Influence of planets on debris discs in star clusters -- II. The impact of stellar density

TL;DR

This study uses numerical simulations to explore how stellar density in star clusters affects debris disc dynamics and planetary system evolution, revealing complex interactions that influence debris retention and orbital properties.

Contribution

It introduces a combined N-body simulation approach to analyze the impact of stellar density on debris discs and planetary systems in star clusters, highlighting the nuanced effects of cluster environment.

Findings

Higher stellar density initially increases the planet's influence range.

Eccentricities and inclinations of debris particles increase with density.

Presence of a planet reduces debris orbital eccentricities and inclinations.

Abstract

We present numerical simulations of planetary systems in star clusters with different initial stellar densities, to investigate the impact of the density on debris disc dynamics. We use LPS+ to combine N-body codes NBODY6++GPU and REBOUND for simulations. We simulate debris discs with and without a Jupiter-mass planet at 50 au, in star clusters with N = 1k - 64k stars. The spatial range of the remaining planetary systems decreases with increasing N. As cluster density increases, the planet's influence range first increases and then decreases. For debris particles escaping from planetary systems, the probability of their direct ejection from the star cluster decreases as their initial semi-major axis (a0) or the cluster density increases. The eccentricity and inclination of surviving particles increase as cluster density increases. The presence of a planet leads to lower eccentricities and inclinations of surviving particles. The radial density distribution of the remaining discs decays exponentially in sparse clusters. We derive a general expression of the gravitational encounter rate. Our results are unable to directly explain the scarcity of debris discs in star clusters. Nevertheless, given that many planetary systems have multiple planets, the mechanism of the planet-cluster combined gravitational influence on the disc remains appealing as a potential explanation.