Pushing planets into an inner cavity by a resonant chain

TL;DR

This study uses hydrodynamical and N-body simulations to explore how resonant chains of planets can be pushed into the inner disc cavity, revealing the influence of disc profiles on planetary system configurations.

Contribution

It provides the first detailed analysis of how outer planets can push inner planets into the disc cavity through resonant chains, highlighting the effects of disc profile steepness.

Findings

Steeper disc profiles more effectively halt planetary chains.

Inner configurations are tighter and more unstable in dead zone models.

Over-stable librations can lead to very compact planetary systems.

Abstract

Context. The orbital distribution of exoplanets indicates an accumulation of super-Earth sized planets close to their host stars in compact systems. When an inward disc-driven migration scenario is assumed for their formation, these planets could have been stopped and might have been parked at an inner edge of the disc, or be pushed through the inner disc cavity by a resonant chain. This topic has not been properly and extensively studied. Using numerical simulations, we investigate the possibility that the inner planets in a resonant chain can be pushed into the disc inner cavity by outer planets. We performed hydrodynamical and N-body simulations of planetary systems embedded in their nascent disc. The inner edge of the disc was represented in two different ways, resembling either a dead zone inner edge (DZ) or a disc inner boundary (IB). The main difference lies in the steepness of the surface density profile. The innermost planet always has a mass of 10 M Earth , with additional outer planets of equal or higher mass. A steeper profile is able to stop a chain of planets more efficiently than a shallower profile. The final configurations in our DZ models are usually tighter than in their IB counterparts, and therefore more prone to instability. We derive analytical expressions for the stopping conditions based on power equilibrium, and show that the final eccentricities result from torque equilibrium. For planets in thinner discs, we found, for the first time, clear signs for over-stable librations in the hydrodynamical simulations, leading to very compact systems. We also found that the popular N-body simulations may overestimate the number of planets in the disc inner cavity.