Neptune trojan formation during planetary instability and migration

Abstract

Aims. We investigate the process of Neptune trojan capture and permanence in resonance up to the present time based on a planetary instability migration model. Methods. We do a numerical simulation of the migration of the giant planets in a planetesimal disk. Several planetesimals became trapped in coorbital resonance with Neptune, but no trojan survived to the end of the integration at 4.5 Gy. We increased the statistics by running synthetic integrations with cloned particles from the original integration and keeping the same migration rates of the planets. Results. For the synthetic integrations, Neptune trojans survived to the end of the simulations. The total mass that corresponds to these surviving trojans is about 1.6 × 10-4 Earth mass and the distributions of eccentricities, inclinations, and libration amplitudes are respectively 0.007-0.173, 4.9°-32.9°, and 6.9°64.3°. In a specific run where Neptune to Uranus mean motion ratio reached 1.963 and decreased to its present value (1.961), many more trojans escaped the coorbital resonance with Neptune and in the end there was an equivalent mass of 5 × 10-5 Earth mass of Neptune trojans. Conclusions. The simulations yielded Neptune trojans that match the orbital distribution of real Neptune trojans quite well. Since planetary migration in an instability model shows the possibility that in the past Neptune was a little farther from the Sun than it is today, it is reasonable to consider this possibility to explain the relatively low mass of Neptune trojans.