Turbulent Disk Viscosity and the Bifurcation of Planet Formation Histories

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 $α$ 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 $M_{\rm p, corot} \sim α^{2/3}$. 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.