Planetesimals in Turbulent DisksPlanetesimals in Turbulent Disks

Mordecai-Mark Mac LowChao-Chin Yang

American Museum of Natural History

Jeffrey S. OishiUniversity of California at Berkeley

Kristen MenouColumbia University

Mordecai-Mark Mac LowChao-Chin Yang

American Museum of Natural History

Jeffrey S. OishiUniversity of California at Berkeley

Kristen MenouColumbia University

• Planetesimals form within gas disksPlanetesimals form within gas disks• Laminar disks cause migrationLaminar disks cause migration• Real disks are MRI turbulent, thoughReal disks are MRI turbulent, though• How do planetesimals behave in more How do planetesimals behave in more

realistic disks?realistic disks?• migrationmigration• orbital ellipticity & inclinationorbital ellipticity & inclination• velocity dispersionvelocity dispersion• dead zonesdead zones

• Planetesimals form within gas disksPlanetesimals form within gas disks• Laminar disks cause migrationLaminar disks cause migration• Real disks are MRI turbulent, thoughReal disks are MRI turbulent, though• How do planetesimals behave in more How do planetesimals behave in more

realistic disks?realistic disks?• migrationmigration• orbital ellipticity & inclinationorbital ellipticity & inclination• velocity dispersionvelocity dispersion• dead zonesdead zones

Numerical TechniquesNumerical Techniques Pencil Code (Brandenburg & Dobler 2002)

http://www.nordita.dk/data/brandenb/pencil-code/

Finite-difference MHD code (w / particles) Sixth-order spatial, third-order time Hyperdiffusion for time-centered scheme Div B = 0 maintained using vector

potential Parallelized along pencils using MPI Height-dependent Ohmic resistivity Shearing-sheet local box w/stratification

Pencil Code (Brandenburg & Dobler 2002) http://www.nordita.dk/data/brandenb/pencil-code/

Finite-difference MHD code (w / particles) Sixth-order spatial, third-order time Hyperdiffusion for time-centered scheme Div B = 0 maintained using vector

potential Parallelized along pencils using MPI Height-dependent Ohmic resistivity Shearing-sheet local box w/stratification

Turbulent MigrationTurbulent Migration

Nelso

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see also:see also:Papaloizou & Nelson 03Papaloizou & Nelson 03Laughlin et al 04Laughlin et al 04Nelson 05Nelson 05

A A random random walk!walk!

tTorq

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How do torques act over multiple How do torques act over multiple orbits?orbits?• Use Use test particlestest particles to follow orbital to follow orbital evolution.evolution.• Following large numbers allows Following large numbers allows quantification of random walks.quantification of random walks.initial conditions:initial conditions:• net flux to maintain constant alphanet flux to maintain constant alpha• zero ellipticity, finite ellipticity orbitszero ellipticity, finite ellipticity orbits• low and high mass disks (constant Q)low and high mass disks (constant Q)• unstratified and stratified ideal MHDunstratified and stratified ideal MHD

Motion of an Individual Particle

Motion of an Individual Particle

Mean radial distance → radial drift Amplitude of epicycles → eccentricity e Amplitude of vertical oscillations → inclination i

Mean radial distance → radial drift Amplitude of epicycles → eccentricity e Amplitude of vertical oscillations → inclination i

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Eccentricity ChangeEccentricity Change

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Adams 04Adams 04 to both to both

excitation excitation and and

dampingdamping

Inclination GrowthInclination Growth

Over a lifetime of 1 Myr, at ROver a lifetime of 1 Myr, at R ~ 30 AU, i < 0.2 ~ 30 AU, i < 0.2 degreesdegrees

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Radial DriftRadial Drift

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quantifies quantifies random walk of random walk of

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thickerthicker thinnerthinner

Dead ZonesDead Zones

cosmic ray ionization (Gammie 96)

dust absorbs charge (Wardle & Ng 99, Sano et al. 00 )

cosmic ray ionization (Gammie 96)

dust absorbs charge (Wardle & Ng 99, Sano et al. 00 )

trace metal ions (Fromang et al 02)

turbulent mixing of ions (Inutsuka & Sano 05, Ilgner & Nelson 06ab, 08, Turner et al. 07)

trace metal ions (Fromang et al 02)

turbulent mixing of ions (Inutsuka & Sano 05, Ilgner & Nelson 06ab, 08, Turner et al. 07)

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ReReMM=3=3

ReReMM=30=30

ReReMM=100=100

ReReMM=∞=∞

Magnetic pressure vs timeMagnetic pressure vs time

Oishi, Mac Low, & Menou 07Oishi, Mac Low, & Menou 07

Dead zones don’t Dead zones don’t cut off accretion cut off accretion

(confirms & (confirms & extends extends Fleming & Fleming &

Stone 2003Stone 2003))

Shakura & Sunyaev Shakura & Sunyaev viscous stress viscous stress

Advection-Diffusion Approx

Advection-Diffusion Approx

Johnson, Goodman, & Menou (2006) Type I migration = advection Turbulent random walk = diffusion Treat using Fokker-Planck model Assumes stationary torques, finite

correlation times. -> diffusion shortens lifetimes on

average, but allows a few to survive to very long times

Johnson, Goodman, & Menou (2006) Type I migration = advection Turbulent random walk = diffusion Treat using Fokker-Planck model Assumes stationary torques, finite

correlation times. -> diffusion shortens lifetimes on

average, but allows a few to survive to very long times

Oishi, Mac Low, & Menou 07Oishi, Mac Low, & Menou 07

Stationary Stationary torque torque distributionsdistributions

Finite Finite correlatiocorrelation times.n times.

Oishi, Mac Low, & Menou (2007)Oishi, Mac Low, & Menou (2007)

Torques Torques decreasdecrease, but e, but do do notnot vanish vanish in dead in dead zoneszones

Oishi, Mac Low, & Menou 07Oishi, Mac Low, & Menou 07

dead zone thickness

MRI diffusion coefficientMRI diffusion coefficient

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Turbulence ParameterTurbulence Parameter

Johnson et al. 06Johnson et al. 06

Nelson 05 found Nelson 05 found = = 0.5 in global, 0.5 in global, unstratified, ideal MRI unstratified, ideal MRI modelsmodels

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Johnson, Goodman & Menou 06Johnson, Goodman & Menou 06

MMSN

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diffusive

advective

planetesimals can planetesimals can be in diffusive be in diffusive regime…regime…

Oishi, Mac Low & Menou 07Oishi, Mac Low & Menou 07

ConclusionsConclusions MRI turbulence excites only modest

growth in eccentricity and inclination. Our shearing-sheet results suggest low

radial velocity dispersions, allowing planetesimal formation by collision.

MRI turbulence will cause populations of small planetesimals to diffuse both inwards and outwards, potentially leading to preservation of a significant fraction against gas-driven migration.

MRI turbulence excites only modest growth in eccentricity and inclination.

Our shearing-sheet results suggest low radial velocity dispersions, allowing planetesimal formation by collision.

MRI turbulence will cause populations of small planetesimals to diffuse both inwards and outwards, potentially leading to preservation of a significant fraction against gas-driven migration.