Planetesimals in Turbulent Disks

1. 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

2. Planetesimals form within gas disks • Laminar disks cause migration • Real disks are MRI turbulent, though • How do planetesimals behave in more realistic disks? • migration • orbital ellipticity & inclination • velocity dispersion • dead zones

3. Numerical 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

4. Turbulent Migration Nelson & Papaloizou 04 A random walk! see also: Papaloizou & Nelson 03 Laughlin et al 04 Nelson 05 Torque t

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

6. Motion of an Individual Particle Yang, Mac Low, & Menou, 2009, in prep • Mean radial distance → radial drift • Amplitude of epicycles → eccentricity e • Amplitude of vertical oscillations → inclination i

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

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

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

10. 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) Dead Zones thicker thinner

11. Magnetic pressure vs time ReM=3 ReM=30 Oishi, Mac Low, & Menou 07 ReM=100 ReM=∞

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

13. 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

14. Stationary torque distributions Finite correlation times. Oishi, Mac Low, & Menou 07

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

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

17. Mp = 10-2 M 0.1 diffusive 1 10  = 0.2 advective MMSN planetesimals can be in diffusive regime… Johnson, Goodman & Menou 06 Oishi, Mac Low & Menou 07

18. 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.