The capture of Trojan asteroids by the giant planets during planetary migration

Of the four giant planets in the Solar system, only Jupiter and Neptune are currently known to possess swarms of Trojan asteroids - small objects that experience a 1:1 mean motion resonance with their host planet. In Lykawka et al., we performed extensive dynamical simulations, including planetary migration, to investigate the origin of the Neptunian Trojan population. Utilizing the vast amount of simulation data obtained for that work, together with fresh results from new simulations, we here investigate the dynamical capture of Trojans by all four giant planets from a primordial trans-Neptunian disc. We find the likelihood of a given planetesimal from this region being captured on to an orbit within Jupiter's Trojan cloud lies between several times 10-6 and 10-5. For Saturn, the probability is found to be in the range < 10-6 to 10-5, whilst for Uranus the probabilities range between 10-5 and 10-4. Finally, Neptune displays the greatest probability of Trojan capture, with values ranging between 10-4 and 10-3. Our results suggest that all four giant planets are able to capture and retain a significant population of Trojan objects from the disc by the end of planetary migration. As a result of encounters with the giant planets prior to Trojan capture, these objects tend to be captured on orbits that are spread over a wide range of orbital eccentricities and inclinations. The bulk of captured objects are to some extent dynamically unstable, and therefore, the populations of these objects tend to decay over the age of the Solar system, providing an important ongoing source of new objects moving on dynamically unstable orbits among the giant planets. Given that a huge population of objects would be displaced by Neptune's outward migration (with a potential cumulative mass a number of times that of the Earth), we conclude that the surviving remnant of the Trojans captured during the migration of the outer planets might be sufficient to explain the currently known Trojan populations in the outer Solar system.