Brian gleim march 23rd 2006 ast 591 instructor rolf jansen
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“The interaction of a giant planet with a disc with MHD turbulence II: The interaction of the planet with the disc” Papaloizou & Nelson 2003, MNRAS 339 (4), 993. Brian Gleim March 23rd, 2006 AST 591 Instructor: Rolf Jansen. Introduction.

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

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Brian gleim march 23rd 2006 ast 591 instructor rolf jansen

“The interaction of a giant planet with a disc with MHD turbulence II:The interaction of the planet with the disc”Papaloizou & Nelson 2003, MNRAS 339 (4), 993

Brian Gleim

March 23rd, 2006

AST 591

Instructor: Rolf Jansen


Introduction

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


Causes of migration

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


Causes of migration1

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)


Paper i turbulent discs

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...


Planet disc model

From paper I: H/r = 0.1

Stress Parameter a = 5x10-3

Stellar Mass = 1 Msolar

Planet Mass must be >3 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

Planet-Disc Model


Initial model setup

Initial Model Setup


Protoplanet model

Protoplanet Model

  • Modeled as Hill sphere @ r = 2.2

  • Roche lobe atmosphere around planet before gap construction complete

  • Not accretion directly onto planet


Protoplanet model1

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


Another problem

Another Problem

  • Directly imbedding planet into disc produces no gap

  • N&P carve out small gap @ r = 2.2

  • Justifed because magnetic energy and stress remain same


Numerical results

Numerical Results

  • Continuity Eq. for disc surface density:

  • Equation of Motion:

  • Indentical to Viscous Disc Theory


Time evolution of model

Time Evolution of Model

  • Simulation ran for 100 planetary orbits

  • Initial gap deepened

  • Accretion onto central parts produced something like central cavity


Time evolution of model1

Time Evolution of Model

  • Magnetic Energy value maintained throughout simulation

  • Protoplanetary perturbations do not have strong global effect on the dynamo


Time evolution of model2

Time Evolution of Model

  • However, planet effects turbulence locally

  • Planet creates an ordered field where material passes through spiral shocks


Protoplanet in disc gap

Protoplanet in Disc Gap


Magnetic field in disc gap

Magnetic Field in Disc Gap


Stress parameter vs time

Stress Parameter vs. Time

  • Magnetic stress is same as without the planet

  • Total stress peaks due to spiral waves launched by protoplanet


Stress vs radius

Stress vs. Radius

  • Total stress and magnetic component become large around planet

  • Further out, value is similar to disc w/o planet


Angular momentum flux

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


Angular momentum flux1

Angular Momentum Flux

  • Flux Profile at later time:

  • Same characteristics: stable pattern of behavior has been established quickly

  • Inward migration results ~104 orbits


Turbulent vs viscous disc

Turbulent vs. Viscous Disc

  • Spiral waves ‘sharper’ in viscous disc


Turbulent vs viscous disc1

Turbulent vs. Viscous Disc

  • Little circular flow around protoplanet

  • Turbulence could effect accretion rate


Turbulent vs viscous disc2

Turbulent vs. Viscous Disc

  • Turbulent disc appears to have smaller stress parameter a

  • Could be artifact of simulation OR magnetic communication across the gap


Conclusions

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


References

References

  • “The interaction of a giant planet with a disc with MHD turbulence II:The interaction of the planet with the disc”Papaloizou & Nelson 2003, MNRAS 339 (4), 993-1005

  • “The interaction of a giant planet with a disc with MHD turbulence I:The initial turbulent disc models”Papaloizou & Nelson 2003a, MNRAS 339, 923

  • Images from:

    • http://astron.berkeley.edu/~gmarcy/0398marcybox4.html

    • http://www.sns.ias.edu/~dejan/CCS/work/SciArt/


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