The Hoffmeister asteroid family

TL;DR

This study analyzes the Hoffmeister asteroid family to determine its age and ejection velocity parameters using dynamical and statistical methods, concluding it is approximately 220 million years old with a low ejection velocity.

Contribution

It introduces a novel approach combining kurtosis analysis and Monte Carlo simulations to constrain the age and ejection velocities of the Hoffmeister family.

Findings

Hoffmeister family is approximately 220 Myr old.

Ejection velocity parameter V_EJ is around 20 m/s.

Family's inclination distribution constrains its age and ejection velocities.

Abstract

The Hoffmeister family is a C-type group located in the central main belt. Dynamically, it is important because of its interaction with the ${\nu}_{1C}$ nodal secular resonance with Ceres, that significantly increases the dispersion in inclination of family members at lower semi-major axis. As an effect, the distribution of inclination values of the Hoffmeister family at semi-major axis lower than its center is significantly leptokurtic, and this can be used to set constraints on the terminal ejection velocity field of the family at the time it was produced. By performing an analysis of the time behaviour of the kurtosis of the $v_W$ component of the ejection velocity field (${\gamma}_2(v_W)$), as obtained from Gauss' equations, for different fictitious Hoffmeister families with different values of the ejection velocity field, we were able to exclude that the Hoffmeister family should be older than 335 Myr. Constraints from the currently observed inclination distribution of the Hoffmeister family suggest that its terminal ejection velocity parameter $V_{EJ}$ should be lower than 25~m/s. Results of a Yarko-YORP Monte Carlo method to family dating, combined with other constraints from inclinations and ${\gamma}_2(v_W)$, indicate that the Hoffmeister family should be $220^{+60}_{-40}$~Myr old, with an ejection parameter $V_{EJ}= 20\pm5$~m/s.