Dynamo theory and magnetorotational instability

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Dynamo theory and magneto-rotational instability
diagnostic interest (CMB)
primordial (decay)
seed field
AGN outflows MRI driven
galactic LS dynamo
helicity losses

• Axel Brandenburg (Nordita)

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The primordial alternativeDecay of field ?
growth of scale

• Starting point EW phase transition
  t10-10 s, B1024 G
• Horizon scale very short 3 cm
• With cosmological expansion 1 AU
• Can field grow to larger scales?

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Inverse cascade of magnetic helicity
argument due to Frisch et al. (1975)
and
Initial components fully helical
and
? k is forced to the left
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3-D simulations
helical vs nonhelical
Initial slope Ek4
Christensson et al. (2001, PRE 64, 056405)
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Helical decay lawBiskamp Müller (1999)
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Revised helical decay law
M. Christensson, M. Hindmarsh, A. Brandenburg
2005, AN 326, 393
H not exactly constant
Assume power law
H follows power law iff r1/2 then
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All length scales scale similarly
integral scale
hel. scale
H/M
M/C
s is correction for finite Rm
R
Q
1/Rm
s
should be s
should be ½2s
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diagnostic interest (CMB)
primordial (decay)
? weak by comparison
seed field
AGN outflows MRI driven
galactic LS dynamo
helicity losses

• Accretion discs
• Corona heated by MRI
• Outflow (also magn tower)

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Alfven and slow magnetosonic wavescoupled to
rotation and shear
Vertical field B0
Alfven frequency
Dispersion relation
effect of rotation, W
effect of shear q
slow magnetosonic
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March 23, 1965 Gemini 3
Gus Grissom John Young docking with Agena
space craft
Analogies
Tidal disruption of a star
Space craft experiment
MRI (Balbus Hawley 1991)
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Nonlinear shearing sheet simulations
Dynamo makes its own turbulence
divergent spectrum
5123 resolution
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Vertical stratification
Brandenburg et al. (1996)
z-dependence of
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Heating near disc boundary
weak z-dependence of energy density
where
Turner (2004)
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Alternative Magnetisation from quasars?
Poynting flux
10,000 galaxies for 1 Gyr, 1044 erg/s each
Similar figure also for outflows from
protostellar disc
B. von Rekowski, A. Brandenburg, W. Dobler, A.
Shukurov, 2003 AA 398, 825-844
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diagnostic interest (CMB)
primordial (decay)
? weak by comparison
seed field
AGN outflows MRI driven
galactic LS dynamo
helicity losses

• Dynamo saturation
• Rm dependent??
• Helicity losses essential

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Close box, no shear resistively limited
saturation
Brandenburg Subramanian Phys. Rep. (2005, 417,
1-209)
Significant field already after kinematic growth
phase
followed by slow resistive adjustment
Blackman Brandenburg (2002, ApJ 579, 397)
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Connection with a effect writhe with internal
twist as by-product
clockwise tilt (right handed)
W
? left handed internal twist
Yousef Brandenburg AA 407, 7 (2003)
both for thermal/magnetic buoyancy
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Helicity fluxes in the presence of shear
Mean field azimuthal average
geometry here relevant to the sun
Mean field with no helicity, e.g.
Vishniac Cho (2001, ApJ 550, 752) Subramanian
Brandenburg (2004, PRL 93, 20500)
Rogachevskii Kleeorin (2003)
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Conclusions

• Primordial B2t-1/2 (if fully helical), not
  B2t-2/3
• Outflows via MRI-heated corona
• Dynamo j.b saturation
• even for WxJ effect
• (only shear, no stratification)
• Helical outflows necessary
• Possible for shear flow

1046 Mx2/cycle (for the sun)