Chains of Rotational Tori and Filamentary Structures Close to High Multiplicity Periodic Orbits in a 3d Galactic Potential

Monthly Notices of the Royal Astronomical Society

Katsanikas

2014

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The investigation of the phase-space properties of structures encountered in a dynamical system is essential for understanding their formation and enhancement. In the present paper we explore the phase space in energy intervals where we have orbits that act as building blocks for boxy-peanut (b/p) and "X-shaped" structures in rotating potentials of galactic type. We underline the significance of the rotational tori around the 3D families x1v1 and x1v1 ′ that have been bifurcated from the planar x1 family. These tori play a multiple role: (i) They belong to quasi-periodic orbits that reinforce the local density. (ii) They act as obstacles for the diffusion of chaotic orbits and (iii) they attract a large number of chaotic orbits that become sticky to them. There are also bifurcations of unstable families (x1v2, x1v2 ′ ). Their unstable asymptotic curves wind around the x1v1 and x1v1 ′ tori generating orbits with hybrid morphologies between that of x1v1 and x1v2. In addition, a new family of multiplicity 2, called x1mul2, is found to be important for the peanut construction. This family produces stickiness phenomena in the critical area of the radial and vertical inner Lindblad resonances (ILRs) and reinforces b/p bulges. Our work shows also that there are peanut-supporting orbits before the vertical ILR. Non-periodic orbits associated with the x1 family secure this contribution as well as the support of b/p structures at several other energy intervals. Non-linear phenomena associated with complex instability of single and double multiplicity families of periodic orbits show that these structures are not interrupted in regions where such orbits prevail. Depending on the main mechanism behind their formation, boxy bulges exhibit different morphological features. Finally our analysis indicates that "X" features shaped by orbits in the neighbourhood of x1v1 and x1v1 ′ periodic orbits are pronounced only in side-on or nearly end-on views of the bar.

Section: The Relative Importance Of Non-periodic Orbits and The X1mul...mentioning

confidence: 98%

The phase space of boxy–peanut and X-shaped bulges in galaxies – I. Properties of non-periodic orbits

Monthly Notices of the Royal Astronomical Society

Katsanikas

2014

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“…At a given energy, as we move from the centre of the main island of a simple-periodic orbit to its borders, we find in the surfaces of section groups of smaller and smaller islands. Since our model is 3D, these groups of islands are invariant tori belonging to the mul-periodic orbits described in our tables (see figures 14 to 17 in Katsanikas et al 2011b). The existence of the mul-periodic orbits creates in phase space a zone of morphological influence, because these p.o.…”

Section: 6mentioning

confidence: 99%

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

Monthly Notices of the Royal Astronomical Society

Athanassoula

2019

Recently, many orbital studies in barred galaxy potentials have revealed the existence of orbits which are not trapped around x1-tree orbits, but could be potentially appropriate building blocks for bars. These findings question the uniqueness of the x1 family as the standard paradigm of orbital motion in galactic bars. The main goal of this paper is to investigate the role that such orbits could play in shaping the morphology of bars. We trace the morphological patterns appearing in the face-on and edge-on views of the non-periodic orbits presented in these studies and we show that they are introduced in the system by second type ("deuxième genre") bifurcations of x1. For this purpose, we use a typical 3D Ferrers bar model and follow the radial and vertical bifurcations of the x1 family considered as being mul-periodic, with mul = 2, 3, 5. The variation of the stability indices of x1 in the mul = 2, 3 cases give us also the 4− and 6−periodic orbits, respectively. We tabulate these orbits including all information necessary to assess their role as appropriate building blocks. We discuss their stability and their extent, as well as their size and morphological evolution, as a function of energy. We conclude that even the most important of the mul-periodic orbits presented in Tables 2 to 5 are less appropriate building blocks for bars than the families of the x1-tree at the same energy.

“…Recently the method has been applied successfully in a series of papers that studied the dynamics in the neighborhood of periodic orbits in a 3D galactic potential [Katsanikas and Patsis 2011, Katsanikas et al 2011a, Katsanikas et al 2011b]. The results of these papers, together with those of the original one by Patsis and Zachilas [1994], as well as further results from work in progress, find a consistency between the shapes of the encountered structures in the 4D spaces of section and the kind of (in)stability of the periodic orbit.…”

Section: Introductionmentioning

confidence: 99%

The Structure of Phase Space Close to Fixed Points in a 4d Symplectic Map

Zachilas

Katsanikas

Int. J. Bifurcation Chaos

2013

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We study the dynamics in the neighborhood of fixed points in a 4D symplectic map by means of the color and rotation method. We compare the results with the corresponding cases encountered in galactic type potentials and we find that they are in good agreement. The fact that the 4D phase space close to fixed points is similar to the 4D representations of the surfaces of section close to periodic orbits, indicates an archetypical 4D pattern for each kind of (in)stability, not only in 3D autonomous Hamiltonian systems with galactic type potentials but for a larger class of dynamical systems. This pattern is successfully visualized with the method we use in the paper.