Dynamical evolution of an eccentric planet and a less massive debris disc

Abstract

We investigate the interaction between an eccentric planet and a less massive external debris disc. This scenario could occur after planet-planet scattering or merging events. We characterise the evolution over a wide range of initial conditions, using a suite of n-body integrations combined with theory. Planets near the disc mid-plane remove the inner debris region, and surviving particles form an eccentric disc apsidally aligned with the planet. The inner disc edge is elliptical and lies just beyond the planet's orbit. Moderately inclined planets ($i_{\rm plt} \gtrsim 20^\circ$ for $e_{\rm plt} = 0.8$) may instead sculpt debris into a bell-shaped structure enveloping the planet's orbit. Finally some highly inclined planets ($i_{\rm plt} \sim 90^\circ$) can maintain a disc orthogonal to the planet's plane. In all cases disc particles undergo rapid evolution, whilst the overall structures evolve more slowly. The shapes of these structures and their density profiles are characterised. The width of the chaotic zone around the planet's orbit is derived in the coplanar case using eccentric Hill radius arguments. This zone is cleared within approximately ten secular or diffusion times (whichever is longer), and debris assumes its final shape within a few secular times. We quantify the planet's migration and show it will almost always be small in this mass regime. Our results may be used to characterise unseen eccentric planets using observed debris features.