Planet-disc interaction in laminar and turbulent discs

¹ Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: moritz.stoll@uni-tuebingen.de; wilhelm.kley@uni-tuebingen.de
² Universitäts-Sternwarte, Ludwig-Maximilians-Universität München, Scheinerstr. 1, 81679 München, Germany
e-mail: picogna@usm.lmu.de

Received: 21 February 2017
Accepted: 13 June 2017

Abstract

In weakly ionised discs turbulence can be generated through the vertical shear instability (VSI). Embedded planets are affected by 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 3D 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 α = 5 × 10^-4. This is compared to the corresponding viscous disc using exactly this α-value. In general we find that the planets have only a weak impact on the disc turbulence. Only for the largest planet (100 M_⊕) does the turbulent activity become enhanced inside of the planet. The depth and width of a gap created by the more massive planets (30,100 M_⊕) 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 ≤ 10 M_⊕) do not open gaps in the disc in either case, but generate for the turbulent disc an overdensity 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. Owing to the finite turbulence level in realistic 3D discs the gap depth will always be limited and migration will not stall in inviscid discs.