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

“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 turbulence II:

  • 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 turbulence II:

  • 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 turbulence II:

  • 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 turbulence II:

  • 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 turbulence II:

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 turbulence II:


Protoplanet model
Protoplanet Model turbulence II:

  • 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 turbulence II:

  • 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 turbulence II:

  • 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 turbulence II:

  • Continuity Eq. for disc surface density:

  • Equation of Motion:

  • Indentical to Viscous Disc Theory


Time evolution of model
Time Evolution of Model turbulence II:

  • 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 turbulence II:

  • 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 turbulence II:

  • However, planet effects turbulence locally

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


Protoplanet in disc gap
Protoplanet in Disc Gap turbulence II:



Stress parameter vs time
Stress Parameter vs. Time turbulence II:

  • Magnetic stress is same as without the planet

  • Total stress peaks due to spiral waves launched by protoplanet


Stress vs radius
Stress vs. Radius turbulence II:

  • 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 turbulence II:

  • 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 turbulence II:

  • 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 turbulence II:

  • Spiral waves ‘sharper’ in viscous disc


Turbulent vs viscous disc1
Turbulent vs. Viscous Disc turbulence II:

  • Little circular flow around protoplanet

  • Turbulence could effect accretion rate


Turbulent vs viscous disc2
Turbulent vs. Viscous Disc turbulence II:

  • Turbulent disc appears to have smaller stress parameter a

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


Conclusions
Conclusions turbulence II:

  • 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 turbulence II:

  • “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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