Effects of Resolution and Local Stability on Galactic Disks: Halo Resolution and Softening on Bar Formation

Using N-body simulations, we examine the impact of dark matter (DM) halo resolution and gravitational softening on bar formation. We generate isolated disk-halo systems with fixed stellar disk parameters, varying the number of halo particles, softening lengths, and halo concentration to modulate disk stability via the central DM fraction. The effects of DM resolution ($\mratio=1$, 10, and 100) on bar formation are less pronounced in more unstable disks, in which the overall evolutionary path is similar except that the lowest DM resolution model suffers gradual bar weakening. Irrespective of the halo resolution, large softening, $\epsdm$, flattens the central halo density profile within the softening scale, impeding angular momentum transfer to the nascent bar and preventing bar formation in more stable models. In unstable models with $\epsdm=0.96 \, \kpc$, a small bar still emerges due to enhanced initial instability and a larger seed perturbation, yet its strength remains capped at $F_2 \approx 0.3$ owing to unresolved central dynamical friction. Despite the destabilizing effect of reduced central DM fractions, our results indicate that deficient central angular momentum exchange can still suppress bar growth. Furthermore, halo softening influences buckling instability, as larger values ($\epsdm=0.30$ and $0.60 \, \kpc$) inhibit central vertical heating, exacerbating radial-vertical velocity dispersion anisotropies and triggering stronger buckling. We recommend adopting $ \mratio \le 10 $, $ \mstar \leq 10^4 \, \Msun $, and $ \epsdm < 0.30\,\mathrm{kpc}$ when investigating the formation and evolution of non-axisymmetric structures in Milky Way-mass galaxies.