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.

Figures (14)

• Figure 1: Rotation curve of the initial conditions of our Galaxy model.
• Figure 2: Snapshots of an isolated $N$-body galactic disk in a live dark halo (Model A). Top row: Stellar surface density. Second row: Dimensionless fast-angle-averaged Hamiltonian (equation \ref{['eq:h']}) in the azimuthal angle-action space at ${\bm J}_{\rm f}=(10,10) \,{\rm kpc}^2\,{\rm Gyr}^{-1}$. Third and fourth rows: Density and initial angular momentum of stars averaged over ${\bm \theta}_{\rm f} \in [0,2\pi]^2$ and ${\bm J}_{\rm f} \in [0,100]^2 \,{\rm kpc}^2\,{\rm Gyr}^{-1}$. As the bar spins down, the bar's corotation resonance (black lines) sweeps toward large $J_\varphi$ and the trapped stars get dragged along with it.
• Figure 3: As in Fig. \ref{['fig:xy_f_Jphi0_H']}, but with a static dark halo (Model B). Since the bar maintains a roughly constant pattern speed after $t\simeq 2 \,{\rm Gyr}$ (Fig. \ref{['fig:bar_properties']}), the bar's resonance is kept fixed and therefore does not develop any distinct contrast with the surrounding phase space.
• Figure 4: Mean initial angular momentum $\bar{J}_{\varphi 0}$ of stars trapped in the bar's corotation resonance as a function of their libration action $J_{\ell}$, color-coded by time. The top panels show results for the live-halo model (Model A), in which the bar slows, while the bottom panels show those for the static-halo model (Model B), in which the bar rotates steadily. The two columns present results for the two distinct resonant islands centered on the Lagrange points $L_4$ and $L_5$. Open circles mark the endpoint (separatrix) at each epoch. The resonance in Model A exhibits a positive gradient in $\bar{J}_{\varphi 0}$ which becomes steeper over time, since the resonance sequentially captures new stars at larger angular momentum as it sweeps and expands in volume. In contrast, the resonance in Model B shows an almost constant flat distribution.
• Figure 5: Linear regression slope between $J_{\ell}$ and $J_{\varphi 0}$ as a function of time. The slope increases significantly in the live-halo model (Model A), whereas it remains nearly constant in the static-halo model (Model B).