On the origin of the Hercules group: II. The Trojan quasi-periodic identity on the orbital level

ABSTRACT The Hercules kinematic group is a stellar anomaly structure observed in the solar neighbourhood (SNd). In the previous paper, we analysed chemical signatures and related the origin of this stellar population to the outer bar. Next to consider is how this alien population migrate out into the SNd. Often, this kinematic structure is associated with bar resonances. In this paper, We consider the driving mechanism of Hercules on the orbital level. We construct a simple Milky Way-like potential model with a slowly rotating long bar and explore some of the stellar orbit families and their stability. With this model, our numerical solutions of the equations of motion show that quasi-periodic orbits trapped around fast-rotating periodic Trojan orbits around the L4 Lagrange point of the bar minor axis can pass through the SNd. When observed in the SNd, they populate the Hercules structure in the $L_Z$–$V_R$ kinematics space. Moreover, the variation in radial coverage in the galactic plane with the SNd kinematics shows good agreement with chemical signatures found in Paper I. Furthermore, the effective potential shows the topology of a volcano, the rim of which limits most orbits to stay inside or outside. Trojan orbits are a stable orbit family that can transport inner Galactic stars out to the SNd. They can explain the stellar kinematics of Hercules, and provide a straightforward basis for its chemical properties. We support that Trojan orbits associated with the slowly rotating Galactic bar explain the Hercules structure observed in the SNd.