Title: Identifying ancient asteroid families: prospecting the original planetesimal population

Abstract: Asteroid families are the remnant fragments of asteroids broken apart by collisions. There are only a few known Main Belt (MB) asteroid families with ages greater than 2 Ga (Brož et al., 2013; Spoto et al., 2015). Estimates based on the family producing collision rate suggest that the lack of >2 Ga-old families may be due to a selection bias in classic techniques used to identify families. Family fragments disperse in their orbital elements, semi-major axis, a, eccentricity, e, and inclination, i, due to secular resonances and the non-gravitational Yarkovsky force. This causes the family fragments to be more difficult to identify with the hierarchical clustering method (HCM), which attempts to find clusters in orbital element space when applied to family fragments’ elements as the fragments age. We have developed a new technique that is insensitive to the spreading of fragments in e and i by searching for V-shaped correlations of family members in a and asteroid diameter, D. A group of asteroids is identified as a collisional family if its boundary in the a vs. 1/D plane has a characteristic V-shape which is due to the size-dependent Yarkovsky effect. The V-shape technique is demonstrated on the known families and families difficult to identify by HCM, and used to discover a 4 Ga-old family linking most dark asteroids in the inner MB not included in any known family (Delbo’ et al., 2017). The 4 Ga-old family reveals asteroids with D > 35 km that do not belong to any asteroid family implying that they originally accreted from the protoplanetary disk and support recent theories on the formation of asteroids (Morbidelli et al., 2009).