Orbits Supporting Bars within Bars

High-resolution observations of the inner regions of barred disk galaxies have revealed many asymmetrical, small-scale central features, some of which are best described as secondary bars. Because orbital time-scales in the galaxy center are short, secondary bars are likely to be dynamically decoupled from the main kiloparsec-scale bars. Here, we show that regular orbits exist in such doubly-barred potentials and that they can support the bars in their motion. We find orbits in which particles remain on loops: closed curves which return to their original positions after two bars have come back to the same relative orientation. Stars trapped around stable loops could form the building blocks for a long-lived, doubly-barred galaxy. Using the loop representation, we can find which orbits support the bars in their motion, and what are the constraints on the sizes and shapes of self-consistent double bars. In particular, it appears that a long-lived secondary bar may exist only when an Inner Lindblad Resonance is present in the primary bar, and that it would not extend beyond this resonance.