Formation of a disc gap induced by a planet: Effect of the deviation from Keplerian disc rotation

TL;DR

This paper presents a new one-dimensional viscous disc model that accounts for deviations from Keplerian rotation and wave propagation, providing a more accurate description of planet-induced gap formation in protoplanetary discs.

Contribution

It introduces a formulation that includes the deviation from Keplerian rotation and wave propagation effects, improving the understanding of gap formation dynamics.

Findings

Deviations from Keplerian rotation promote radial angular momentum transfer.

Wave propagation widens and shallows the gap compared to instantaneous damping.

The model aligns well with recent hydrodynamic simulations.

Abstract

The gap formation induced by a giant planet is important in the evolution of the planet and the protoplanetary disc. We examine the gap formation by a planet with a new formulation of one-dimensional viscous discs which takes into account the deviation from Keplerian disc rotation due to the steep gradient of the surface density. This formulation enables us to naturally include the Rayleigh stable condition for the disc rotation. It is found that the derivation from Keplerian disc rotation promotes the radial angular momentum transfer and makes the gap shallower than in the Keplerian case. For deep gaps, this shallowing effect becomes significant due to the Rayleigh condition. In our model, we also take into account the propagation of the density waves excited by the planet, which widens the range of the angular momentum deposition to the disc. The effect of the wave propagation makes the gap wider and shallower than the case with instantaneous wave damping. With these shallowing effects, our one-dimensional gap model is consistent with the recent hydrodynamic simulations.