标题： 霍夫迈斯特小行星族 显示英文标题

标题： The Hoffmeister asteroid family

摘要： 霍夫迈斯特家族是一个位于主带中心的C型集团。 从动力学角度来看，它很重要，因为它与谷神星的${\nu}_{1C}$节点长期共振，这显著增加了低半长轴家族成员的倾角离散度。 作为结果，霍夫迈斯特家族在半长轴低于其中心的倾角值分布明显呈尖峰态，这可以用来对家族形成时的最终喷射速度场设置限制。 通过对从高斯方程得到的喷射速度场的$v_W$分量（${\gamma}_2(v_W)$）的峰度随时间变化的分析，针对具有不同喷射速度场值的虚构霍夫迈斯特家族进行分析，我们能够排除霍夫迈斯特家族年龄超过335百万年的可能性。 目前观测到的霍夫迈斯特家族倾角分布的限制表明，其最终喷射速度参数$V_{EJ}$应低于25~m/s。 结合其他来自倾角和${\gamma}_2(v_W)$的限制，雅科-约普蒙特卡洛方法对家族年代的计算结果表明，霍夫迈斯特家族应为$220^{+60}_{-40}$~百万年，喷射参数为$V_{EJ}= 20\pm5$~m/s。 显示英文摘要

摘要： 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.