1976)
AB
a   13   ω  u  j  b / 0 
Helicity fluxes to alleviate
catastrophic quenching
Brandenburg (2005, ApJ)
d
A  B  2 J  B    F
dt
1046 Mx2/cycle
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Magnetic helicity flux
d
A  B  2
dt
εB
 2 J  B    Fm
d
a  b  2
dt
εB
 2 j  b    Ff
• EMF and resistive
terms still dominant
• Fluxes import at
large Rm ~ 1000
• Rm based on kf
• Smaller by 2p
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Magnetic helicity flux
d
A  B  2
dt
εB
 2 J  B    Fm
d
a  b  2
dt
εB
 2 j  b    Ff
Gauge-invariant in steady state!
• EMF and resistive
terms still dominant
• Fluxes import at
large Rm ~ 1000
• Rm based on kf
• Smaller by 2p
Del Sordo, Guerrero, Brandenburg (2012, MNRAS, submitted)
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Coronal mass ejections from helical structures
This is how it looks like…
Gibson et al. (2002)
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(ii) Helicity from solar wind
Matthaeus et al. (1982)
Measure correlation function
M ij (r )  Bi (x) B j (x  r )
In Fourier space, calculate
M ij  Bi ( x) B j ( x)
magnetic energy and helicity spectra
M ij (k )   ij  ki k j E (k )
 i ijk kk H (k )
M ij  Bi ( x) B j ( x)
 Should be done with Ulysses data away from equatorial plane
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Measuring 1-D correlation tensor
Taylor hypothesis:
R  R0  u Rt
~
H (k R )  4 Im BT (k R ) BN* (k R ) / k R
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Bi-helical fields from Ulysses
• Taylor hypothesis
• Broad k bins
• Southern latitude
with opposite sign
• Small/large distances
• Positive H at large k
• Break point with
distance to larger k
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Comparison
• Field in solar wind is clearly bi-helical
• ...but not as naively expected
• Need to compare with direct and meanfield simulations
• Recap of dynamo bi-helical fields
Helicity
LS
SS
Dynamo
+
-
Solar wind
-
+
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Dynamos with exterior  CMEs?
Warnecke, Brandenburg, Mitra (2011, A&A, 534, A11)
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Warnecke, Brandenburg, Mitra (2011, A&A, in press)
Shell dynamos with ~CMEs
Strong fluctuations, but positive in north
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To carry negative flux: need positive gradient
Brandenburg, Candelaresi, Chatterjee
(2009, MNRAS 398, 1414)
dhm
 2a B 2  2t J  B    Fm
dt
dhf
 2a B 2  2t J  B    Ff
dt
Sign reversal makes sense!
(iii) How deep are sunspots rooted?
Hindman et al. (2009, ApJ)
• Solar activity may not be so deeply rooted
• The dynamo may be a distributed one
• Near-surface shear important
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Two alternative sunspot origins
Kosovichev et al. (2000)
Theories for shallow spots:
(i) Collapse by suppression
of turbulent heat flux
(ii) Negative pressure effects
from <uiuj> vs BiBj26
Negative effective magnetic pressure instability
• Gas+turb.
press equil.
• B increases
• Turb. press.
Decreases
• Net effect?
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Thanks to the Astrophysics
group at Nordita
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Conclusions
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Interest in predicting solar activity
Cyclonic convection ( helicity)
Near surface shear  migratory dynamo
Bi-helical fields, inverse cascade
Solar wind also bi-helical field, but reversed
Formation of active regions and sunspots by
negative effective magnetic pressure inst.
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