Turbulent Disk Viscosity and the Bifurcation of Planet Formation Histories

TL;DR

This study uses simulations to show how disk viscosity influences planet migration, leading to different planetary system architectures, and explains observed disk structures through a bifurcation driven by viscosity variations.

Contribution

It introduces a semi-analytic model demonstrating how varying disk viscosity causes a bifurcation in planet migration paths, affecting planetary system outcomes and disk structures.

Findings

High viscosity disks lead to inward migration and compact systems.

Low viscosity disks allow outward migration, creating extended rings and gaps.

Corotation mass scales with viscosity as M_p, corot ∼ α^{2/3}.

Abstract

ALMA observations of dust ring/gap structures in a minority but growing sample of protoplanetary disks can be explained by the presence of planets at large disk radii - yet the origins of these planets remains debated. We perform planet formation simulations using a semi-analytic model of the HL Tau disk to follow the growth and migration of hundreds of planetary embryos initially distributed throughout the disk, assuming either a high or low turbulent $\alpha$ viscosity. We have discovered that there is a bifurcation in the migration history of forming planets as a consequence of varying the disk viscosity. In our high viscosity disks, inward migration prevails and yields compact planetary systems, tempered only by planet trapping at the water iceline around 5 au. In our lower viscosity models however, low mass planets can migrate outward to twice their initial orbital radii, driven by a radially extended region of strong outward-directed corotation torques located near the heat transition (where radiative heating of the disk by the star is comparable to viscous heating) - before eventually migrating inwards. We derive analytic expressions for the planet mass at which the corotation torque dominates, and find that this "corotation mass" scales as $M_{\rm p, corot} \sim \alpha^{2/3}$. If disk winds dominate the corotation torque, the corotation mass scales linearly with wind strength. We propose that the observed bifurcation in disk demographics into a majority of compact dust disks and a minority of extended ring/gap systems is a consequence of a distribution of viscosity across the disk population.