A study of 3-dimensional shapes of asteroid families with an application to Eos

TL;DR

This paper introduces a new method to analyze the 3D shapes of asteroid families, exemplified on the Eos family, confirming its age and explaining its non-isotropic features through simulations.

Contribution

The paper presents a rigorous, simple method for comparing observed asteroid family shapes with N-body simulations, accounting for background populations and size distributions.

Findings

Successfully explained the non-isotropic features of Eos family.

Confirmed the age of Eos family as approximately 1.3 Gyr.

Method applicable to other asteroid families.

Abstract

In order to fully understand the shapes of asteroids families in the 3-dimensional space of the proper elements $(a_{\rm p}, e_{\rm p}, \sin I_{\rm p})$ it is necessary to compare observed asteroids with N-body simulations. To this point, we describe a rigorous yet simple method which allows for a selection of the observed asteroids, assures the same size-frequency distribution of synthetic asteroids, accounts for a background population, and computes a $\chi^2$ metric. We study the Eos family as an example, and we are able to fully explain its non-isotropic features, including the distribution of pole latitudes $\beta$. We confirm its age $t = (1.3\pm0.3)\,{\rm Gyr}$; while this value still scales with the bulk density, it is verified by a Monte-Carlo collisional model. The method can be applied to other populous families (Flora, Eunomia, Hygiea , Koronis, Themis, Vesta, etc.).