Planetesimal and Protoplanet Dynamics in a Turbulent Protoplanetary Disk: Ideal Unstratified Disks

TL;DR

This study uses local shearing box simulations to analyze how magneto-rotational turbulence affects planetesimal and planetary core dynamics, revealing growth in orbital properties and implications for planet formation.

Contribution

First direct orbital integration in a local model showing turbulence-driven growth of orbital properties and migration behaviors in a protoplanetary disk.

Findings

Orbital properties grow as a random walk over time.

Velocity dispersions are low enough to prevent collisional destruction.

Type I migration dominates over stochastic torques for planetary cores.

Abstract

The dynamics of planetesimals and planetary cores may be strongly influenced by density perturbations driven by magneto-rotational turbulence in their natal protoplanetary gas disks. Using the local shearing box approximation, we perform numerical simulations of planetesimals moving as massless particles in a turbulent, magnetized, unstratified gas disk. Our fiducial disk model shows turbulent accretion characterized by a Shakura-Sunyaev viscosity parameter of $\alpha \sim 10^{-2}$, with root-mean-square density perturbations of $\sim$10%. We measure the statistical evolution of particle orbital properties in our simulations including mean radius, eccentricity, and velocity dispersion. We confirm random walk growth in time of all three properties, the first time that this has been done with direct orbital integration in a local model. We find that the growth rate increases with the box size used at least up to boxes of eight scale heights in horizontal size. However, even our largest boxes show velocity dispersions sufficiently low that collisional destruction of planetesimals should be unimportant in the inner disk throughout its lifetime. Our direct integrations agree with earlier torque measurements showing that type I migration dominates over diffusive migration by stochastic torques for most objects in the planetary core and terrestrial planet mass range. Diffusive migration remains important for objects in the mass range of kilometer-sized planetesimals. Discrepancies in the derived magnitude of turbulence between local and global simulations of magneto-rotationally unstable disks remains an open issue, with important consequences for planet formation scenarios.