Estimating the depth of gaps opened by planets in eccentric orbit

TL;DR

This paper develops an empirical scaling relation to estimate the depth of gaps in protoplanetary discs caused by eccentric planets, aiding understanding of planet-disc interactions and dust ring formations.

Contribution

It introduces a new empirical model for gap depth as a function of planetary and disc parameters, calibrated with hydrodynamical simulations for moderate eccentricities.

Findings

The scaling relation accurately predicts gap depth for eccentricities up to 4h.

The model matches simulation results within a surface density contrast of 100.

Provides a basis for more detailed models of gap profiles in eccentric planetary systems.

Abstract

Planets can carve gaps in the surface density of protoplanetary discs. The formation of these gaps can reduce the corotation torques acting on the planets. In addition, gaps can halt the accretion of solids onto the planets as dust and pebbles can be trapped at the edge of the gap. This accumulation of dust could explain the origin of the ring-like dust structures observed using high-resolution interferometry. In this work we provide an empirical scaling relation for the depth of the gap cleared by a planet on an eccentric orbit as a function of the planet-to-star mass ratio $q$, the disc aspect ratio $h$, Shakura-Sunyaev viscosity parameter $\alpha$, and planetary eccentricity $e$. We construct the scaling relation using a heuristic approach: we calibrate a toy model based on the impulse approximation with 2D hydrodynamical simulations. The scaling reproduces the gap depth for moderate eccentricities ($e\leq 4h$) and when the surface density contrast outside and inside the gap is $\leq 10^{2}$. Our framework can be used as the basis of more sophisticated models aiming to predict the radial gap profile for eccentric planets.