Planet-disc interaction in laminar and turbulent discs

Abstract

In weakly ionized discs turbulence can be generated through the vertical shear instability (VSI). Embedded planets feel a stochastic component in the torques acting on them which can impact their migration. In this work we study the interplay between a growing planet embedded in a protoplanetary disc and the VSI-turbulence. We performed a series of three-dimensional hydrodynamical simulations for locally isothermal discs with embedded planets in the mass range from 5 to 100 Earth masses. We study planets embedded in an inviscid disc that is VSI unstable, becomes turbulent and generates angular momentum transport with an effective $\alpha = 5 \cdot 10^{-4}$. This is compared to the corresponding viscous disc using exactly this $\alpha$-value. In general we find that the planets have only a weak impact on the disc turbulence. Only for the largest planet ($100 M_\oplus$) the turbulent activity becomes enhanced inside of the planet. The depth and width of a gap created by the more massive planets ($30, 100 M_\oplus$) in the turbulent disc equal exactly that of the corresponding viscous case, leading to very similar torque strengths acting on the planet, with small stochastic fluctuations for the VSI disc. At the gap edges vortices are generated that are stronger and longer lived in the VSI disc. Low mass planets (with $M_p \leq 10 M_\oplus$) do not open gaps in the disc in both cases but generate for the turbulent disc an over-density behind the planet that exerts a significant negative torque. This can boost the inward migration in VSI turbulent discs well above the Type I rate. Due to the finite turbulence level in realistic three-dimensional discs the gap depth will always be limited and migration will not stall in inviscid discs.