Origin and Dynamical Evolution of Neptune Trojans - I: Formation and Planetary Migration

We present the results of detailed dynamical simulations of the effect of the migration of the four giant planets on both the transport of pre-formed Neptune Trojans, and the capture of new Trojans from a trans-Neptunian disk. We find that scenarios involving the slow migration of Neptune over a large distance (50Myr to migrate from 18.1AU to its current location) provide the best match to the properties of the known Trojans. Scenarios with faster migration (5Myr), and those in which Neptune migrates from 23.1AU to its current location, fail to adequately reproduce the current day Trojan population. Scenarios which avoid disruptive perturbation events between Uranus and Neptune fail to yield any significant excitation of pre-formed Trojans (transported with efficiencies between 30 and 98% whilst maintaining the dynamically cold nature of these objects). Conversely, scenarios with periods of strong Uranus-Neptune perturbation lead to the almost complete loss of such pre-formed objects. In these cases, a small fraction (~0.15%) of these escaped objects are later recaptured as Trojans prior to the end of migration, with a wide range of eccentricities (<0.35) and inclinations (<40 deg). In all scenarios (including those with such disruptive interaction between Uranus and Neptune) the capture of objects from the trans-Neptunian disk (through which Neptune migrates) is achieved with efficiencies between ~0.1 and ~1%. The captured Trojans display a wide range of inclinations (<40 deg for slow migration, and <20 deg for rapid migration) and eccentricities (<0.35), and we conclude that, given the vast amount of material which undoubtedly formed beyond the orbit of Neptune, such captured objects may be sufficient to explain the entire Neptune Trojan population. (Shortened version)

💡 Research Summary

This paper investigates how the migration of the four giant planets—Jupiter, Saturn, Uranus, and Neptune—shaped the present-day population of Neptune Trojans (NTs). Using high‑resolution N‑body integrations, the authors explore two complementary sources for NTs: (1) “pre‑formed” Trojans that already occupied the 1:1 resonance with Neptune at the time of its formation, and (2) objects captured from a massive trans‑Neptunian disk that Neptune sweeps through as it migrates outward.

Four migration scenarios are examined. Neptune’s initial semimajor axis is set either at 18.1 AU (a relatively compact configuration) or at 23.1 AU (a more distant start). For each starting point, two migration timescales are considered: a rapid 5 Myr migration and a slow 50 Myr migration. Within each of these four cases, the authors further differentiate between “weak” and “strong” Uranus–Neptune interactions, the latter representing episodes where the two planets experience close encounters that strongly perturb each other’s orbits.

The simulations contain 10⁴ test particles initially placed in the Neptune L4/L5 regions (the pre‑formed cohort) and 10⁵ particles distributed uniformly between 30 and 50 AU to model the external planetesimal disk. The dynamical evolution of each particle is followed throughout the migration, and the final orbital elements (eccentricity e, inclination i) of those that survive as NTs are recorded.

Key findings are:

1. Transport of pre‑formed Trojans – In the slow‑migration, weak‑interaction case, 30 %–98 % of the original Trojans survive, retaining low e and i (i.e., a dynamically cold population). When strong Uranus–Neptune perturbations occur, the pre‑formed cohort is almost entirely lost; only ~0.15 % of the escaped bodies are recaptured just before migration ends, and these have a broad range of e (<0.35) and i (<40°). Rapid migration leads to a similarly low survival fraction regardless of interaction strength.

2. Capture from the trans‑Neptunian disk – Capture efficiencies range from ~0.1 % to ~1 % depending on migration speed and interaction strength. Slow migration produces captured Trojans with inclinations up to 40°, while rapid migration limits inclinations to ≲20°. Eccentricities in all cases stay below 0.35.

3. Comparison with observations – The known NTs (≈30 objects) display e up to ~0.35 and i up to ~30°, including a handful of high‑inclination members. The slow‑migration, weak‑interaction scenario reproduces both the low‑inclination “cold” component (surviving pre‑formed Trojans) and the high‑inclination “hot” component (captured disk objects). Rapid migration fails to generate enough high‑i objects, and the distant‑start (23.1 AU) runs do not match the observed distribution at all.

4. Mass budget – Assuming a primordial disk mass of ~30 M⊕, a capture efficiency of 0.1 %–1 % would deliver 0.03–0.3 M⊕ of material into the Trojan clouds, far exceeding the estimated current NT mass (~10⁻⁴ M⊕). Thus, the disk provides ample material to populate the entire NT swarm.

5. Hybrid formation model – The authors propose that the real Solar System likely experienced a combination of the two mechanisms. If Uranus–Neptune interactions were mild, most pre‑formed Trojans survive while a modest fraction of disk objects are captured, yielding a mixed population. If strong interactions occurred, the pre‑formed Trojans are essentially erased and the Trojan cloud is built almost entirely from captured disk material. This hybrid picture naturally explains the observed spread in e and i, as well as the overall number of NTs.

In conclusion, the most plausible evolutionary pathway for Neptune Trojans involves a slow (≈5 × 10⁷ yr) outward migration of Neptune from ~18 AU, coupled with relatively weak Uranus–Neptune perturbations. Under these conditions, both the survival of a dynamically cold pre‑formed component and the efficient capture of a dynamically hot component from the trans‑Neptunian disk are achieved, reproducing the full range of orbital properties seen today. Scenarios with rapid migration or a more distant starting point fail to match the data and are therefore disfavored.