# An opening criterion for dust gaps in protoplanetary discs

## TL;DR

This paper develops an analytical criterion for dust gap opening by low-mass planets in protoplanetary discs, validated with 3D simulations, aiding in interpreting high-resolution disc observations.

## Contribution

It extends dust radial drift theory to include planetary and viscous forces, providing new criteria for dust gap formation and planet mass estimates.

## Key findings

- Analytical grain size-dependent dust gap opening criterion.
- Estimate of the dust gap's outer edge location.
- Minimum Stokes number for planet-induced dust gaps.

## Abstract

We aim to understand under which conditions a low mass planet can open a gap in viscous dusty protoplanetary discs. For this purpose, we extend the theory of dust radial drift to include the contribution from the tides of an embedded planet and from the gas viscous forces. From this formalism, we derive i) a grain size-dependent criterion for dust gap opening in discs, ii) an estimate of the location of the outer edge of the dust gap and iii) an estimate of the minimum Stokes number above which low-mass planets are able to carve gaps which appear only in the dust disc. These analytical estimates are particularly helpful to appraise the minimum mass of an hypothetical planet carving gaps in discs observed at long wavelengths and high resolution. We validate the theory against 3D SPH simulations of planet-disc interaction in a broad range of dusty protoplanetary discs. We find a remarkable agreement between the theoretical model and the numerical experiments.