Origin and dynamical evolution of Neptune Trojans - II. Long-term evolution

Abstract

We present results examining the fate of the Trojan clouds produced in our previous work. We find that the stability of Neptunian Trojans seems to be strongly correlated to their initial post-migration orbital elements, with those objects that survive as Trojans for billions of years displaying negligible orbital evolution. The great majority of these survivors began the integrations with small eccentricities (e < 0.2) and small libration amplitudes (A < 30 - 40{\deg}). The survival rate of "pre-formed" Neptunian Trojans (which in general survived on dynamically cold orbits (e < 0.1, i < 5 - 10{\deg})) varied between ~5 and 70%. By contrast, the survival rate of "captured" Trojans (on final orbits spread across a larger region of e-i element space) were markedly lower, ranging between 1 and 10% after 4 Gyr. Taken in concert with our earlier work, we note that planetary formation scenarios which involve the slow migration (a few tens of millions of years) of Neptune from an initial planetary architecture that is both resonant and compact (aN < 18 AU) provide the most promising fit of those we considered to the observed Trojan population. In such scenarios, we find that the current day Trojan population would number ~1% of that which was present at the end of the planet's migration, with the bulk being sourced from captured, rather than pre-formed objects. We note, however, that even those scenarios still fail to reproduce the currently observed portion of the Neptune Trojan population moving on orbits with e < 0.1 but i > 20{\deg}. Dynamical integrations of the currently observed Trojans show that five out of the seven are dynamically stable on 4 Gyr timescales, while 2001 QR322, exhibits significant dynamical instability. The seventh Trojan object, 2008 LC18, has such large orbital uncertainties that only future studies will be able to determine its stability.