Potential Vorticity Evolution of a Protoplanetary Disk with An Embedded Protoplanet

We present two-dimensional inviscid hydrodynamic simulations of a protoplanetary disk with an embedded planet, emphasizing the evolution of potential vorticity (the ratio of vorticity to density) and its dependence on numerical resolutions. By analyzing the structure of spiral shocks made by the planet, we show that progressive changes of the potential vorticity caused by spiral shocks ultimately lead to the excitation of a secondary instability. We also demonstrate that very high numerical resolution is required to both follow the potential vorticity changes and identify the location where the secondary instability is first excited. Low-resolution results are shown to give the wrong location. We establish the robustness of a secondary instability and its impact on the torque onto the planet. After the saturation of the instability, the disk shows large-scale nonaxisymmetry, causing the torque on the planet to oscillate with large amplitude. The impact of the oscillating torque on the protoplanet’s migration remains to be investigated. Subject headings: accretion, accretion disks — hydrodynamics — planetary systems: protoplanetary disks 1 Applied Physics Division, MS B227, Los Alamos National Laboratory, NM 87545; [email protected] 2 Theoretical Division, MS B284, Los Alamos National Laboratory, NM 87545; [email protected]; [email protected] 3 ISR Division, MS D466, Los Alamos National Laboratory, NM 87545; [email protected] Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Czech Republic; [email protected] 5 Department of Astronomy, University of Illinois at Urbana-Champaign, Urbana, IL 61801; [email protected] 6 Department of Physics & Astronomy, Rice University, Houston, TX 77005; [email protected] UCO/Lick Observatory, University of California, Santa Cruz, CA 95064; [email protected]