The origin of the Hercules stream, the most prominent velocity substructure in the Solar neighbour disc stars, is still under debate. Recent accurate measurements of position, velocity, and metallicity provided by Tycho Gaia Astrometric Solution (TGAS) and RAdial Velocity Experiments (RAVE) have revealed that the Hercules stream is most clearly seen in the metal-rich region ([Fe/H] > 0), while it is not clearly seen in lower metallicity region ([Fe/H] < -0.25). By using a large number of chemo-dynamical 2D test-particle simulations with a rotating bar and/or spiral arms, we find that the observed [Fe/H] dependence of the Hercules stream is a natural consequence of the inside-out formation of the stellar disc and the existence of highly non-closed orbits in the rotating frame of the bar or spiral arms. Our successful models that reproduce the observed properties of the Hercules stream include not only fast-bar-only and fast-bar+spiral models, but also slow-bar+spiral models. This indicates that it is very difficult to estimate the pattern speed of the bar or spiral arms based only on the observations of the Hercules stream in the Solar neighbourhood. As a by-product of our simulations, we make some predictions about the locations across the Galactic plane where we can observe velocity bimodality that is not associated with the Hercules stream. These predictions can be tested by the Gaia Data Release 2, and such a test will improve our understanding of the evolution of the Milky Way stellar disc.
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