On Eccentric Protoplanetary Disks I -- How Eccentric are Planet-Perturbed Disks?

TL;DR

This paper investigates the eccentricity of planet-perturbed protoplanetary disks using hydrodynamical simulations, deriving a semi-analytic model that matches simulations and aids interpretation of observed disk eccentricities.

Contribution

It provides a quantitative model for the steady-state eccentricity of disks influenced by planets, linking eccentricity to disk and planetary parameters, and validates it with simulations.

Findings

Eccentricity scales with planet-to-star mass ratio and disk aspect ratio.

Semi-analytic eccentricity profile agrees within 30% with simulations.

Model helps interpret observed eccentric protoplanetary disks.

Abstract

Protoplanetary disks can become eccentric when planets open deep gaps within, but how eccentric are they? We answer this question by analyzing two-dimensional hydrodynamical simulations of planet-disk interaction. The steady state eccentricity of the outer disk (outside of the planet's orbit) is described as a balance between eccentricity excitation by the 1:3 eccentric Lindblad resonance and eccentricity damping by gas pressure. This eccentricity scales with $q(\frac{h_p}{r_p})^{(-1)}(\frac{r_{gap}}{r_p})^{(a-\frac{b}{2}-2)}$, where $q$ is the planet-to-star mass ratio, $\frac{h_p}{r_p}$ is the disk aspect ratio, $\frac{r_{gap}}{r_p}$ is the radial position of the outer gap edge divided by the planet's position, and $a$ and $b$ are the negative exponents in the disk's surface density and temperature power law profiles, respectively. We derive a semi-analytic eccentricity profile that agrees with numerical simulations to within 30%. Our result is a first step to quantitatively interpret observations of eccentric protoplanetary disks, such as MWC 758, HD 142527, IRS 48, and CI Tau.