Giga-Year Evolution of Jupiter Trojans and the Asymmetry Problem

TL;DR

This study uses long-term numerical simulations to analyze the evolution and asymmetry of Jupiter Trojans over billions of years, revealing that primordial factors likely influence their current population imbalance.

Contribution

It provides new insights into the dynamical evolution of Jupiter Trojans and introduces updated proper elements, highlighting the primordial origin of their asymmetry.

Findings

Approximately 23% of L4 Trojans escaped after 4.5 Gyr.

The asymmetry between L4 and L5 populations increases over time.

Chaotic diffusion alone cannot explain the current asymmetry.

Abstract

We present a series of numerical integrations of observed and fictitious Jupiter Trojan asteroids, under the gravitational effects of the four outer planets, for time-spans comparable with the age of the Solar System. From these results we calculate the escape rate from each Lagrange point, and construct dynamical maps of "permanence" time in different regions of the phase space. Fictitious asteroids in L4 and L5 show no significant difference, showing almost identical dynamical maps and escape rates. For real Trojans, however, we found that approximately 23% o f the members of the leading swarm escaped after 4.5 Gyrs, while this number increased to 28.3% for L5. This implies that the asymmetry between the two populations increases with time, indicating that it may have been smaller at the time of formation/capture of these asteroids. Nevertheless, the difference in chaotic diffusion cannot, in itself, account for the current observed asymmetry (~40%), and must be primarily primordial and characteristic of the capture mechanism of the Trojans. Finally, we calculate new proper elements for all the numbered Trojans using the semi-analytical approach of Beaug\'e and Roig (2001), and compare the results with the numerical estimations by Bro\v{z} and Rosehnal (2011). For asteroids that were already numbered in 2011, both methods yield very similar results, while significant differences were found for those bodies that became numbered after 2011.