Gap Opening by Extremely Low Mass Planets in a Viscous Disk

TL;DR

This study uses numerical simulations to determine the conditions under which very low mass planets can open gaps in viscous protoplanetary disks, challenging previous criteria and showing that even Neptune-mass planets can open gaps in low-viscosity environments.

Contribution

It provides a new criterion for gap formation by low-mass planets, showing that gap opening depends on disk viscosity and scale height rather than just Hill radius.

Findings

Planets with smaller Hill radius than disk scale height can open gaps.

No minimum mass needed for gap opening at very low viscosity.

Gap width scales with disk scale height, not Hill radius.

Abstract

By numerically integrating the compressible Navier-Stokes equations in two dimensions, we calculate the criterion for gap formation by a very low mass (q ~10^{-4}) protoplanet on a fixed orbit in a thin viscous disk. In contrast with some previously proposed gap-opening criteria, we find that a planet can open a gap even if the Hill radius is smaller than the disk scale height. Moreover, in the low-viscosity limit, we find no minimum mass necessary to open a gap for a planet held on a fixed orbit. In particular, a Neptune-mass planet will open a gap in a minimum mass solar nebula with suitably low viscosity (\alpha <10^{-4}). We find that the mass threshold scales as the square root of viscosity in the low mass regime. This is because the gap width for critical planet masses in this regime is a fixed multiple of the scale height, not of the Hill radius of the planet.