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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“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

  • 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

  • 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 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

  • 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...


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


Protoplanet Model

  • Modeled as Hill sphere @ r = 2.2

  • Roche lobe atmosphere around planet before gap construction complete

  • Not accretion directly onto planet


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

  • 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

  • Continuity Eq. for disc surface density:

  • Equation of Motion:

  • Indentical to Viscous Disc Theory


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 Model

  • Magnetic Energy value maintained throughout simulation

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


Time Evolution of Model

  • However, planet effects turbulence locally

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


Protoplanet in Disc Gap


Magnetic Field in Disc Gap


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

  • Total stress and magnetic component become large around planet

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


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 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

  • Spiral waves ‘sharper’ in viscous disc


Turbulent vs. Viscous Disc

  • Little circular flow around protoplanet

  • Turbulence could effect accretion rate


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

  • 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

  • “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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