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Giant Planet-Disc Interaction with MHD Turbulence: Numerical Simulation Study

This study explores the interaction between a giant planet and a disc with MHD turbulence, focusing on the causes and effects of migration. The numerical simulation results demonstrate how the planet's presence influences the disc dynamics, including angular momentum transport and mass accretion rates. Different parameters, such as stress distribution and magnetic field effects, are investigated to understand the complex phenomena involved in the planet-disc system.

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Giant Planet-Disc Interaction with MHD Turbulence: Numerical Simulation Study

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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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