On the Erigone family and thez₂secular resonance

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 ν 6 and z 1 secular resonances, the z 2 resonance is characterized by one stable equilibrium point at σ = 180• in the z 2 resonance plane (σ, dσ dt ), where σ is the resonant angle of the z 2 resonance. Diffusion in this plane occurs on timescales of ≃ 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.

Asteroid families interacting with secular resonances

“…A similar behavior was observed for the population of asteroids currently inside the M2:1A meanmotion resonance [21]. The minimum time needed to reach a steady-state could therefore be used to set lower limits on the age of the Erigone family Carruba et al [14] analyzed the resonant angle of all simulated particles, and computed the fraction of family members in z 2 resonant states as a function of time. Fig.…”

“…There are asteroid families interacting with non-linear secular resonances of the z k sequence. More than 75% of the members of the Agnia [46] and Padua [9] families are on librating states of the z 1 =g − g 6 + s − s 6 resonance, while 14% of the members of the Erigone family are in librating states of the z 2 = 2(g − g 6 ) + s − s 6 resonance [14]. The Agnia family, which is now know to have the sub-family of (3395) Jitka [42], was the first group identified to have the majority of its members in librating states of a non-linear secular resonance.…”

“…Concerning other families, Carruba et al [14] showed that the K ′ 2 (z 2 ) = K ′ 2 = K 2 /K 1 = √ 1 − e 2 (3 − cos i) quantity is not preserved for asteroids members of the Erigone family. Yet, it is possible to obtain information on the age of this group from secular dynamics.…”

“…Carruba et al [14] generated a fictitious Erigone family with optimal V EJ parameter, as found with Yarko-YORP methods, and integrated this group over 400 My, beyond the maximum possible value of the age of this group. They then analyzed the resonant argument σ of the z 2 secular resonance for all simulated particles.…”

The young Datura asteroid family

“…Consequently, the orbital eccentricity and inclination show long-term oscillations with this period and this effect makes determination of their proper values uncertain. The z 2 resonance is rather weak, such that its width is only 0.2−0.3 arcsec yr −1 in the Datura zone (e.g., Milani & Knežević 1994;Carruba et al 2016a). In order to confirm the membership of small asteroids in the Datura family, especially for those residing on badly constrained orbits for which we do not have proper elements computed, we performed the following test.…”