Jupiter Trojan asteroids are located around L4 and L5 Lagrangian points on relatively stable orbits, in 1:1 MMR with Jupiter. However, not all of them lie in orbits that remain stable over the age of the Solar System. Unstable zones allow some Trojans to escape in time scales shorter than the Solar System age. This may contribute to populate other small body populations. In this paper, we study this process by performing long-term numerical simulations of the observed Trojans, focusing on the trajectories of those that leave the resonance. The orbits of current Trojans are taken as initial conditions and their evolution is followed under the gravitational action of the Sun and the planets. We find the rate of escape of Trojans from L5, ~1.1 times greater than from L4. The majority of escaped Trojans have encounters with Jupiter although they have encounters with the other planets too. Almost all escaped Trojans reach the comet zone, ~90% cross the Centaur zone and only L4 Trojans reach the transneptunian zone. Considering the real asymmetry between L4 and L5, we show that 18 L4 Trojans and 14 L5 Trojans with diameter D > 1 km are ejected from the resonance every Myr. The contribution of the escaped Trojans to other minor body populations would be negligible, being the contribution from L4 and L5 to JFCs and no-JFCs almost the same, and the L4 contribution to Centaurs and TNOs, orders of magnitude greater than that of L5. Considering the collisional removal, besides the dynamical one, and assuming that Trojans that escape due to collisions follow the same dynamical behavior that the ones removed by dynamics, we would have a minor contribution of Trojans to comets and Centaurs. However, there would be some specific regions were escaped Trojans could be important such as ACOs, Encke-type comets, S-L 9-type impacts on Jupiter and NEOs.
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