Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber

DUGARO, A.; ZANARDI, M.; DE ELÍA, G. C.; NAOZ, S.

ASTRONOMY AND ASTROPHYSICS

EDP SCIENCES S A

Lugar: Paris; Año: 2019 vol. 627 p. 1 - 15

0004-6361

AIMS: We analyze the behavior of the argument of pericenter $omega_2$ of an outer particle in the elliptical restricted three-body problem, focusing on the $omega_2$ resonance or inverse Lidov-Kozai resonance.   METHODS: First, we calculate the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle´s $omega_2$ precession rate $(domega_2/dau)$. Then, we derive analytical criteria that determine the vanishing of the $omega_2$ quadrupole precession rate $(domega_2/dau)_{ext{quad}}$ for different values of the inner perturber´s eccentricity $e_1$. Finally, we use such analytical considerations and describe the behavior of $omega_2$ of outer particles extracted from N-body simulations developed in a previous work.RESULTS: Our analytical study indicates that the values of the inclination $i_2$ and the ascending node longitude $Omega_2$ associated with the outer particle that vanish $(domega_2/dau)_{ext{quad}}$ strongly depend on the eccentricity $e_1$ of the inner perturber. In fact, if $e_1 $ 0.40825), $(domega_2/dau)_{ext{quad}}$ is only vanished for particles whose $Omega_2$ circulates (librates). For $e_1$ between 0.25 and 0.40825, $(domega_2/dau)_{ext{quad}}$ can be vanished for any particle for a suitable selection of pairs ($Omega_2$, $i_2$). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate and high values of $e_1$. Moreover, such a resonance produces distinctive features in the evolution of a particle in the ($Omega_2$, $i_2$) plane. In fact, if $omega_2$ librates and $Omega_2$ circulates, the extremes of $i_2$ at $Omega_2 =$ 90$^{circ}$ and 270$^{circ}$ do not reach the same value, while if $omega_2$ and $Omega_2$ librate, the evolutionary trajectory of the particle in the ($Omega_2$, $i_2$) plane evidences an asymmetry respect to $i_2 =$ 90$^{circ}$. The evolution of $omega_2$ associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation.