Deep and wide gaps by super Earths in low-viscosity discs

TL;DR

This paper introduces a simplified model to analyze planet-induced gaps in protoplanetary discs, revealing a new low-viscosity regime where gaps are deeper and wider than previously estimated, especially for low-mass planets.

Contribution

The authors develop an analytical and numerical framework to study gap formation in low-viscosity discs, identifying a novel regime where classical relations do not apply.

Findings

Gaps can be significantly deeper and wider in low-viscosity discs.

A new low-viscosity regime is identified where classical scaling relations fail.

Deeper gaps take longer to reach equilibrium.

Abstract

Planets can open cavities (gaps) in the protoplanetary gaseous discs in which they are born by exerting gravitational torques. Viscosity counters these torques and limits the depletion of the gaps. We present a simple one-dimensional scheme to calculate the gas density profile inside gaps by balancing the gravitational and viscous torques. By generalizing the results of Goodman & Rafikov (2001), our scheme properly accounts for the propagation of angular momentum by density waves. This method allows us to easily study low-viscosity discs, which are challenging for full hydrodynamical simulations. We complement our numerical integration by analytical equations for the gap's steady-state depth and width as a function of the planet's to star's mass ratio $\mu$, the gas disc's aspect ratio $h$, and its Shakura & Sunyaev viscosity parameter $\alpha$. Specifically, we focus on low-mass planets ($\mu<\mu_{\rm th}\equiv h^3$) and identify a new low-viscosity regime, $\alpha<h(\mu/\mu_{\rm th})^5$, in which the classical analytical scaling relations are invalid. Equivalently, this low-viscosity regime applies to every gap that is depleted by more than a factor of $(\mu_{\rm th}/\mu)^3$ relative to the unperturbed density. We show that such gaps are significantly deeper and wider than previously thought, and consequently take a longer time to reach equilibrium.