High resolution simulations of unstable modes in a collisionless disc

We present N-body simulations of unstable spiral modes in a dynamically cool collisionless disc. We show that spiral modes grow in a thin collisionless disk in accordance with the analytical perturbation theory. We use the particle-mesh code SUPERBOX with nested grids to follow the evolution of unstable spirals that emerge from an unstable equilibrium state. We use a large number of particles (up to 40 million particles) and high-resolution spatial grids in our simulations (128^3 cells). These allow us to trace the dynamics of the unstable spiral modes until their wave amplitudes are saturated due to nonlinear effects. In general, the results of our simulations are in agreement with the analytical predictions. The growth rate and the pattern speed of the most unstable bar-mode measured in N-body simulations agree with the linear analysis. However the parameters of secondary unstable modes are in lesser agreement because of the still limited resolution of our simulations.