Identification of asteroid families in Trojans and Hildas

Abstract

A simple empirical method of asteroid proper elements calculation is proposed. The method uses distributions of osculating orbital elements, such as longitude of ascending node, inclination and longitude of perihelion, and eccentricity. These distributions make it possible to obtain forced elements. The forced elements define long-periodic variations of osculating elements. The proper elements are calculated by elimination of the short- and long-periodic perturbations from the osculating ones. In this paper, the short-period perturbations were removed by means of numerical integration, whereas the removal of long-periodic terms was done by using the coordinate transformation formula. The derived proper elements are accurate enough to search for asteroid families. The method is effective in both non-resonant and resonant cases. As an example, the asteroids in 3:2 and 1:1 mean-motion resonances with Jupiter were investigated. The proper elements were calculated for all multi-opposition asteroids in these zones. Due to the large number of the asteroids real families are clearly apparent in distributions of the proper elements. An approach similar to the hierarchical clustering method was used for identification of the families. Using this technique, two robust asteroid families of (1911) Schubart and (153) Hilda were identified in the Hilda-group. And four families were found among L4-trojans: (3548) Eurybates, (2148) Epeios, (624) Hektor, and (9799) 1996RJ. The taxonomy of these families was analysed. The most tight and populated families consist of C and X asteroids, while the D-type asteroids predominate in the background population. No reliable families have been identified near the libration point L5.