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

Abstract

Following our earlier work studying the formation of the Neptunian Trojan population during the planet's migration, we present results examining the eventual fate of the Trojan clouds produced in that work. A large number of Trojans were followed under the gravitational influence of the giant planets for a period of at least 1Gyr. 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°). The survival rate of 'pre-formed' Neptunian Trojans [which in general survived on dynamically cold orbits (e < 0.1,i < 5°-10°)] varied between ∼5 and 70percent, depending on the precise detail of their initial orbits. In contrast, the survival rate of 'captured' Trojans (on final orbits spread across a larger region of the e-i element space) was markedly lower, ranging between 1-10 per cent after 4 Gyr. Taken in concert with our earlier work and the broad i-distribution of the observed Trojan population, 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 present-day Trojan population would number ∼1 per cent of that which was present at the end of the planet's migration (i.e. survival rate of ∼1 per cent), with the bulk being sourced from captured, rather than pre-formed objects. We note, however, that even those scenarios still fail to reproduce the presently observed portion of the Neptune Trojan population moving on orbits with e < 0.1 but i > 20°. Dynamical integrations of the presently observed Trojans show that five out of the seven are dynamically stable on time-scales comparable to the age of the Solar system, while 2001 QR322 exhibits significant dynamical instability on time-scales of less than 1 Gyr. The seventh Trojan object, 2008 LC18, was only recently discovered and has such large orbital uncertainties that only future studies will be able to determine its stability. © 2010 The Authors Monthly Notices of the Royal Astronomical Society © 2010 RAS.