2019A&A...627A..17D

Aims. We analyze the behavior of the argument of pericenter ω₂ of an outer particle in the elliptical restricted three-body problem, focusing on the ω₂ resonance or inverse Lidov-Kozai resonance. Methods. First, we calculated the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle's ω₂ precession rate (dω₂/dτ). Then, we derived analytical criteria that determine the vanishing of the ω₂ quadrupole precession rate (dω₂/dτ)_quad for different values of the inner perturber's eccentricity e₁. Finally, we used such analytical considerations and described the behavior of ω₂ of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i₂ and the ascending node longitude Ω₂ associated with the outer particle that vanish (dω₂/dτ)_quad strongly depend on the eccentricity e₁ of the inner perturber. In fact, if e₁<0.25 (>0.40825), (dω₂/dτ)_quad is only vanished for particles whose Ω₂ circulates (librates). For e₁ between 0.25 and 0.40825, (dω₂/dτ)_quad can be vanished for any particle for a suitable selection of pairs (Ω₂, i₂). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate, and high values of e₁. Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω₂, i₂) plane. In fact, if ω₂ librates and Ω₂ circulates, the extremes of i₂ at Ω₂=90° and 270° do not reach the same value, while if ω₂ and Ω₂ librate, the evolutionary trajectory of the particle in the (Ω₂, i₂) plane shows evidence of an asymmetry with respect to i₂=90°. The evolution of ω₂ associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation.