Eccentric gap induced by a super-Jupiter mass planet

A giant planet embedded in a protoplanetary disk opens a gap by tidal interaction, and properties of the gap strongly depend on the planetary mass and disk parameters. Many numerical simulations of this process have been conducted, but detailed simulations and analysis of gap formation by a super-Jupiter mass planet have not been thoroughly conducted. We performed two-dimensional numerical hydrodynamic simulations of the gap formation process by a super-Jupiter mass planet and examined the eccentricity of the gap. When the planet is massive, the radial motion of gas is excited, causing the eccentricity of the gap's outer edge to increase. Our simulations showed that the critical planetary mass for the eccentric gap was $\sim3~M_{\rm J}$ in a disk with $\alpha=4.0\times10^{-3}$ and $h/r=0.05$, a finding that was consistent with that reported in a previous work. The critical planetary mass for the eccentric gap depends on the viscosity and the disk scale height. We found that the critical mass could be described by considering a dimensionless parameter related to the gap depth. The onset of gap eccentricity enhanced the surface density inside the gap, shallowing the gap more than the empirical relation derived in previous studies for a planet heavier than the critical mass. Therefore, our results suggest that the mass accretion rate, which strongly depends on the gas surface density in the gap is also enhanced for super-Jupiter mass planets. These results may substantially impact the formation and evolution processes of super-Jupiter mass planets and population synthesis calculations.