# The role of gap edge instabilities in setting the depth of planet gaps in protoplanetary discs

## TL;DR

This study investigates how gap edge instabilities, especially Rossby wave instability, influence the depth of planet-induced gaps in protoplanetary discs, revealing the importance of two-dimensional effects and torque distribution modeling.

## Contribution

It demonstrates that gap edge instabilities critically affect gap depth and highlights the importance of two-dimensional modeling and improved torque approximations for accurate predictions.

## Key findings

- Two-dimensional gaps are shallower than one-dimensional gaps for the same initial conditions.
- Rossby wave instability influences the equilibrium gap depth in two-dimensional discs.
- Improved torque density models from three-dimensional simulations reduce discrepancies between 1D and 2D models.

## Abstract

It is known that an embedded massive planet will open a gap in a protoplanetary disc via angular momentum exchange with the disc material. The resulting surface density profile of the disc is investigated for one dimensional and two dimensional disc models and, in agreement with previous work, it is found that one dimensional gaps are significantly deeper than their two dimensional counterparts for the same initial conditions. We find, by applying one dimensional torque density distributions to two dimensional discs containing no planet, that the excitement of the Rossby wave instability and the formation of Rossby vortices play a critical role in setting the equilibrium depth of the gap. Being a two dimensional instability, this is absent from one dimensional simulations and does not limit the equilibrium gap depth there. We find similar gap depths between two dimensional gaps formed by torque density distributions, in which the Rossby wave instability is present, and two dimensional planet gaps, in which no Rossby wave instability is present. This can be understood if the planet gap is maintained at marginal stability, even when there is no obvious Rossby wave instability present. Further investigation shows the final equilibrium gap depth is very sensitive to the form of the applied torque density distribution, and using improved one dimensional approximations from three dimensional simulations can go even further to reducing the discrepancy between one and two dimensional models, especially for lower mass planets. This behaviour is found to be consistent across discs with varying parameters.