Chaotic motion and spiral structure in self‐consistent models of rotating galaxies

Dissipationless N-body models of rotating galaxies, iso-energetic to a non-rotating model, are examined as regards the mass in regular and in chaotic motion. Iso-energetic means that they have the same mass and the same binding energy and they are near the same scalar virial equilibrium, but their total amount of angular momentum is different. The values of their spin parameters λ are near the value λ= 0.22 of our Galaxy. We distinguish particles moving in regular and in chaotic orbits and we show that the spatial distribution of these two sets of particles is much different. The rotating models are characterized by larger fractions of mass in chaotic motion (up to the level of ≈65 per cent) compared with the fraction of mass in chaotic motion in the non-rotating iso-energetic model (which is on the level of ≈32 per cent). Furthermore, the Lyapunov numbers of the chaotic orbits in the rotating models become by about one order of magnitude larger than in the non-rotating model. This impressive enhancement of chaos is produced, partly by the more complicated distribution of mass, induced by the rotation, but mainly by the resonant effects near corotation. Chaotic orbits are concentrated preferably in values of the Jacobi integral around the value of the effective potential at the corotation radius. We find that density waves form a central rotating bar embedded in a thin and a thick disc with exponential mean radial profile of the surface density. A surprising new result is that long living spiral arms are excited on the disc, composed almost completely by chaotic orbits. The bar excites an m= 2 mode of spiral waves on the surface density distribution of the disc, emanating from the corotation radius. The bar goes temporarily out of phase with respect to an excited spiral wave, but it comes in phase again in less that a period of rotation. As a consequence, spiral arms show an intermittent behaviour. They are deformed, fade or disappear temporarily, but they grow again re-forming a well-developed spiral pattern. Spiral arms are discernible up to 20 or 30 rotations of the bar (lasting for about a Hubble time). The relative power of the spiral m= 2 mode with respect to all other fluctuations on the surface density is initially about 50 per cent, but it is reduced by a factor of about 2 or 3 at the end of the Hubble time.