Potential Vorticity Evolution of a Protoplanetary Disk with an Embedded Protoplanet

We present two-dimensional inviscid hydrodynamic simulations of aprotoplanetary disk with an embedded planet, emphasizing the evolution ofpotential vorticity (the ratio of vorticity to density) and its dependence onnumerical resolutions. By analyzing the structure of spiral shocks made by theplanet, we show that progressive changes of the potential vorticity caused byspiral shocks ultimately lead to the excitation of a secondary instability. Wealso demonstrate that very high numerical resolution is required to both followthe potential vorticity changes and identify the location where the secondaryinstability is first excited. Low-resolution results are shown to give thewrong location. We establish the robustness of a secondary instability and itsimpact on the torque onto the planet. After the saturation of the instability,the disk shows large-scale non-axisymmetry, causing the torque on the planet tooscillate with large amplitude. The impact of the oscillating torque on theprotoplanet's migration remains to be investigated.Comment: 17 pages total with 9 figures (Fig.4,5,9 are in .jpg), accepted to Ap