Hilda Asteroids as Possible Probes of Jovian Migration

Abstract

We show that the peculiar eccentricity distribution of the Hilda asteroids, objects that librate at the 3 : 2 mean motion resonance with Jupiter, as well as their distribution about the resonance itself, can be nicely reproduced from captured field asteroids if Jupiter has migrated sunward by about 0.45 AU over a time greater than 100,000 years. The latter is a lower limit and longer times are more likely, while the former quantity depends to some degree on the initial eccentricity distribution, but a fit to the observations fails unless it lies in the range of 0.4 to about 0.5 AU, where the lower value is particularly well established. We have included some integrations comparable to the solar system's age to show that many Hilda orbits with a broad range of proper eccentricity, ep, and, most importantly, those with ep < 0.10, are stable over such times. The observed fact that there are very few Hildas with ep < 0.10 strengthens the case for a migration greater than about 0.4 AU because, as we discuss, processes intimately linked with it eliminate most of the low-ep bodies automatically. A relatively much smaller but not negligible number of orbits at the 4 : 3 resonance are similarly stable, and one possible reason needing further investigation for the near-absence of real bodies of any eccentricity there (one asteroid) might be traced to the passage of Jupiter and Saturn through a 5 : 2 orbital resonance.