Type II Migration due to Multiple-Embedded Planets in Protoplanetary Disks

Investigating the formation and evolution of protoplanetary disks allows us to understand the process of planet formation and migration. Specifically, planet-disk interactions shape planetary orbits through migration and produce substructures within disks such as spirals, vortices, and gaps. For planetary masses equal to or greater than ~1 𝑀_J the Lindblad torque comprises of a positive torque applied to the planet by its inner wake and a negative torque generated by its outer wake. The planet gives angular momentum to the outer disk (the region beyond the planet's orbital radius) while absorbing some from the inner disk. There is also the corotational torque, which is the torque due to disk material that on average corotates with the planet. When the torque exerted by the planet on the disk exceeds the viscous torque, it results in the formation of an annular gap around the planet's orbit. This non-linear regime is called Type II migration.

Singular embedded planet-disk interactions have helped us understand the foundations of planetary migration, however, the logical extension of this theory to massive multi-planet systems is still not well understood. Using Athena++, a hydrodynamics code, we conduct 2-D simulations of gap formation resulting from single-embedded and multiple-embedded planets ranging from Super-Earth to Jupiter masses within a locally isothermal protoplanetary disk. From this, we can analyze the surface density of the gap formations, calculate the total torque of the planet-disk interaction, and determine the migrational direction of the planets. We also focus on determining the relationship of gap-width and gap-depth between the single and multiple planet cases. This analysis can help us understand the feasibility of proposed planetary migration models such as the Grand Tack Hypothesis.