Dynamical portrait of the Hoffmeister asteroid family

Abstract

The (1726) Hoffmeister asteroid family is located in the middle of the Main Belt, between 2.75 and 2.82 AU. It draws our attention due to its unusual shape when projected to the semi-major axis vs. inclination plane. Actually, the distribution of family members as seen in this plane clearly suggests different dynamical evolution for the two parts of the family delimited in terms of semi-major axis.Therefore, we investigate here the dynamics of the family members aiming primarily to explain the observed unusual shape, but we also reconstruct the evolution of the whole family in time, and estimated its age.The Hoffmeister family is close to the fourth degree secular resonance z1=g-g6+s-s6, and in the neighborhood of the most massive asteroid (1) Ceres, each of these possibly being responsible for the strange shape of the family. To identify which ones, if any, among the different possible dynamical mechanisms are actually at work here, we performed a set of numerical integrations. We integrate the orbits of test particles over 300 Myr, as the age of the Hoffmeister family was previously roughly estimated to be 300 ± 200 Myr. Moreover, in order to identify and isolate the main perturber(s), we repeat four times the integrations using each time a different dynamical model, taking or not into account the Yarkovsky effect and dwarf planet Ceres as a perturbing body.Our results reveal the significant role of a so far overlooked dynamical aspect, namely a secular resonance between the dwarf planet Ceres and other asteroids. In particular, we show that the post-impact evolution of the Hoffmeister asteroid family is a direct consequence of the nodal secular resonance with Ceres.