Resonances in barred galaxies

The inner parts of many spiral galaxies are dominated by bars. These are strong non-axisymmetric features which significantly affect orbits of stars and dark matter particles. One of the main effects is the dynamical resonances between galactic material and the bar. We detect and characterize these resonances in N-body models of barred galaxies by measuring angular and radial frequencies of individual orbits. We found narrow peaks in the distribution of orbital frequencies with each peak corresponding to a specific resonance. We found five different resonances in the stellar disc and two in the dark matter. The corotation resonance (CR) and the inner and outer Lindblad resonances are the most populated. The spatial distributions of particles near resonances are wide. For example, the inner Lindblad resonance is not localized at a given radius. Particles near this resonance are mainly distributed along the bar and span a wide range of radii. On the other hand, particles near the CR are distributed in two broad areas around the two stable Lagrange points. The distribution resembles a wide ring at the corotation radius. Resonances capture disc and halo material in near-resonant orbits. Our analysis of orbits in both N-body simulations and simple analytical models indicates that resonances tend to prevent the dynamical evolution of this trapped material. Only if the bar evolves as a whole, resonances drift through the phase space. In this case particles anchored near resonant orbits track the resonance shift and evolve. The criteria to ensure a correct resonant behaviour discussed by Weinberg and Katz can be achieved with few millions particles because the regions of trapped orbits near resonances are large and evolving.