Tree-ring Structure of Galactic Bar Resonance in N -body Simulations

Abstract We study the structure and evolution of the Galactic bar’s resonant phase space in self-consistent N -body simulations of the Milky Way, with and without perturbations from the Sagittarius dwarf galaxy. In an idealized disk evolution model in which stars are perturbed solely by a bar that spins down due to dynamical friction against the dark matter halo, it is predicted that stars trapped in the bar’s corotation resonance form a characteristic “tree-ring” structure in phase space: as the resonance expands in volume while sweeping outwards, it sequentially captures surrounding stars at its surface, such that stars captured earlier in the inner disk are found preferentially near the core of the resonance. However, it has not been clear whether such a structure persists in a more realistic galactic disk subject to a variety of time-dependent perturbations, in particular those by spiral arms and passing satellite galaxies. This paper demonstrates that the predicted tree-ring structure indeed emerges in a realistic noisy environment using self-consistent N -body simulations. Despite the presence of spiral arms, encounters with the Sagittarius dwarf galaxy, as well as fluctuations in the bar’s pattern speed, and not least numerical noise—all of which drive stellar diffusion in phase space—, the tree-ring structure remains well-preserved in the slow angle-action space. Our results demonstrate that the tree-ring structure of the bar’s resonance is a robust signal of the bar’s spin down, and hence its discovery in the Milky Way implies the existence of a dark matter halo that removed angular momentum from the bar.