Dynamics of Jupiter Trojans during the 2:1 mean motion resonance crossing of Jupiter and Saturn

In the early phase of the Solar system evolution, while the outer planets migrated due to their interaction with a planetesimal disc, Jupiter may have crossed the 2:1 mean motion resonance with Saturn. It is well known that this dynamical event has profound consequences on the evolution of an alleged initial Trojan population of Jupiter. In this paper, we analyse in details the dynamics of Jupiter Trojans during the resonance crossing. We find that orbital instability is not confined to the central 2:1 resonance region but occurs in a more extended region where secular and secondary resonances perturb the Trojan orbits while the planets approach, cross and leave the 2:1 resonance. In addition, Jupiter and Saturn are locked after the resonance crossing in an apsidal corotation which has an additional destabilizing effect on Trojans. The synergy of the secular resonance, secondary resonances and apsidal corotation is needed to fully remove an initial Trojan population. New Trojans can be temporarily captured from the planetesimal disc while Jupiter crosses this extended instability region. After the disappearance of major secondary resonances, the secular resonance and the break of the apsidal corotation, the temporarily captured Trojans are locked and can remain stable over long time-scales