Collisional parameters of planetesimal belts, precursor of debris disks, perturbed by a nearby giant planet

TL;DR

This paper develops a new algorithm to compute collision parameters in planetesimal belts influenced by nearby giant planets, revealing how planetary eccentricity and initial conditions affect dust production and collisional evolution.

Contribution

The authors introduce a novel method to calculate collision probabilities and impact velocities considering secular perturbations and eccentricity-pericentre coupling in planetesimal belts.

Findings

Higher planetary eccentricity increases dust erosion rates.

Initial belt conditions significantly influence collisional activity.

Only small bodies are expected to fragment over 4 Gyr in active belts.

Abstract

Planetesimal belts are invoked to explain the prolonged existence of debris disks. Important parameters to model their collisional evolution and to compute the dust production rate are the intrinsic probability of collision $P_i$ and the mean impact velocity $U_c$. If a planet orbits close to the belt, the values of both these parameters are affected by its secular perturbations yielding a strong correlation between eccentricity $e$ and pericentre longitude $\varpi$. We adopt a new algorithm to compute both $P_i$ and $U_c$ in presence of various levels of secular correlation due to different ratios between proper and forced eccentricity. We tested this algorithm in a standard case with a Jupiter--sized planet orbiting inside a putative planetesimal belt finding that it is less collisionally active compared to a self--stirred belt because of the $e - \varpi$ coupling. The eccentricity of the planet is an important parameter in determining the amount of dust production since the erosion rate is 10 times faster when the planet eccentricity increases from 0.1 to 0.6. Also the initial conditions of the belt (either warm or cold) and its average inclination strongly affects $P_i$ and $U_c$ and then its long term collisional evolution in presence of the planet. We finally apply our method to the planetesimal belts supposedly refilling the dust disks around HD 38529 and $\epsilon$ Eridani. In the most collisionally active configurations, only a small fraction of bodies smaller than 100 km are expected to be fragmented over a time--span of 4 Gyr.