Diffusive Migration of Low‐Mass Protoplanets in Turbulent Disks

Torque fluctuations due to magnetorotational turbulence in proto-planetarydisks may greatly influence the migration patterns and survival probabilitiesof nascent planets. Provided that the turbulence is a stationary stochasticprocess with finite amplitude and correlation time, the resulting diffusivemigration can be described with a Fokker-Planck equation, which we reduce to anadvection-diffusion equation. We calibrate the coefficients with existingturbulent-disk simulations and mean-migration estimates, and solve the equationboth analytically and numerically. Diffusion tends to dominate over advectionfor planets of low-mass and those in the outer regions of proto-planetarydisks, whether they are described by the Minimum Mass Solar Nebula (MMSN) or byT-Tauri alpha disks. Diffusion systematically reduces the lifetime of mostplanets, yet it allows a declining fraction of them to survive for extendedperiods of time at large radii. Mean planet lifetimes can even be formallyinfinite (e.g. in an infinite steady MMSN), though median lifetimes are alwaysfinite. Surviving planets may linger near specific radii where the combinedeffects of advection and diffusion are minimized, or at large radii, dependingon model specifics. The stochastic nature of migration in turbulent diskschallenges deterministic planet formation scenarios and suggests instead that awide variety of planetary outcomes are possible from similar initialconditions. This would contribute to the diversity of (extrasolar) planetarysystems.Comment: 31 pages, 7 figures, accepted for publication in Ap