The influence of numerical parameters on tidally triggered bar formation
  The joint influence of numerical parameters such as the number of particles N, the gravitational softening length $\epsilon$ and the time-step $\Delta t$ is investigated in the context of galaxy simulations. For isolated galaxy models we have performed a convergence study and estimated the numerical parameters ranges for which the relaxed models do not deviate significantly from its initial configuration. By fixing N, we calculate the range of the mean interparticle separation $\lambda(r)$ along the disc radius. We have found that in the simulations with N=1310720 particles $\lambda$ varies by a factor of 6, and the corresponding final Toomre's parameters Q change by only about 5 per cent. By decreasing N, the $\lambda$ and Q ranges broaden. Large $\epsilon$ and small N cause an earlier bar formation. For a given set of parameters the disc heating is smaller with the Plummer softening than with the spline softening. For galaxy collision models numerical simulations indicate that the properties of the formed bars strongly depend upon the selection of N and $\epsilon$. Large values of the gravitational softening parameter and a small number of particles results in the rapid formation of a well defined, slowly rotating bar. On the other hand, small values of $\epsilon$ produce a small, rapidly rotating disc with tightly wound spiral arms, and subsequently a weak bar emerges. We have found that by increasing N, the bar properties converge and the effect of the softening parameter diminishes. Finally, in some cases short spiral arms are observed at the ends of the bar that change periodically from trailing to leading and vice-versa - the wiggle. 
R. F. Gabbasov, M. A. Rodriguez-Meza, Jaime Klapp, and Jorge L.   Cervantes-Cota