Characterising the efficiency of the hierarchical clustering method

The Hierarchical Clustering Method (HCM) is the de-facto clustering algorithm in the search for groups of “family” asteroids that were formed due to the breakup of a larger parent body. In this work, we feed to the HCM a number of synthetic asteroid families at different positions in the main belt and of different dynamical ages. We then measure how effectively the algorithm can recover the family members, while minimising the inclusion of non-family members. The three metrics of “accuracy”, “precision”, and “recall” were used to characterise the HCM efficiency. The most important factor in the HCM’s ability to cluster families was found to be the relative number density between the family and the asteroid background it is situated in. We compared families to the background in a parameter space defined by proper orbital elements semi-major axis, eccentricity, and inclination (a, e, i), and for families approximately four times denser than the background ∼ 50% of the original family is recovered independently of age. However, to reach these relative densities for families older than 2 Gyr it was necessary to artificially reduce the synthetic background population. We conclude that older families would be all but undetectable in the real main belt, using the HCM. • As asteroid families age, they disperse into and mingle with background asteroids. • Efficiency is primarily decreased through missed family bodies, and not interlopers. • Families older than 2 Gyr are significantly harder to find. • This leads to the phenomena of asteroid family halos, and scarcity in older families.