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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.

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

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  1. “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

  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)

  5. 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...

  6. 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

  7. Initial Model Setup

  8. Protoplanet Model • Modeled as Hill sphere @ r = 2.2 • Roche lobe atmosphere around planet before gap construction complete • Not accretion directly onto planet

  9. 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

  10. 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

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

  12. Time Evolution of Model • Simulation ran for 100 planetary orbits • Initial gap deepened • Accretion onto central parts produced something like central cavity

  13. Time Evolution of Model • Magnetic Energy value maintained throughout simulation • Protoplanetary perturbations do not have strong global effect on the dynamo

  14. Time Evolution of Model • However, planet effects turbulence locally • Planet creates an ordered field where material passes through spiral shocks

  15. Protoplanet in Disc Gap

  16. Magnetic Field in Disc Gap

  17. Stress Parameter vs. Time • Magnetic stress is same as without the planet • Total stress peaks due to spiral waves launched by protoplanet

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

  19. 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

  20. Angular Momentum Flux • Flux Profile at later time: • Same characteristics: stable pattern of behavior has been established quickly • Inward migration results ~104 orbits

  21. Turbulent vs. Viscous Disc • Spiral waves ‘sharper’ in viscous disc

  22. Turbulent vs. Viscous Disc • Little circular flow around protoplanet • Turbulence could effect accretion rate

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

  24. 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

  25. 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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