The role of secular resonances in the history of Trojans

We have investigated the possible role of secular resonances in the dynamic al evolution of Trojans during the early phases of the Solar System. Accord ing to our previous studies (Marzari and Scholl 1998a, 1998b) a significant population of planetesimals can be captured in Jupiter and Saturn Trojan o rbits by the mass growth of the two planets. If we compare the implications of our model with the present Trojan populations, two severe problems aris e: (1) All the captured planetesimals have low inclinations while the obser ved Jupiter Trojans have significantly higher inclinations exceeding even 2 0 degrees. (2) No Trojan has been discovered near Saturn's Lagrangian point s. In the present paper, we show that the presence of secular resonances in th e Trojan regions of both Jupiter and Saturn may explain this contradiction between our model for Trojan capture and observations. We relate the high inclinations of Jupiter Trojans to the nu(16) secular re sonance, even if this resonance is effective in pumping up inclinations for orbits with comparatively large libration amplitudes of about 60 degrees ( by "libration amplitude" here we mean the difference between the maximum an d minimum values of the critical argument). How do we explain then the pres ent small libration-high inclination Trojans? If we combine the effects of the vie secular resonance with other dynamical and physical processes affec ting Trojan orbits, the present dynamical structure of Jupiter Trojans may be explained as follows: (a) During the growth of Jupiter and Saturn: Troja ns with large libration amplitudes and low inclinations are trapped. Librat ion amplitudes decrease slightly due to continuing proto-planetary growth. Eventually, synergy between Kozai resonance and proto-planetary growth may yield some Trojans with inclinations up to about 10 degrees (Marzari and Sc holl 1998b). (b) After the growth of Jupiter and Saturn has been completed: Trojans with large libration amplitudes near the nu(16) secular resonance increase their orbital inclinations up to 20 degrees while keeping their la rge libration amplitudes. We show in this paper that the nu(16) is effectiv e also at initial inclinations lower than 4 degrees. (c) Collisions reduce libration amplitudes (Marzari and Scholl 1998b) while the inclinations rema in high. High-inclination Trojans are then displaced in more stable orbits. (d) Collisions and dynamical outflow (Levison et al. 1997) shape the prese nt Trojan population. The absence of observed Saturn Trojan orbits was attributed by previous stu dies to instability caused by the neighboring 5:2 resonance with Jupiter (D e la Barre et al. 1996, Mikkola and Innanen 1989, Innanen and Mikkola 1992) . By integrating the trajectories of test bodies started in Saturn Trojan o rbits, we show that the main source for instability is the presence of the mixed secular resonance 2<(omega)over bar>(S) -<(omega)over bar>(J) - <(ome ga)over bar>(T) (S for Saturn, J for Jupiter, and T for Trojan) inside the libration regions around L4 and L5, The crossing of this secular resonance destabilizes on a short time scale (10(5) years) most of the planetesimals trapped in low-libration Trojan orbits, and it is also responsible for the slow outflow of the remaining large librators. The nu(6) resonance may cont ribute to the instability of low-libration Saturn Trojan orbits on a much s horter time scale. (C) 2000 Academic Press.