Survival of Trojan-type companions of Neptune during primordial planet migration

We investigate the survivability of Trojan-type companions of Neptune during primordial radial migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. We adopt the usual planet migration model in which the migration speed decreases exponentially with a characteristic time scale τ (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus1000 test particle Neptune Trojans with initial distributions of orbital eccentricity, inclination, and libration amplitude similar to those of the known jovian Trojans asteroids. We analyze these simulations to measure the survivability of Neptune’s Trojans as a function of migration rate. We nd that orbital migration with the characteristic time scale τ = 106 years allows about 35 % of pre-existing Neptune Trojans to survive to 5τ, by which time the giant planets have essentially reached their nal orbits. In contrast, slower migration with τ = 107 years yields only a 5 % probability of Neptune Trojans surviving to a time of 5τ. Interestingly, we nd that the loss of Neptune Trojans during planetary migration is not a random diusion process. Rather, losses occur almost exclusively during discrete episodes when Trojan particles are swept by secondary resonances associated with mean-motion commensurabilities of Uranu