Collisional Velocities and Rates in Resonant Planetesimal Belts

TL;DR

This paper calculates how resonances affect collision velocities and rates among small bodies in planetary belts, revealing increased collision rates especially for Trojans, impacting dust production and object lifetimes.

Contribution

It introduces a combined celestial mechanics and statistical physics approach to quantify collisional velocities and rates in resonant planetesimal belts, highlighting the impact of resonances.

Findings

Resonant lock has a small effect on collisional velocities.

Resonant belts have about twice the collisional rates of non-resonant belts.

Trojans can have collisional rates up to ten times higher than non-resonant objects.

Abstract

We consider a belt of small bodies around a star, captured in one of the external or 1:1 mean-motion resonances with a massive perturber. The objects in the belt collide with each other. Combining methods of celestial mechanics and statistical physics, we calculate mean collisional velocities and collisional rates, averaged over the belt. The results are compared to collisional velocities and rates in a similar, but non-resonant belt, as predicted by the particle-in-a-box method. It is found that the effect of the resonant lock on the velocities is rather small, while on the rates more substantial. The collisional rates between objects in an external resonance are by about a factor of two higher than those in a similar belt of objects not locked in a resonance. For Trojans under the same conditions, the collisional rates may be enhanced by up to an order of magnitude. Our results imply, in particular, shorter collisional lifetimes of resonant Kuiper belt objects in the solar system and higher efficiency of dust production by resonant planetesimals in debris disks around other stars.