Asteroid families interacting with secular resonances

Asteroid families are formed as the result of collisions. Large fragments are ejected with speeds of the order of the escape velocity from the parent body. After a family has been formed, the fragments' orbits evolve in the space of proper elements because of gravitational and non-gravitational perturbations, such as the Yarkovsky effect. Disentangling the contribution to the current orbital position of family members caused by the initial ejection velocity field and the subsequent orbital evolution is usually a difficult task. Among the more than 100 asteroid families currently known, some interact with linear and non-linear secular resonances. Linear secular resonances occur when there is a commensurability between the precession frequency of the longitude of the pericenter (g) or of the longitude of node (s) of an asteroid and a planet, or a massive asteroid. The linear secular resonance most effective in increasing an asteroid eccentricity is the ν₆ , that corresponds to a commensurability between the precession frequency g of an asteroid and Saturn's g₆ . Non-linear secular resonances involve commensurabilities of higher order, and can often be expressed as combinations of linear secular resonances. This is the case, for instance, of the z_k = k(g -g₆) +(s -s₆) resonances. Asteroid families that are crossed by, or even have a large portion of their members, in secular resonances are of particular interest in dynamical astronomy. First, they often provide a clear evidence of asteroid orbit evolution due to the Yarkovsky effect. Second, conserved quantities of secular dynamics can be used to set valuable constraints on the magnitude of the original ejection velocity field. For the case of the ν₆ secular resonance, objects in anti-aligned (paradoxal) librating states can be prevented to achieve high values of eccentricity and remain long-term stable (the case for members of the Tina family). Finally, by changing the value of inclination of family members, and, indirectly, of the v_W component of the observed ejection velocity field, nodal secular resonances with massive asteroids or dwarf planets, such as the s -s_C secular resonance with Ceres, can cause v_W to become more and more leptokurtic (i.e., more peaked and with larger tails than that of a Gaussian distribution). By simulating fictitious asteroid families and by requiring that the current value of the Pearson kurtosis of v_W , γ₂(v_W) , be attained, independent constraints on the value of families ages can be obtained for families affected by these kinds of resonances.