Asteroid families. I - Identification by hierarchical clustering and reliability assessment

Abstract

Substantial discrepancies between the existing classifications and inconsistencies with the results of physical studies have motivated a research program aimed at deriving an improved classification of asteroids in dynamical families. We analyzed a set of 4100 numbered asteroids, whose proper elements had been computed by a new second-order, fourth-degree secular perturbation theory [Milani and Knežević 1990, Celestial Mech. (submitted)], and checked with numerical integrations to assess their long-term stability. A multivariate data analysis technique (hierarchical clustering) was applied to build for each zone of the belt a dendrogram in the space of proper elements, with a distance function related to the incremental velocity needed for orbital change after ejection from a fragmented parent body. Families were then identified by comparing this dendrogram with a similar one, derived for a quasirandom distribution of elements matching the large-scale structure of the real distribution. A significance parameter was associated with each family, measuring its departure from random concentrations, and two robustness parameters were obtained by repeating the classification procedure after varying the elements by small amounts (consistent with the results of numerical tests of their long-term stability) and changing the coefficients of the distance function. The most significant and robust families are those associated with Themis, Eos, and Koronis, that collectively include about 14% of the known main-belt population; but 12 more reliable and robust families were found throughout the belt, most of which partially match those found in previous classifications. In the Flora region of the inner belt, a reliable identification of families is difficult, since the background has a high density and the accuracy of proper eccentricities and inclinations is poor, mainly because of the proximity to the strong ν6 secular resonance. Other results include: a relatively populous Eunomia family, lacking large C-type members; a small family having Vesta as its largest object; the disappearance of the unlikely association in one family (Nysa-Hertha) of M, F, and E types; the existence of two small, but robust families with sizeable largest members in the Themis region, at moderate inclinations.