The effect of sculpting planets on the steepness of debris-disc inner edges

TL;DR

This study explores how planets sculpt debris-disc inner edges and demonstrates that the steepness of these edges can reveal planet properties, helping to break degeneracies in interpreting disc observations.

Contribution

It introduces an analytic model linking disc edge steepness to planet mass and excitation, and assesses the impact of collisions on observable disc features.

Findings

Steepness of disc edges depends on planet-to-star mass ratio and initial excitation.

Collisions flatten but do not erase planet-induced edge signatures.

Many observed edges are inconsistent with purely collisional or non-migrating planet models.

Abstract

Debris discs are our best means to probe the outer regions of planetary systems. Many studies assume that planets lie at the inner edges of debris discs, akin to Neptune and the Kuiper Belt, and use the disc morphologies to constrain those otherwise-undetectable planets. However, this produces a degeneracy in planet mass and semimajor axis. We investigate the effect of a sculpting planet on the radial surface-density profile at the disc inner edge, and show that this degeneracy can be broken by considering the steepness of the edge profile. Like previous studies, we show that a planet on a circular orbit ejects unstable debris and excites surviving material through mean-motion resonances. For a non-migrating, circular-orbit planet, in the case where collisions are negligible, the steepness of the disc inner edge depends on the planet-to-star mass ratio and the initial-disc excitation level. We provide a simple analytic model to infer planet properties from the steepness of ALMA-resolved disc edges. We also perform a collisional analysis, showing that a purely planet-sculpted disc would be distinguishable from a purely collisional disc and that, whilst collisions flatten planet-sculpted edges, they are unlikely to fully erase a planet's signature. Finally, we apply our results to ALMA-resolved debris discs and show that, whilst many inner edges are too steep to be explained by collisions alone, they are too flat to arise through completed sculpting by non-migrating, circular-orbit planets. We discuss implications of this for the architectures, histories and dynamics in the outer regions of planetary systems.