Apsidal asymmetric-alignment of Jupiter Trojans

Abstract

The most distant Kuiper belt objects exhibit the clustering in their orbits, and this anomalous architecture could be caused by Planet 9 with large eccentricity and high inclination. We then suppose that the orbital clustering of minor planets may be observed somewhere else in the solar system. In this paper, we consider the over 7000 Jupiter Trojans from the Minor Planet Center, and find that they are clustered in the longitude of perihelion ϖ, around the locations ϖJ + 60○ and ϖJ − 60○ (ϖJ is the longitude of perihelion of Jupiter) for the L4 and L5 swarms, respectively. Then we build a Hamiltonian system to describe the associated dynamical aspects for the co-orbital motion. The phase space displays the existence of the apsidally aligned islands of libration centered on Δϖ = ϖ − ϖJ ≈ ±60○, for the Trojan-like orbits with eccentricities e < 0.1. Through a detailed analysis, we have shown that the observed Jupiter Trojans with proper eccentricities ep < 0.1 spend most of their time in the range of |Δϖ| = 0 − 120○, while the more eccentric ones with ep > 0.1 are too few to affect the orbital clustering within this Δϖ range for the entire Trojan population. Our numerical results further prove that, even starting from a uniform Δϖ distribution, the apsidal alignment of simulated Trojans similar to the observation can appear on the order of the age of the solar system. We conclude that the apsidal asymmetric-alignment of Jupiter Trojans is robust, and this new finding can be helpful to design the survey strategy in the future.

Asymmetry in the number of L4 and L5 Jupiter Trojans driven by jumping Jupiter

“…Recently, we noticed the apsidal asymmetric-alignment of Jupiter Trojans (Li et al 2021). We have shown that the L4 and L5 swarms are both clustered in the longitude of perihelion ( ), around the locations that are +60 • and −60 • away from Jupiter's longitude of perihelion ( J ) respectively.…”

The Von Zeipel–Lidov–Kozai Effect inside Mean Motion Resonances with Applications to Trans-Neptunian Objects

“…The first case is that, when  is equal to that of the resonant center, the magnitude of S becomes zero, meaning that the small body is initially placed at the resonant center. As discussed in the introduction, such a special case with S = 0 has been adopted as an assumption in formulating secular models (Kozai 1985;Yoshikawa 1989;Nesvorný et al 2002;Wan & Huang 2007;Saillenfest et al 2017;Li et al 2021;Pons & Gallardo 2022). The second case is that, when  is equal to that of the saddle point (or the dynamical separatrix), S is equal to the area bounded by the dynamical separatrices, and in this case the assumption that the two degrees of freedom are separable in frequencies fails, leading to the fact that S is no longer an adiabatic invariant (Wisdom 1985;Tennyson et al 1986;Neishtadt 1987;Neishtadt & Sidorenko 2004).…”

“…The simplest approach is to assume the critical argument associated with the MMR at the libration center (Kozai 1985;Yoshikawa 1989;Nesvorný et al 2002;Wan & Huang 2007;Saillenfest et al 2017;Li et al 2021;Pons & Gallardo 2022). By fixing the resonant angle or its amplitude to zero (this assumption corresponds to an adiabatic invariant equal to zero, as discussed later), the degree of freedom associated with MMR disappears and the dynamical model immediately reduces to a one-degree-of-freedom integrable system.…”

The von Zeipel-Lidov-Kozai effect inside mean motion resonances with applications to trans-Neptunian objects

“…The first case is that, when H is equal to that of the resonant center, the magnitude of S becomes zero, meaning that the small body is initially placed at the resonant center. As discussed in the introduction, such a special case with S = 0 has been adopted as an assumption in formulating secular models (Kozai 1985;Yoshikawa 1989;Nesvornỳ et al 2002;Wan & Huang 2007;Saillenfest et al 2017;Li et al 2021;Pons & Gallardo 2022). The second case is that, when H is equal to that of the saddle point (or the dynamical separatrix), S is equal to the area bounded by the dynamical separatrices and, in this case, the assumption that the two degrees of freedom are separable in frequencies is failed, leading to the fact that S is no longer an adiabatic invariant (Wisdom 1985;Neishtadt 1987;Neishtadt & Sidorenko 2004;Tennyson et al 1986).…”

“…The simplest approach is to assume the critical argument associated with the MMR at the libration center (Kozai 1985;Yoshikawa 1989;Nesvornỳ et al 2002;Wan & Huang 2007;Saillenfest et al 2017;Li et al 2021;Pons & Gallardo 2022). By fixing the resonant angle or its amplitude to zero (this assumption corresponds to an adiabatic invariant equal to zero, as discussed latter), the degree of freedom associated with MMR disappears and the dynamical model immediately reduces to a one-degree-of-freedom integrable system.…”