Apsidal asymmetric-alignment of Jupiter Trojans

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 $varpi$, around the locations $varpi_{mbox{{J}}}+60^{circ}$ and $varpi_{mbox{{J}}}-60^{circ}$ ($varpi_{mbox{{J}}}$ 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 $Deltavarpi=varpi-varpi_{mbox{{J}}}approxpm60^{circ}$, 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 $e_p<0.1$ spend most of their time in the range of $|Deltavarpi|=0-120^{circ}$, while the more eccentric ones with $e_p>0.1$ are too few to affect the orbital clustering within this $Deltavarpi$ range for the entire Trojan population. Our numerical results further prove that, even starting from a uniform $Deltavarpi$ 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.