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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

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Introduction n 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

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Causes of Migration n Standard picture involves torques between a laminar viscous disc and a Jovian protoplanet exciting spiral waves, producing an inward migration n Massive protoplanet can open an annular gap in disc n Form of gap & gas accretion rate: function of visc., planet mass, height

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Causes of Migration n Protoplanet orbits in gap, interacts with outer disc n Leads to inward migration ~10 5 yr n Balbus & Hawley (1991): angular momentum transport, inward migration also originates from magnetorotational instability (MRI)

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Paper I: Turbulent Discs n Focused on turbulent disc models prior to introducing a perturbing protoplanet n Cylindrical disc models; no vertical stratification n Assume disc is adequately ionized for ideal MHD conditions; consider models with no net magnetic flux n Now on to planet-disc interaction...

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Planet-Disc Model n From paper I: H/r = 0.1 Stress Parameter = 5x10 -3 Stress Parameter = 5x10 -3 n Stellar Mass = 1 M solar n Planet Mass must be >3 Jupiter masses: consider 5 M Jupiter n Thinner discs and less massive planets are more desirable: H/r = 0.05 /1 M Jupiter n Both are computationally impossible now

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Initial Model Setup

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

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Protoplanet Model n Nelson et al. (2000): matter accretes from atmosphere onto planet n Cannot simulate that here: effect on mag. field difficult n Atmosphere gains matter, not planet

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Another Problem n Directly imbedding planet into disc produces no gap n N&P carve out small gap @ r = 2.2 n Justifed because magnetic energy and stress remain same

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

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

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

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

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Protoplanet in Disc Gap

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Magnetic Field in Disc Gap

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

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

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Angular Momentum Flux n High Reynolds stress immediately outside gap n High Magnetic stress at large radii n Magnetic stress is non-zero through gap, transferring L without tidal torque

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Angular Momentum Flux n Flux Profile at later time: n Same characteristics: stable pattern of behavior has been established quickly n Inward migration results ~10 4 orbits

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

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

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

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Conclusions n Demonstrated many of phenomena seen in laminar viscous disc n Planet launched spiral waves that transport angular momentum Turbulent disc has smaller Turbulent disc has smaller –Mag. fields transport L across the gap n Magnetic breaking around planet –Might slow mass accretion rate

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References n “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 n “The interaction of a giant planet with a disc with MHD turbulence I: The initial turbulent disc models” Papaloizou & Nelson 2003a, MNRAS 339, 923 n Images from: –http://astron.berkeley.edu/~gmarcy/0398marcybox4.html –http://www.sns.ias.edu/~dejan/CCS/work/SciArt/

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