High- and Low-$\alpha$ Disk Stars Separate Dynamically at all Ages

There is a dichotomy in the Milky Way in the $[\alpha/$Fe]-[Fe/H] plane, in which stars fall into high-$\alpha$, and low-$\alpha$ sequences. The high-$\alpha$ sequence comprises mostly old stars, and the low-$\alpha$ sequence comprises primarily young stars. The origin of this dichotomy is uncertain. To better understand how the high- and low-$\alpha$ stars are affiliated, we examine if the high- and low-$\alpha$ sequences have distinct orbits at all ages, or if age sets the orbital properties of stars irrespective of their $\alpha$-enhancement. Orbital actions $J_R$, $J_z$, and $J_\phi$ (or $L_z$) are our labels of stellar dynamics. We use ages for 58,278 LAMOST stars (measured to a precision of 40\%) within $\leq$2kpc of the Sun and we calculate orbital actions from proper motions and parallaxes given by Gaia's DR2. We find that \emph{at all ages}, the high- and low-$\alpha$ sequences are dynamically distinct. This implies separate formation and evolutionary histories for the two sequences; a star's membership in the high- or low-$\alpha$ sequence indicates its dynamical properties at a given time. We use action space to make an efficient selection of halo stars and subsequently report a group of old, low-$\alpha$ stars in the halo, which may be a discrete population from an infall event.