Resonances and the morphology of spirals in N-body simulations

We find, by means of N-body simulations, non-linear spiral modes that last from four to seven pattern rotations and secure a grand-design morphology to the models. Their dynamical behavior includes the termination of the strong, symmetric, logarithmic stellar spirals inside their 4:1 resonance radius, as foreseen from the orbital theory and from SPH gasdynamical models. The spiral modes start along theΩ−κ/2 curve and have weak extensions beyond the 4:1 resonance. Strong, bisymmetric logarithmic spirals end at about 2–3 exponential disk scale lengths. A central oval distortion is always present in the models. In many cases we have more than one dominant mode existing over different distance intervals. For each of these spiral modes we find the regions of resonances as determined by its pattern speed. We observe that the dynamics of the mode are locally influenced by the presence of the resonances.