““The interaction of a giant planet with The interaction of a giant planet with a disc with MHD turbulence II:a disc with MHD turbulence II:

The interaction of the planet with the The interaction of the planet with the disc”disc”

Papaloizou & Nelson 2003, MNRAS 339 (4), 993Papaloizou & Nelson 2003, MNRAS 339 (4), 993

Brian GleimBrian GleimMarch 23rd, 2006March 23rd, 2006

AST 591 AST 591 Instructor: Rolf JansenInstructor: Rolf Jansen

IntroductionIntroduction Discovery of giant planets close to Discovery of giant planets close to

their star has led to the idea that their star has led to the idea that they migrated inwards due to they migrated inwards due to gravitational interaction with the gravitational interaction with the gaseous discgaseous disc

Causes of MigrationCauses of Migration Standard picture involves torques Standard picture involves torques

between a laminar viscous disc and a between a laminar viscous disc and a Jovian protoplanet exciting spiral Jovian protoplanet exciting spiral waves, producing an inward migrationwaves, producing an inward migration

Massive protoplanet can open an Massive protoplanet can open an annular gap in discannular gap in disc

Form of gap & gas accretion rate: Form of gap & gas accretion rate: function of visc., planet mass, heightfunction of visc., planet mass, height

Causes of MigrationCauses of Migration Protoplanet orbits in gap, interacts Protoplanet orbits in gap, interacts

with outer discwith outer disc Leads to inward migration ~10Leads to inward migration ~1055 yr yr Balbus & Hawley (1991): angular Balbus & Hawley (1991): angular

momentum transport, inward momentum transport, inward migration also originates from migration also originates from magnetorotational instability (MRI)magnetorotational instability (MRI)

Paper I: Turbulent DiscsPaper I: Turbulent Discs Focused on turbulent disc models prior Focused on turbulent disc models prior

to introducing a perturbing protoplanetto introducing a perturbing protoplanet Cylindrical disc models; no vertical Cylindrical disc models; no vertical

stratificationstratification Assume disc is adequately ionized for Assume disc is adequately ionized for

ideal MHD conditions; consider models ideal MHD conditions; consider models with no net magnetic fluxwith no net magnetic flux

Now on to planet-disc interaction...Now on to planet-disc interaction...

Planet-Disc ModelPlanet-Disc Model From paper I: H/r From paper I: H/r

= 0.1= 0.1 Stress Parameter Stress Parameter

= 5x10 = 5x10-3-3

Stellar Mass = Stellar Mass = 1 M1 Msolarsolar

Planet Mass must Planet Mass must be >3 Jupiter be >3 Jupiter masses: consider 5 masses: consider 5 MMJupiterJupiter

Thinner discs and Thinner discs and less massive less massive planets are more planets are more desirable: H/r = desirable: H/r = 0.05 /1 M0.05 /1 MJupiterJupiter

Both are Both are computationally computationally impossible nowimpossible now

Initial Model SetupInitial Model Setup

Protoplanet ModelProtoplanet Model Modeled as Hill Modeled as Hill

sphere @ r = 2.2sphere @ r = 2.2 Roche lobe Roche lobe

atmosphere around atmosphere around planet before gap planet before gap construction construction completecomplete

Not accretion Not accretion directly onto planetdirectly onto planet

Protoplanet ModelProtoplanet Model Nelson et al. (2000): Nelson et al. (2000):

matter accretes matter accretes from atmosphere from atmosphere onto planetonto planet

Cannot simulate Cannot simulate that here: effect on that here: effect on mag. field difficultmag. field difficult

Atmosphere gains Atmosphere gains matter, not planetmatter, not planet

Another ProblemAnother Problem Directly imbedding planet into disc Directly imbedding planet into disc

produces no gapproduces no gap N&P carve out small gap @ r = 2.2N&P carve out small gap @ r = 2.2 Justifed because magnetic energy Justifed because magnetic energy

and stress remain sameand stress remain same

Numerical ResultsNumerical Results Continuity Eq. for Continuity Eq. for

disc surface density:disc surface density:

Equation of Motion:Equation of Motion:

Indentical to Viscous Indentical to Viscous Disc TheoryDisc Theory

Time Evolution of ModelTime Evolution of Model Simulation ran for Simulation ran for

100 planetary orbits100 planetary orbits Initial gap Initial gap

deepeneddeepened Accretion onto Accretion onto

central parts central parts produced produced something like something like central cavitycentral cavity

Time Evolution of ModelTime Evolution of Model Magnetic Energy Magnetic Energy

value maintained value maintained throughout throughout simulationsimulation

Protoplanetary Protoplanetary perturbations do perturbations do not have strong not have strong globalglobal effect on effect on the dynamo the dynamo

Time Evolution of ModelTime Evolution of Model However, planet However, planet

effects turbulence effects turbulence locallylocally

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

Protoplanet in Disc GapProtoplanet in Disc Gap

Magnetic Field in Disc GapMagnetic Field in Disc Gap

Stress Parameter vs. TimeStress Parameter vs. Time Magnetic stress is Magnetic stress is

same as without same as without the planetthe planet

Total stress peaks Total stress peaks due to spiral due to spiral waves launched waves launched by protoplanetby protoplanet

Stress vs. RadiusStress vs. Radius Total stress and Total stress and

magnetic magnetic component component become large become large around planetaround planet

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

Angular Momentum FluxAngular Momentum Flux High Reynolds High Reynolds

stress immediately stress immediately outside gapoutside gap

High Magnetic High Magnetic stress at large radiistress at large radii

Magnetic stress is Magnetic stress is non-zero through non-zero through gap, transferring L gap, transferring L without tidal torquewithout tidal torque

Angular Momentum FluxAngular Momentum Flux Flux Profile at later Flux Profile at later

time:time: Same Same

characteristics: characteristics: stable pattern of stable pattern of behavior has been behavior has been established quicklyestablished quickly

Inward migration Inward migration results ~10results ~1044 orbits orbits

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

discdisc

Turbulent vs. Viscous DiscTurbulent vs. Viscous Disc Little circular flow around protoplanetLittle circular flow around protoplanet

Turbulence could effect accretion rateTurbulence could effect accretion rate

Turbulent vs. Viscous DiscTurbulent vs. Viscous Disc Turbulent disc Turbulent disc

appears to have appears to have smaller stress smaller stress parameter parameter

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

ConclusionsConclusions Demonstrated many of phenomena Demonstrated many of phenomena

seen in laminar viscous discseen in laminar viscous disc Planet launched spiral waves that Planet launched spiral waves that

transport angular momentumtransport angular momentum Turbulent disc has smaller Turbulent disc has smaller

– Mag. fields transport L across the gapMag. fields transport L across the gap Magnetic breaking around planetMagnetic breaking around planet

– MightMight slow mass accretion rate slow mass accretion rate

ReferencesReferences ““The interaction of a giant planet with a disc with The interaction of a giant planet with a disc with

MHD turbulence II:MHD turbulence II:The interaction of the planet with the disc”The interaction of the planet with the disc”Papaloizou & Nelson 2003, MNRAS 339 (4), 993-1005Papaloizou & Nelson 2003, MNRAS 339 (4), 993-1005

““The interaction of a giant planet with a disc with The interaction of a giant planet with a disc with MHD turbulence I:MHD turbulence I:The initial turbulent disc models”The initial turbulent disc models”Papaloizou & Nelson 2003a, MNRAS 339, 923Papaloizou & Nelson 2003a, MNRAS 339, 923

Images from:Images from:– http://astron.berkeley.edu/~gmarcy/http://astron.berkeley.edu/~gmarcy/

0398marcybox4.html0398marcybox4.html– http://www.sns.ias.edu/~dejan/CCS/work/SciArt/http://www.sns.ias.edu/~dejan/CCS/work/SciArt/