On Eccentric Protoplanetary Disks. I. How Eccentric are Planet-perturbed 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 ( h p / r p ) − 1 r gap / r p a − b 2 − 2 , where q is the planet-to-star mass ratio, h p / r p is the disk aspect ratio, 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 semianalytic 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.