THE WAVELET TRANSFORM - A NEW TOOL FOR ASTEROID FAMILY DETERMINATION

An analysis based on the wavelet transform has been performed in order to identify families in the proper elements space of asteroids. This multi-scale analysis has been made on a set of 4100 proper element computed by a new second order fourth-degree secular perturbation theory (Milani and Knezevic 1990). A metric has been defined in the proper element space in order to give a dynamical definition of families. This metric is related to the incremental velocity needed for orbital change after the ejection from a fragmented parent body. A degree of significance has been established from the same analysis on a quasi-random distribution, matching the large scale structure of the real distribution. The influence of the metric has been tested as well as the sensitivity of families to small variations of the proper elements within the accuracy of the theory. A cross comparison has been made between these results and the families obtained from the same data by another method (Zappala et al. 1990). A good agreement between these two different methods has been established not only for the well known populous families, but also for the little ones the existence of which seemed before to depend on the method used.