Three-Dimensional Simulations of Planet-Induced Gap Openings in Protoplanetary Disks

As they form, planets excite spiral waves which steepen into shocks and open annular gaps in their natal protoplanetary disks. Recent studies have shown that a single planet can open multiple gaps at the radial locations where each spiral wave steepens into a shock. However, these previous studies are limited to a two-dimensional space where the vertical structure of gaps and vertical gas motions within and around gaps cannot be examined. In this paper, we investigate the formation of multiple gaps by a planet using three-dimensional hydrodynamic simulations. We show that a singular planet can open multiple gaps in three-dimensional spaces and that the radial location of the gaps shows an excellent agreement between two- and three-dimensional simulations. The gas around both the primary gap (the gap opening around the planet's orbit) and secondary gaps (gaps opening at a distance from the planet's orbit) experiences a downward motion toward the disk midplane and encounters azimuthal velocity asymmetry. We discuss the observational implications of these velocity structures and note future impacts of using three-dimensional simulations.