The Growth of the MRI in Protoplanetary Disks

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The Growth of the MRI in Protoplanetary Disks

• Mark Wardle
• Macquarie University
• Sydney, Australia

Protoplanetary disks Magnetic diffusion MRI with
diffusion Ionisation equilibrium Live and Dead
zones
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• Minimum-mass solar nebula
• (Weidenschilling 1977 Hayashi 1981)

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Kitamura et al 2002 ApJ
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• Protostellar disks are poorly conducting
• high density implies low conductivity
• recombinations relatively rapid
• drag on charged particles
• deeper layers shielded from ionising radiation
  for r lt 5 AU
• x-ray attenuation column 10 g/cm2
• cosmic ray attenuation column 100 g/cm2
• dead zone near midplane (Gammie 1996)

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• Magnetic diffusion regimes

fully ionized partially ionized
Ideal MHD ions and electrons tied to field ions, electrons and neutrals tied to field
Ambipolar neutrals decoupled
Hall ions decoupled ions and neutrals decoupled
Ohmic ions and electrons decoupled ions, electrons and neutrals decoupled
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• If the only charged species are ions and
  electrons,
• Three distinct diffusion regimes

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Wardle 2007
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Magnetorotational instability
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• Resistivity calculations
• minimum mass solar nebula
• assume isothermal in z-direction
• ionisation by cosmic rays and/or x-rays from
  central star
• simple reaction scheme following Nishi, Nakano
  Umebayashi (1993)
• H,H3,He,C,molecular (M) and metal ions (M),
  e-, and charged grains
• extended to allow high grain charge (T larger
  than in molecular clouds)
• adopt model for grains
• results for no grains or 0.1 mm grains
  presented here
• evaluate resistivity components
• when can the field couple to the shear in the
  disc?
• which form of diffusion is dominant?

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x-ray ionisation rate
cosmic rays
Igea Glassgold 1999
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• Reaction scheme

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Abundances 1AU, no grains
e
M
m
C
He
log?z(s-1)
H
log n / nH
z / h
Wardle 2007
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Resistivities 1AU, no grains
poor coupling (? h cs)
Ambipolar
log h (cm2s-1)
Hall
1 G
0.1 G
Ohmic
z / h
Wardle 2007
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Wardle 2007
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MRI growth rate (?)
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MRI growth rate (?)
no Hall diffusion
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Salmeron Wardle 2005
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Salmeron Wardle 2005
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Abundances 1AU, 0.1mm grains
m
C
He
M
e
log?z(s-1)
0
H
log n / nH
1
-11
-4
2
-12
-3
3
-13
-2
-14
z / h
Wardle 2007
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Wardle 2007
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MRI growth rate (?)
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Wardle 2007
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MRI growth rate (?)
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MRI growth rate (?)
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MRI growth rate (?)
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MRI growth rate (?)
no Hall diffusion
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Salmeron Wardle 2008
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• Notes
• No grains coupling can be maintained even at the
  midplane at 1AU
• Hall diffusion dominates
• ?active 1700 g cm2
• Grains increase magnetic diffusion
• 1 AU 0.1 µm ?active 2 g cm2
• 3 µm ?active 80 g cm2
• 5 AU 1 µm ?active ?total
• No cosmic rays?
• in absence of grains, X-rays ? ?active 150 g
  cm2 at 1AU
• with grains, X-rays dominate ionization of active
  layer in any case
• Increase disk mass?
• ?active unchanged
• Small grains?
• aaaargh

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• Dead zones vs live zones
• critical for disk evolution
• vertical and radial transport
• grain evolution
• planet migration
• external ionizing sources
• cosmic rays (maybe) dominate at midplane
• x-rays dominate at surface
• stellar energetic particles?
• poisoning of magnetic coupling by grains
• dead zone boundary grains just able to soak up
  most electrons
• key grain parameter Integral a n(a) da
• e.g, 103 cf standard 0.1 µm grains keeps
  midplane alive at 1 AU in MMSN