Distinguishing between order and chaos in a simple barred galaxy model

We use a simple dynamical model in order to investigate the regular or chaotic character of orbits in a barred galaxy with a central, spherically symmetric, dense nucleus and a flat disk. In particular, we explore how the total orbital energy influences the overall orbital structure of the system, by computing in each case the percentage of regular, sticky and chaotic orbits. In an attempt to distinguish safely and with certainty between ordered and chaotic motion, we apply the Smaller ALingment Index (SALI) as a chaos detector to extensive samples of orbits obtained by integrating numerically the basic equations of motion as well as the variational equations. We integrate large sets of initial conditions of orbits in several types of two dimensional planes for better understanding of the orbital properties. Our numerical calculations suggest, that the value of the energy has a huge impact on the percentages of the orbits, thus indicating that a rotating barred galaxy is indeed a very interesting stellar quantity.