On the Erigone family and the $z_2$ secular resonance

TL;DR

This paper investigates the Erigone asteroid family, using secular resonance dynamics to estimate its age, confirming previous estimates and providing new constraints based on resonance behavior.

Contribution

It introduces a novel approach using $z_2$ secular resonance dynamics to independently constrain the age of the Erigone family.

Findings

Resonance diffusion timescale is approximately 12 My.

Minimum time to reach steady-state librator population is about 90 My.

Resonance analysis supports a family age less than 300 My.

Abstract

The Erigone family is a C-type group in the inner main belt. Its age has been estimated by several researchers to be less then 300 My, so it is a relatively young cluster. Yarko-YORP Monte Carlo methods to study the chronology of the Erigone family confirm results obtained by other groups. The Erigone family, however, is also characterized by its interaction with the $z_2$ secular resonance. While less than 15% of its members are currently in librating states of this resonance, the number of objects, members of the dynamical group, in resonant states is high enough to allow to use the study of dynamics inside the $z_2$ resonance to set constraints on the family age. Like the ${\nu}_{6}$ and $z_1$ secular resonances, the $z_2$ resonance is characterized by one stable equilibrium point at $\sigma = 180^{\circ}$ in the $z_2$ resonance plane $(\sigma, \frac{d\sigma}{dt})$, where $\sigma$ is the resonant angle of the $z_2$ resonance. Diffusion in this plane occurs on timescales of $\simeq 12$ My, which sets a lower limit on the Erigone family age. Finally, the minimum time needed to reach a steady-state population of $z_2$ librators is about 90 My, which allows to impose another, independent constraint on the group age.