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The velocity-space distribution of the solar neighbourhood stars showscomplex substructures. Most of the previous studies use static potentials toinvestigate their origins. Instead we use a self-consistent $N$-body model ofthe Milky Way, whose potential is asymmetric and evolves with time. In thispaper, we quantitatively evaluate the similarities of the velocity-spacedistributions in the $N$-body model and that of the solar neighbourhood, usingKullback-Leibler divergence (KLD). The KLD analysis shows the time evolutionand spatial variation of the velocity-space distribution. The KLD fluctuateswith time, which indicates the velocity-space distribution at a fixed positionis not always similar to that of the solar neighbourhood. Some positions showvelocity-space distributions with small KLDs (high similarities) morefrequently than others. One of them locates at $(R,\phi)=(8.2\;\mathrm{kpc},30^{\circ})$, where $R$ and $\phi$ are the distance from the galactic centreand the angle with respect to the bar's major axis, respectively. The detectionfrequency is higher in the inter-arm regions than in the arm regions. In thevelocity maps with small KLDs, we identify the velocity-space substructures,which consist of particles trapped in bar resonances. The bar resonances havesignificant impact on the stellar velocity-space distribution even though thegalactic potential is not static.

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