Orbital dynamics of three-dimensional bars - I. The backbone of three-dimensional bars. A fiducial case

Abstract

A B S T R A C TIn this series of papers we investigate the orbital structure of three-dimensional (3D) models representing barred galaxies. In the present introductory paper we use a fiducial case to describe all families of periodic orbits that may play a role in the morphology of threedimensional bars. We show that, in a 3D bar, the backbone of the orbital structure is not just the x1 family, as in two-dimensional (2D) models, but a tree of 2D and 3D families bifurcating from x1. Besides the main tree we have also found another group of families of lesser importance around the radial 3:1 resonance. The families of this group bifurcate from x1 and influence the dynamics of the system only locally. We also find that 3D orbits elongated along the bar minor axis can be formed by bifurcations of the planar x2 family. They can support 3D bar-like structures along the minor axis of the main bar. Banana-like orbits around the stable Lagrangian points build a forest of 2D and 3D families as well. The importance of the 3D x1-tree families at the outer parts of the bar depends critically on whether they are introduced in the system as bifurcations in z or in _ z.

The formation of stellar nuclear discs in bar-induced gas inflows

“…The ND is perpendicular to the main bar, which is horizontal 1 in Fig. 4 and is therefore most likely supported by the x2 family of bar orbits, which is elongated in this way (Skokos, Patsis & Athanassoula 2002). (The x3 orbits, which are also elongated perpendicular to the bar, are generally unstable (e.g.…”

A Unified Framework for the Orbital Structure of Bars and Triaxial Ellipsoids

“…x y z W W W = 2:−2:−1" (these are also referred to as "x1v1" orbits by Skokos et al 2002a). Also seen is the 3: −2:0 resonance.…”

“…Indeed, studies of orbits in 2D N-body bars largely confirmed the picture arising from the study of periodic orbits and showed that many regular orbits elongated along the bar were parented by x1 orbits, a small fraction were parented by retrograde x4 orbits (Sparke & Sellwood 1987), and none were parented by prograde x2 orbits. The realization that bars can also undergo buckling instabilities (Combes & Sanders 1981;Raha et al 1991), which makes them develop substantial vertical thickness and peanut-shaped morphologies, led to the study of periodic orbits in three-dimensional bars (Pfenniger 1984;Martinet & de Zeeuw 1988;Pfenniger & Friedli 1991;Skokos et al 2002aSkokos et al , 2002b. It was shown that theappearance of specific morphological features in images of bars, such as the X-shape and peanut features seen in edge-on bars and the boxy/rectangular isophotes and "ansae" of face-on bars, could be explained by orbits trapped around specific periodic orbit families (Patsis et al 2002(Patsis et al , 2003(Patsis et al , 2010.…”

“…It was shown that theappearance of specific morphological features in images of bars, such as the X-shape and peanut features seen in edge-on bars and the boxy/rectangular isophotes and "ansae" of face-on bars, could be explained by orbits trapped around specific periodic orbit families (Patsis et al 2002(Patsis et al , 2003(Patsis et al , 2010. The introduction of a thirddimension did not drastically change the picture of the nature of periodic orbits, and it was found that 3D bars are composed primarily of vertical bifurcations (resonances) of the x1 family and a few additional families (e.g., Pfenniger & Friedli 1991;Skokos et al 2002aSkokos et al , 2002b. Most studies of periodic orbits in analytic potentials consider prograde x2 orbits (but not retrograde x4 orbits) to be another fundamental building block of bars (Skokos et al 2002a;Binney & Tremaine 2008).…”

“…The introduction of a thirddimension did not drastically change the picture of the nature of periodic orbits, and it was found that 3D bars are composed primarily of vertical bifurcations (resonances) of the x1 family and a few additional families (e.g., Pfenniger & Friedli 1991;Skokos et al 2002aSkokos et al , 2002b. Most studies of periodic orbits in analytic potentials consider prograde x2 orbits (but not retrograde x4 orbits) to be another fundamental building block of bars (Skokos et al 2002a;Binney & Tremaine 2008). In our study we do not find any orbits parented by the periodic prograde x2 orbit in our initial bar model, but we do find orbits that are parented by the periodic retrograde x4 orbit-a result that is consistent with previous studies (Sparke & Sellwood 1987;Pfenniger & Friedli 1991;Voglis et al 2007).…”