How the planetary eccentricity influences the pebble isolation mass

TL;DR

This study explores how planetary eccentricity affects the pebble isolation mass in protoplanetary discs through hydrodynamical simulations, revealing a dependence on disc viscosity and implications for planetary core growth.

Contribution

It provides a new fitting formula for pebble isolation mass as a function of eccentricity and disc turbulence, extending understanding beyond circular orbit assumptions.

Findings

Eccentric planets can reach a smaller pebble isolation mass than circular ones at low turbulence.

High turbulence prevents planets from fully stalling pebble flow, affecting core growth limits.

Maximum rocky core mass varies significantly with disc viscosity, influencing planet formation outcomes.

Abstract

We investigate the pebble isolation mass for a planet on a fixed eccentric orbit in its protoplanetary disc by conducting a set of 2D hydrodynamical simulations including dust turbulent diffusion. A range of planet eccentricities up to $e=0.2$ is adopted. Our simulations also cover a range of $\alpha-$turbulent viscosities, and for each pair $\{\alpha,e\}$ the pebble isolation mass is estimated as the minimum planet mass in our simulations such that solids with a Stokes number $\gtrsim 0.05$ do not flow across the planet orbit and remain trapped around a pressure bump outside the planet gap. For $\alpha<10^{-3}$, we find that eccentric planets reach a well-defined pebble isolation mass, which can be smaller than for planets on circular orbits when the eccentricity remains smaller than the disc's aspect ratio. We provide a fitting formula for how the pebble isolation mass depends on planet eccentricity. However, for $\alpha > 10^{-3}$, eccentric planets cannot fully stall the pebbles flow, and thus do not reach a well-defined pebble isolation mass. Our results suggest that the maximum mass reached by rocky cores should exhibit a dichotomy depending on the disc turbulent viscosity. While being limited to ${\cal O}(10\,M_\oplus)$ in low-viscosity discs, this maximum mass could reach much larger values in discs with a high turbulent viscosity in the planet vicinity. Our results further highlight that pebble filtering by growing planets might not be as effective as previously thought, especially in high-viscosity discs, with important implications to protoplanetary discs observations.