Boxy Orbital Structures in Rotating Bar Models

Abstract

We investigate regular and chaotic two-dimensional (2D) and three-dimensional (3D) orbits of stars in models of a galactic potential consisting in a disk, a halo and a bar, to find the origin of boxy components, which are part of the bar or (almost) the bar itself. Our models originate in snapshots of an N -body simulation, which develops a strong bar. We consider three snapshots of the simulation and for the orbital study we treat each snapshot independently, as an autonomous Hamiltonian system. The calculated corotation-to-bar-length ratios indicate that in all three cases the bar rotates slowly, while the orientation of the orbits of the main family of periodic orbits changes along its characteristic. We characterize the orbits as regular, sticky, or chaotic after integrating them for a 10 Gyr period by using the GALI 2 index. Boxiness in the equatorial plane is associated either with quasi-periodic orbits in the outer parts of stability islands, or with sticky orbits around them, which can be found in a large range of energies. We indicate the location of such orbits in diagrams, which include the characteristic of the main family. They are always found about the transition region from order to chaos. By perturbing such orbits in the vertical direction we find a class of 3D non-periodic orbits, which have boxy projections both in their face-on and side-on views.

The orbital content of bars: the origin of ‘non-x1-tree’, bar-supporting orbits

“…Thus in (b) they are found in the middle of stability islands coming in pairs, above and below (red) and left and right (black) of the central island that belongs to x1. role in explaining boxiness in the central region of the bar(Patsis & Katsanikas 2014b;Chaves-Velasquez et al 2017). Similar morphologies are also encountered in the face-on views of the orbits in figure 7 (third and fourth row) in GLA, in figure 2 in KPP, in figure 4 (1st row) in VSAD and in figure 5 (third column) in WAM.…”

“…Independently of their origin and their regular or sticky-chaotic character, the supported elliptical morphologies on the equatorial plane are almost identical and are ubiquitous in papers about orbits in barred galaxy models (e.g. the orbits in figure 6, 3rd row in AVSD; the orbits in figure 3, 1st row and the orbits in figure 10 in Chaves-Velasquez et al (2017); the orbits in figures 6, 1st row and figure 7, 1st and 2nd rows, in GLA; the orbits in figures 3 and 4 in KPP; the orbit in figure 15 in PKa; the orbits in figure 1, three first rows, in figure 3, 1st row, right, and figure 4, 4th and 5th row in VSAD; the orbits in figures 10 and 11 in WM-D etc.). In order to avoid elliptical shapes in the (x, y) projections of the orbits, one has to deviate more from the initial conditions of the x1 or x1-tree orbits and consider orbits close to the edges of the stability islands (both at their "regular" and their "chaotic" side).…”

“…We have to note that the possibility of the appearance of a morphological feature when sticky-chaotic orbits are integrated for long time cannot be a priori excluded. In PKb, in Tsigaridi & Patsis (2015) and in Chaves-Velasquez et al (2017) such orbits are proposed for explaining the face-on X features that appears in some galactic bars.…”

“…In order to avoid elliptical shapes in the (x, y) projections of the orbits, one has to deviate more from the initial conditions of the x1 or x1-tree orbits and consider orbits close to the edges of the stability islands (both at their "regular" and their "chaotic" side). This can lead to single (only in one projection), or double (both in their face-on and edge-on views) boxiness of orbits of galactic bars (Chaves-Velasquez et al 2017) and can be particularly important for the structure of the peanuts when we consider orbits in the vILR resonance region (PKb).…”

“…Besides the x1v1 and x1v2 edge-on profiles, the next common morphology that is encountered in the various models, is a boxy one, with sharply defined edges, but without a particular morphology inside the box. The mechanism that favours the appearance of such a structure, instead of a particular edge-on shape, is presented in PKb and in Chaves-Velasquez et al (2017). Apart from the cases that are presented in these two papers, many examples of boxy orbits can be found in the relevant literature, as e.g.…”