Catastrophic aquenching alleviated by helicity flux and shear

1
Catastrophic a-quenching alleviated by helicity
flux and shear

• Axel Brandenburg (Nordita, Copenhagen)
• Christer Sandin (Uppsala)
• Collaborators Eric G Blackman (Rochester),
• Kandu Subramanian (IUCAA, Pune), Petri Käpylä
  (Oulu)

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Theoretical framework aW model

• Cycle frequency

• Migration direction

Migration away from equator
? meridional circulation
Penalty to pay for a
Pouquet, Frisch, Leorat (1976)
(in practice anisotropic)
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Internal twist as feedback on a (Pouquet, Frisch,
Leorat 1976)
How can this be used in practice?
Need a closure for ltj.bgt
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Example of bi-helical structure
Yousef Brandenburg (2003, AA)
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Tilt ?? pol. field regeneration
Blackman Brandenburg (2003, ApJ)
standard dynamo picture
? internal twist as dynamo feedback
N-shaped (north) S-shaped (south)
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Sigmoidal filaments
(from S. Gibson)
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Examples ofhelical structures
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History of a quenching
catastrophic a quenching Rm dependent
(Vainshtein Cattaneo
1972, Gruzinov Diamond 1994-96)
conventional a quenching e.g., aB-3,
independent of Rm (Moffatt 1972, Rüdiger 1973)
periodic box simulations saturation at
super-equipartition, but after resistive
time (Brandenburg 2001)
open domains removal of magnetic waste by
helicity flux (Blackman Field 2000, Kleeorin et
al 2000-2003)
Dynamical quenching
Kleeorin Ruzmaikin (1982)
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Current helicity flux

• Advantage over magnetic helicity
• ltj.bgt is what enters a effect
• Can define helicity density

Rm also in the numerator
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Full time evolution
Significant field already after kinematic growth
phase
followed by slow resistive adjustment
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Helical MHD turbulence

• Helically forced turbulence (cyclonic events)
• Small large scale field grows exponentially
• Past saturation slow evolution
• ? Explained by magnetic helicity equation

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Large scale vs small scale losses
Diffusive large scale losses ? lower saturation
level (Brandenburg Dobler 2001)
Periodic box
with LL losses
Small scale losses (artificial) ? higher
saturation level ? still slow time scale
Numerical experiment remove field for kgt4 every
1-3 turnover times (Brandenburg et al. 2002)
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Significance of shear

• a ? transport of helicity in k-space
• Shear ? transport of helicity in x-space
• Mediating helicity escape (? plasmoids)
• Mediating turbulent helicity flux

Expression for current helicity flux
(first order smoothing, tau approximation)
Schnack et al.
Vishniac Cho (2001, ApJ)
Expected to be finite on when there is shear
Arlt Brandenburg (2001, AA)
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Simulating solar-like differential rotation

• Still helically forced turbulence
• Shear driven by a friction term
• Normal field boundary condition

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Impose toroidal field ? measure a
previously
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Helicity fluxes at large and small scales
Negative current helicity net production in
northern hemisphere
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Helical turbulence with shearand diffusive model
corona
By field at periphery of box
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Conclusions

• Connection between a-effect and helicity flux
• a-effect produces LS (300Mm) magnetic helicity
• ( north, - south) ? SS magnetic helicity
  as waste
• Surface losses observed component from SS (lt
  30Mm)
• (- north, south), about 1046 Mx2/cycle
• a at least 30 times larger with open boundary
  conditions
• Presence of shear important
• Currently include low plasma beta exterior