Magnetic fields in protoplanetary discs

1
Magnetic fields in protoplanetary discs

• Mark Wardle
• Macquarie University
• Raquel Salmeron1
• University of Sydney

1Present address University of Chicago
2

• Introduction
• Magnetic fields play an important role during
  star formation
• Pmag is 30100 times Pgas in molecular clouds
• energy density of magnetic field, fluid motions
  and self-gravity are similar
• field removes angular momentum from cloud cores
• breakdown of flux freezing solves magnetic flux
  problem
• Role of magnetic field in final stages of
  formation and subsequent evolution of
  protoplanetary discs is unclear
• dynamo?
• MHD turbulence (magnetorotational instability)?
• disc-driven MHD winds?
• disc corona?
• How strong is the magnetic field?
• How strongly is it coupled to the material in the
  disc?
• disc is weakly ionised

3

• How strong is the magnetic field?
• Expect B gt 10 mG given the strength in cloud
  cores
• Compression during formation of disk and star
• Shear in disc
• magnetorotational instability
• dynamo action
• Equipartition field in the minimum solar nebula
• Evidence for 0.1 1 G fields in the solar nebula
  at 1AU

4

• Is the magnetic field coupled to the matter?
• 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 1 g/cm2
• cosmic ray attenuation column 100 g/cm2

Gammie 1996
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• Conductivity

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• Magnetic diffusion

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• Criterion for coupling

8
Sano Stone 2002a
9

• Resistivity calculations
• minimum solar nebula
• assume isothermal in z-direction
• ionisation by cosmic rays and 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
• none, single size grains, MRN size distribution,
  MRNice mantles, extended MRN, etc
• 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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• Ionisation products

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• Reaction scheme

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Abundances 1AU, no grains
e
M
m
C
He
z(s-1)
H
log n / nH
z / h
13
Resistivities 1AU, no grains
shear
Ambipolar
log h (cm2s-1)
Hall
1 G
0.1 G
Ohmic
z / h
14
Resistivities 1AU, no grains
z / h
0
1
Ohmic
2
3
log nH (cm-3)
Hall
4
Ambipolar
5
log B (G)
15
Abundances 1AU, 0.1mm grains
m
C
He
M
e
z(s-1)
0
H
log n / nH
1
-11
-4
2
-12
-3
3
-13
-2
-14
z / h
16
Resistivities 1AU, 0.1mm grains
Ambipolar
Hall
1 G
shear
log h (cm2s-1)
0.1 G
Ohmic
z / h
17
Resistivities 1AU, 0.1mm grains
z / h
0
1
Ohmic
2
3
log nH (cm-3)
Hall
4
Ambipolar
5
log B (G)
18
Resistivities 1AU, 1mm grains
z / h
0
1
Ohmic
2
3
log nH (cm-3)
Hall
4
Ambipolar
5
log B (G)
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• Magnetorotational instability (MRI)
• magnetic field couples different radii in disc
• tension transfers angular momentum outwards
• kh gt 1 required to fit in disc, i.e. vA/cs lt 1
• resulting turbulence transports angular momentum
  outwards

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Salmeron Wardle MNRAS submitted
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Salmeron Wardle
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Salmeron Wardle
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Salmeron Wardle
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Salmeron PhD thesis
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• Summary
• Entire disk cross-section is magnetically active
  in the absence of grains.
• When grains are present, coupling occurs at 2-3
  scale heights.
• dead zone and active layers
• Hall diffusion generally dominates in the active
  regions.
• affects vector evolution of B
• Ohmic diffusion is dominant only at very low
  field strengths
• Ambipolar diffusion important for strong fields
  or large heights
• Ambipolar and Hall resistivities depend on field
  strength
• potential for interesting behaviour (eg. Sano
  Stone 2002b)
• Dynamics may modify ionisation equilibrium
• grain size distribution
• advection

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• Magnetically-driven jets

Blandford Payne 1982
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Wardle 1997 IAU Coll. 163 (astro-ph)
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Wardle 1997 IAU Coll. 163 (astro-ph)
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Sano Stone 2002b