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Impact of bar resonances in the velocity-space distribution of the solar neighbourhood stars in a self-consistent $N$-body Galactic disc simulation

The velocity-space distribution of the solar neighbourhood stars shows complex substructures. Most of the previous studies use static potentials to investigate their origins. Instead we use a self-consistent $N$-body model of the Milky Way, whose potential is asymmetric and evolves with time. In this paper, we quantitatively evaluate the similarities of the velocity-space distributions in the $N$-body model and that of the solar neighbourhood, using Kullback-Leibler divergence (KLD). The KLD analysis shows the time evolution and spatial variation of the velocity-space distribution. The KLD fluctuates with time, which indicates the velocity-space distribution at a fixed position is not always similar to that of the solar neighbourhood. Some positions show velocity-space distributions with small KLDs (high similarities) more frequently than others. One of them locates at $(R,ϕ)=(8.2\;\mathrm{kpc}, 30^{\circ})$, where $R$ and $ϕ$ are the distance from the galactic centre and the angle with respect to the bar's major axis, respectively. The detection frequency is higher in the inter-arm regions than in the arm regions. In the velocity maps with small KLDs, we identify the velocity-space substructures, which consist of particles trapped in bar resonances. The bar resonances have significant impact on the stellar velocity-space distribution even though the galactic potential is not static.