The stability of unevenly spaced planetary systems

TL;DR

This study investigates the dynamical stability of multi-planet systems with uneven orbital spacings through extensive N-body simulations, revealing how non-uniform separations significantly influence orbital crossing times and collision likelihoods.

Contribution

It introduces a detailed analysis of stability in systems with non-uniform planetary spacings, extending previous models based on uniform separations.

Findings

Reducing one planetary spacing shortens crossing time by an order of magnitude.

First collisions are linked to the initial closest separation pair.

Existing formulas for evenly spaced systems need updating for realistic, uneven systems.

Abstract

Studying the orbital stability of multi-planet systems is essential to understand planet formation, estimate the stable time of an observed planetary system, and advance population synthesis models. Although previous studies have primarily focused on ideal systems characterized by uniform orbital separations, in reality a diverse range of orbital separations exists among planets within the same system. This study focuses on investigating the dynamical stability of systems with non-uniform separation. We considered a system with 10 planets with masses of $10^{-7}$ solar masses around a central star with a mass of $1$ solar mass. We performed more than 100,000 runs of N-body simulations with different parameters. Results demonstrate that reducing merely one pair of planetary spacing leads to an order of magnitude shorter orbital crossing times that could be formulated based on the Keplerian periods of the closest separation pair. Furthermore, the first collisions are found to be closely associated with the first encounter pair that is likely to be the closest separation pair initially. We conclude that when estimating the orbital crossing time and colliding pairs in a realistic situation, updating the formula derived for evenly spaced systems would be necessary.