Planetesimals in Turbulent Disks Mordecai-Mark Mac Low Chao-Chin Yang American Museum of Natural History Jeffrey S. Oishi University of California at Berkeley Kristen Menou Columbia University Mordecai-Mark Mac Low Chao-Chin Yang American Museum of Natural History Jeffrey S. Oishi University of California at Berkeley Kristen Menou Columbia 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 realistic disks?How do planetesimals behave in more 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 realistic disks?How do planetesimals behave in more realistic disks? migrationmigration orbital ellipticity & inclinationorbital ellipticity & inclination velocity dispersionvelocity dispersion dead zonesdead zones

Numerical Techniques  Pencil Code ( Brandenburg & Dobler 2002 )  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 )  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 Migration Nelson & Papaloizou 04 see also: Papaloizou & Nelson 03 Laughlin et al 04 Nelson 05 A random walk! t Torque

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

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 Yang, Mac Low, & Menou, 2009, in prep

Eccentricity Change Yang, Mac Low & Menou 2009, in prep extends semi- analytic result of Ogihara, Ida & Morbidelli 07, based on Laughlin Steinacker & Adams 04 to both excitation and damping

Inclination Growth Over a lifetime of 1 Myr, at R ~ 30 AU, i < 0.2 degrees Yang, Mac Low & Menou 2009, in prep

Radial Drift Yang, Mac Low & Menou 2009, in prep quantifies random walk of Nelson & Papaloizou 05

thickerthinner Dead 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)

Oishi, Mac Low, & Menou 07 Re M =3 Re M =30 Re M =100 Re M =∞ Magnetic pressure vs time

Oishi, Mac Low, & Menou 07 Dead zones don’t cut off accretion (confirms & extends Fleming & Stone 2003 ) Shakura & Sunyaev viscous stress

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 07 Stationary torque distributions Finite correlation times.

Oishi, Mac Low, & Menou (2007) Torques decrease, but do not vanish in dead zones

Oishi, Mac Low, & Menou 07 dead zone thickness MRI diffusion coefficient Turbulence Parameter Johnson et al. 06 Nelson 05 found  = 0.5 in global, unstratified, ideal MRI models

Johnson, Goodman & Menou 06 MMSN  = 0.2 M p = M  diffusive advective planetesimals can be in diffusive regime… Oishi, Mac Low & Menou 07

Conclusions  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.