1
The interaction of a giant planet with a disc
with MHD turbulence IIThe interaction of the
planet with the discPapaloizou Nelson 2003,
MNRAS 339 (4), 993

• Brian Gleim
• March 23rd, 2006
• AST 591
• Instructor Rolf Jansen

2
Introduction

• Discovery of giant planets close to their star
  has led to the idea that they migrated inwards
  due to gravitational interaction with the gaseous
  disc

3
Causes of Migration

• Standard picture involves torques between a
  laminar viscous disc and a Jovian protoplanet
  exciting spiral waves, producing an inward
  migration
• Massive protoplanet can open an annular gap in
  disc
• Form of gap gas accretion rate function of
  visc., planet mass, height

4
Causes of Migration

• Protoplanet orbits in gap, interacts with outer
  disc
• Leads to inward migration 105 yr
• Balbus Hawley (1991) angular momentum
  transport, inward migration also originates from
  magnetorotational instability (MRI)

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Paper I Turbulent Discs

• Focused on turbulent disc models prior to
  introducing a perturbing protoplanet
• Cylindrical disc models no vertical
  stratification
• Assume disc is adequately ionized for ideal MHD
  conditions consider models with no net magnetic
  flux
• Now on to planet-disc interaction...

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Planet-Disc Model

• From paper I H/r 0.1
• Stress Parameter a 5x10-3
• Stellar Mass 1 Msolar
• Planet Mass must be gt3 Jupiter masses consider 5
  MJupiter

• Thinner discs and less massive planets are more
  desirable H/r 0.05 /1 MJupiter
• Both are computationally impossible now

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Initial Model Setup
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Protoplanet Model

• Modeled as Hill sphere _at_ r 2.2
• Roche lobe atmosphere around planet before gap
  construction complete
• Not accretion directly onto planet

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Protoplanet Model

• Nelson et al. (2000) matter accretes from
  atmosphere onto planet
• Cannot simulate that here effect on mag. field
  difficult
• Atmosphere gains matter, not planet

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Another Problem

• Directly imbedding planet into disc produces no
  gap
• NP carve out small gap _at_ r 2.2
• Justifed because magnetic energy and stress
  remain same

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Numerical Results

• Continuity Eq. for disc surface density
• Equation of Motion
• Indentical to Viscous Disc Theory

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Time Evolution of Model

• Simulation ran for 100 planetary orbits
• Initial gap deepened
• Accretion onto central parts produced something
  like central cavity

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Time Evolution of Model

• Magnetic Energy value maintained throughout
  simulation
• Protoplanetary perturbations do not have strong
  global effect on the dynamo

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Time Evolution of Model

• However, planet effects turbulence locally
• Planet creates an ordered field where material
  passes through spiral shocks

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Protoplanet in Disc Gap
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Magnetic Field in Disc Gap
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Stress Parameter vs. Time

• Magnetic stress is same as without the planet
• Total stress peaks due to spiral waves launched
  by protoplanet

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Stress vs. Radius

• Total stress and magnetic component become large
  around planet
• Further out, value is similar to disc w/o planet

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Angular Momentum Flux

• High Reynolds stress immediately outside gap
• High Magnetic stress at large radii
• Magnetic stress is non-zero through gap,
  transferring L without tidal torque

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Angular Momentum Flux

• Flux Profile at later time
• Same characteristics stable pattern of behavior
  has been established quickly
• Inward migration results 104 orbits

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Turbulent vs. Viscous Disc

• Spiral waves sharper in viscous disc

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Turbulent vs. Viscous Disc

• Little circular flow around protoplanet
• Turbulence could effect accretion rate

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Turbulent vs. Viscous Disc

• Turbulent disc appears to have smaller stress
  parameter a
• Could be artifact of simulation OR magnetic
  communication across the gap

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Conclusions

• Demonstrated many of phenomena seen in laminar
  viscous disc
• Planet launched spiral waves that transport
  angular momentum
• Turbulent disc has smaller a
• Mag. fields transport L across the gap
• Magnetic breaking around planet
• Might slow mass accretion rate

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References

• The interaction of a giant planet with a disc
  with MHD turbulence IIThe interaction of the
  planet with the discPapaloizou Nelson 2003,
  MNRAS 339 (4), 993-1005
• The interaction of a giant planet with a disc
  with MHD turbulence IThe initial turbulent disc
  modelsPapaloizou Nelson 2003a, MNRAS 339, 923
• Images from
• http//astron.berkeley.edu/gmarcy/0398marcybox4.h
  tml
• http//www.sns.ias.edu/dejan/CCS/work/SciArt/