Orbit evolution in growing stellar bars: Bar-supporting orbits at the vertical ILR region

We investigate the evolution of orbital shapes at the Inner Lindblad Resonance region of a rotating three-dimensional bar, the mass of which is growing with time. We evaluate in time-dependent models, during a 5 Gyr period, the importance of orbits with initial conditions known to play a significant role in supporting peanut-like structures in autonomous systems. These orbits are the central family of periodic orbits (x1) and vertical perturbations of it, orbits of its standard three-dimensional bifurcations at the region (x1v1 and x1v2), as well as orbits in their neighbourhood. The knowledge of the regular or chaotic character of these orbits is essential as well, because it allows us to estimate their contribution to the support of a rotating bar and, more importantly, the dynamical mechanisms that make it possible. This is calculated by means of the GALI2 index. We find that orbital patterns existing in the autonomous case, persist for longer times in the more massive bar models, and even more so in a model in which the central spheroid component of our adopted galactic potential becomes rather insignificant. The peanut-supporting orbits which we find, have a regular or, in most cases, a weakly chaotic character. There are cases in which orbits starting close to unstable periodic orbits in an autonomous model behave as regular and support the bar when its mass increases with time. An approximation for the orbital dynamics of our non-autonomous models at a certain time, can be considered that of the corresponding frozen system around that time.