On the highly inclined $v_W$ leptokurtic asteroid families

Abstract

$v_W$ leptokurtic asteroid families are families for which the distribution of the normal component of the terminal ejection velocity field $v_W$ is characterized by a positive value of the $γ_2$ Pearson kurtosis, i.e., they have a distribution with a more concentrated peak and larger tails than the Gaussian one. Currently, eight families are known to have $γ_2(v_W) > 0.25$. Among these, three are highly inclined asteroid families, the Hansa, Barcelona, and Gallia families. As observed for the case of the Astrid family, the leptokurtic inclination distribution seems to be caused by the interaction of these families with node secular resonances. In particular, the Hansa and Gallia family are crossed by the $s-s_V$ resonance with Vesta, that significantly alters the inclination of some of their members. In this work we use the time evolution of $γ_2(v_W)$ for simulated families under the gravitational influence of all planets and the three most massive bodies in the main belt to assess the dynamical importance (or lack of) node secular resonances with Ceres, Vesta, and Pallas for the considered families, and to obtain independent constraints on the family ages. While secular resonances with massive bodies in the main belt do not significantly affect the dynamical evolution of the Barcelona family, they significantly increase the $γ_2(v_W)$ values of the simulated Hansa and Gallia families. Current values of the $γ_2(v_W)$ for the Gallia family are reached over the estimated family age only if secular resonances with Vesta are accounted for.