Yarkovsky-evolved asteroid dynamical families: a correlation between their present properties and the impact geometry?

The original orbital elements of the members of a dynamical family are subject to changes, some connected to the overall dynamical evolution, and others due to the Yarkovsky effect (mainly the diurnal effect). While the former term may be analyzed in terms of proper elements, the latter one introduces a sort of ageing of proper elements. However, the Yarkovsky-driven mobility depends on the spin vector of a fragment- after the collisional and, possibly, the reaccumulation processes; the spin vector is not -in general -randomly oriented, but connected to the impact geometry and to the physical properties of the collision. Thus the spin vector and the initial ejection velocity may be strongly correlated. In this paper we try, on the basis of simplified assumptions, to discuss how the original distribution of family members in the space of orbital elements evolves in time, due to the Yarkovsky effect, and how far this evolution may differ according to different impact geometries and physical assumptions.