Mathematics
Scientific paper
Feb 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994aj....107..772z&link_type=abstract
Astronomical Journal (ISSN 0004-6256), vol. 107, no. 2, p. 772-801
Mathematics
67
Asteroid Belts, Asteroids, Astronomical Catalogs, Classifications, Cluster Analysis, Statistical Analysis, Hierarchies, Robustness (Mathematics), Spatial Distribution
Scientific paper
A new search for statistically significant groupings has been carried out in a sample of 6212 main belt asteroids, including 2220 unnumbered multiopposition objects. We have classified 2114 asteroids in 20 groupings with the highest degree of statistical significance; up to 242 other asteroids belong to up to 29 groupings which could be accepted by relaxing -- to various degrees -- the reliability requirements. Although this total could be contaminated by a small percentage of interlopers, it is clear that the family asteroids are a significant fraction of the total main belt population; this conclusion is insensitive to the threshold of reliability for the families. Proper elements by Milani & Knezevic, version 5.7 (1992) were used, and a fully automated hierarchical clustering method, improving on that of Zappala et al. (1990), was applied to identify significant asteroid groupings plunged into a nonuniform quasi-random background. The groupings detected in this way have different degrees of statistical reliability and robustness, both against small variations of the proper elements and against different choices of the metric used to define distances in the proper elements space; the effects of some nonlinear secular resonances lying nearby the groupings were also dealt with. Among the 20 significant and robust groupings identified in our search, we found 7 populous and compact 'clusters,' with fairly reliable memberships, and 5 broader 'clans,' whose boundaries and internal structure are still uncertain; in addition, a few tens of marginally significant and/or weaker 'clumps' were detected. Among the clusters, several 'families' can be confirmed by physical data and interpreted as the result of single collisional events, ranging from giant craters to complete disruptions. On the contrary, for the clans, both the dynamical structure and the available physical information suggest a more complex collisional history. The results presented here and the comparisons with previous work show that the main features of our family classification are stable and reliable enough to guide future physical studies of asteroids; however, a further increase of the starting set of osculating elements may add important details on the structure of individual families, and lead to the discovery of new ones, originated from smaller parent bodies.
Cellino Alberto
Farinella Paolo
Milani Andrea
Zappalá Vincenzo
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