Asteroid families age determination: the role of the physical effects
Authors: Dell'Oro Aldo , Boccenti Jacopo , Spoto Federica , Paolicchi Paolo , Knezevic Zoran 
Published: October 2020

The availability of &#160;large data set of asteroids &#160;proper elements madepossible in recent years a deeper and deeper analysis of the structureof the &#160;asteroid dynamical families in &#160;the Main Belt (Milani &#160;et al.,2014). At the same time the &#160;Yarkovsky effect, the importance of whichhas been &#160;largely recognized, &#160;has imposed &#160;a new &#160;data interpretationparadigm. &#160; Precisely &#160;the &#160;Yarkovsky &#160;effect &#160;is &#160;the &#160;basis &#160;of &#160;oneestimation method &#160;of the age &#160;of the asteroid families &#160;analyzing theshape of the family members &#160;distribution in the plane diameter versusproper semimajor axes, the so called V-shape (Spoto et al., 2015).This very important &#160;goal has been achieved under &#160;the assumption thatthe &#160;post-formation &#160;evolution of &#160;the &#160;semimajor &#160;axes producing &#160;theV-shape &#160;structure was &#160;linear &#160;in time &#160;and &#160;dominates their &#160;presentdispersion. &#160;In &#160;particular the &#160;impact of the &#160;initial values &#160;of thefragments ejection &#160;velocities, determining the initial &#160;dispersion ofthe semimajor &#160;axes, is supposed &#160;to be marginal, &#160;assumption probablycorrect for old enough families. If &#160;this is not the case, the initialejection velocity &#160;field introduces a more &#160;or less large bias &#160;in theage &#160;determination. &#160;We &#160;conducted a &#160;series of &#160;numerical experimentssimulating &#160;the &#160;formation and &#160;dynamical &#160;evolution &#160;of the &#160;asteroidfamilies in order to evaluate the extent of this bias.Moreover in &#160;our model we &#160;included a series of &#160;mechanisms concerningthe initial &#160;break-up outcomes. &#160;In particular &#160;two aspects &#160;have beentaken &#160;into &#160; account: &#160;the &#160; effect &#160;of &#160;the &#160; initial &#160;gravitationalre-accumulation &#160;on the &#160;structure of &#160;the V-shape &#160;and the &#160;effect ofpossible &#160;correlations between &#160;spin direction &#160;and ejection &#160;velocitydirection (Milani et &#160;al., 2019). We show how the &#160;former effect couldbe responsible of &#160;some systematic features of &#160;the V-shape structure,while &#160;the second &#160;can in &#160;some &#160;cases mitigate &#160;the bias &#160;in the &#160;agedetermination introduced by the initial ejection field.Finally we discuss the role of &#160;the family members spin axes evolutiondue to &#160;non destructive &#160;collisions, affecting &#160;the efficiency &#160;of theYarkovsky-driven &#160;semimajor axis &#160;mobility. &#160;We show &#160;how this &#160;lattermechanism modifies the determination of the age.&#160;References:Milani A., Cellino A., Knezevic Z., Novakovic B., Spoto F., Paolicchi P.2014.Asteroid families classification: Exploiting very large datasets.Icarus, 239, 46-73.Spoto F., Milani A., Knezevic Z.2015.Asteroid family ages.Icarus, 257, 275-289.Milani A., Knezevic Z., Spoto F., Paolicchi P.2019.Asteroid cratering families: recognition and collisional interpretation.Astronomy and Astrophysics, 622, A47.