Collision rates of planetesimals near mean-motion resonances

TL;DR

This paper uses N-body simulations to study how planetesimal collisions near mean-motion resonances create observable dust structures, which can reveal properties of perturbing planets in protoplanetary disks.

Contribution

It demonstrates that collision rate profiles near mean-motion resonances produce distinct features that depend on planetary mass and eccentricity, offering a new method to infer planetary properties from dust observations.

Findings

Collision profiles show bumps or dips depending on resonance libration width.

Features depend on planet mass and eccentricity.

Observable in nearby disks with ALMA if radial drift is minimal.

Abstract

In circumstellar discs, collisional grinding of planetesimals produces second-generation dust. While it remains unclear whether this ever becomes a major component of the total dust content, the presence of such dust, and potentially the substructure within, it can be used to explore a disc's physical conditions. A perturbing planet produces nonaxisymmetric structures and gaps in the dust, regardless of its origin. The dynamics of planetesimals, however, will be very different than that of small dust grains due to weaker gas interactions. Therefore, planetesimal collisions could create dusty disc structures that would not exist otherwise. In this work, we use N-body simulations to investigate the collision rate profile of planetesimals near mean-motion resonances. We find that a distinct bump or dip feature is produced in the collision profile, the presence of which depends on the libration width of the resonance and the separation between the peri- and apocenter distances of the edges of the resonance. The presence of one of these two features depends on the mass and eccentricity of the planet. Assuming that the radial dust emission traces the planetesimal collision profile, the presence of a bump or dip feature in the dust emission at the 2:1 mean-motion resonance can constrain the orbital properties of the perturbing planet. This assumption is valid, so long as radial drift does not play a significant role during the collisional cascade process. Under this assumption, these features in the dust emission should be marginally observable in nearby protoplanetary disks with ALMA.