STRUCTURE AND EVOLUTION OF LONG-LIVED SPIRAL PATTERNS IN GALAXIES

We use N-body simulations to study the non-linear evolution of spontan eous and tidally induced spiral patterns in galaxies on time-scales of several rotation periods of the disc. We find that the patterns can s ometimes survive with an almost constant amplitude for five revolution s or more, and tend to be regenerated after disappearing temporarily. The pattern velocity is such that the corotation radius is where the s elf-gravity as measured by the swing amplification of the m = 2 compon ent is strongest, and the amplitude of the pattern is larger when swin g amplification is stronger. The shape of the spirals is independent o f the origin of the pattern, and corresponds to the critical wave numb er kappa(2)/2 pi G mu, where mu is the disc surface density. The patte rn survives longer if the self-gravity of the disc is strong. For a gi ven disc model the life-time of the pattern depends on its amplitude, with stronger patterns having shorter life-times. If self-gravity is w eak, the dominant tidal effect is a kinematic spiral at the inner Lind blad resonance.