Yarkovsky V-shape identification of asteroid families

There are only a few known main belt (MB) asteroid families with ages greater than 2 Gyr (Bro\v{z} et al. 2013, Spoto et al. 2015). Estimates based on the family producing collision rate suggest that the lack of >2 Gyr-old families may be due to a selection bias in current 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, close encounters with massive asteroids and the non-gravitational Yarkovsky force. This causes the family fragments to be indistinguishable from the background of the main belt making them more difficult to identify with the hierarchical clustering method (HCM) with increasing family age. The discovery of the Eulalia and new Polana families in the inner belt relied on new techniques because Yarkovsky spreading made them too disperse to be identified using the classical HCM. The technique used to discover the new Polana and Eulalia families is modified to identify asteroid families by searching for correlations between $a$ and asteroid diameter, $D$, or absolute magnitude, $H$. A group of asteroids is identified as a collisional family if its boundary in the $a$ vs. 1/$D$ or $a$ vs. $H$ planes has a characteristic V-shape which is due to the size dependent Yarkovsky spreading. The V-shape boundary is identified with two separate techniques. The first identifies a border by measuring the drop between the number of objects inside and outside of the border. The second identifies the V-shape border by measuring the number density of objects in $a$ vs. 1/$D$,$H$ space. The V-shape techniques are demonstrated on known families Erigone, Vesta, Koronis, and families difficult to identify by HCM such as Flora, Baptistina, new Polana, Eulalia and Karin. Application of the technique in a search for >2 Gyr-old families throughout the MB is discussed.