arXiv subjects

P. A. Patsis

Publications and source records attributed to P. A. Patsis.

At least 19 recordsLinked to original sources

arXiv2021

Chaoticity in the vicinity of complex unstable periodic orbits in galactic type potentials

We investigate the evolution of phase space close to complex unstable periodic orbits in two galactic type potentials. They represent characteristic morphological types of disc galaxies, namely barred and normal (non-barred) spiral galaxies. These potentials are known for providing building blocks to support observed features such as the peanut, or X-shaped bulge, in the former case and the spiral arms in the latter. We investigate the possibility that these structures are reinforced, apart by regular orbits, also by orbits in the vicinity of complex unstable periodic orbits. We examine the evolution of the phase space structure in the immediate neighbourhood of the periodic orbits in cases where the stability of a family presents a successive transition from stability to complex instability and then to stability again, as energy increases. We find that we have a gradual reshaping of invariant structures close to the transition points and we trace this evolution in both models. We conclude that for time scales significant for the dynamics of galaxies, there are weakly chaotic orbits associated with complex unstable periodic orbits, which should be considered as structure-supporting, since they reinforce the morphological features we study.

astro-ph.GA↗

arXiv2020

The orbital content of bars: The origin of 'non-x1-tree', bar-supporting orbits

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 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 multi periodic, with multi = 2, 3, 5. The variation of the stability indices of x1 in the multi = 2, 3 cases give us also the four- and six- 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 multi-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.

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arXiv2018

Dynamics of thick, open spirals in Perlas potentials

The PERLAS potential has been successfully used in many studies related with the dynamics of the spiral arms \textit{on} the equatorial plane of normal (non-barred) spiral galaxies. In the present work we extend these studies by investigating the three-dimensional dynamics of the spiral arms in the same type of potential. We consider a typical open, logarithmic, spiral pattern of pitch angle 25$^{\circ}$ and we examine the stellar orbits that can support it as the ratio of the masses of the spiral over the disk component ($M_{s}/M_{d}$) varies. We indicate the families of `three-dimensional' periodic orbits that act as the backbone of the spiral structure and we discuss their stability in the models we present. We study further the quasi-periodic and non-periodic orbits in general that follow spiral-supporting orbits as the $M_{s}/M_{d}$ ratio increases. We find that a bisymmetric spiral with 25$^{\circ}$ pitch angle is better supported by orbits in models with $0.03\lessapprox M_{s}/M_{d} \lessapprox 0.07$. In these cases a strong spiral pattern is supported between the radial 2:1 and 4:1 resonances, while local enhancements of the imposed spirals are encountered in some models between 4:1 and corotation. A characteristic bar-like structure is observed in all models at radii smaller than the radius of the 2:1 resonance.

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arXiv2017

Boxy Orbital Structures in Rotating Bar Models

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.

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arXiv2015

Slowly rotating bars-Morphologies introduced by bistability in barred-spiral galactic potentials

We investigate the orbital dynamics of a \textit{barred-spiral} model when the system is rotating slowly and corotation is located beyond the end of the spiral arms. In the characteristic of the central family of periodic orbits we find a "bistable region". In the response model we observe a ring surrounding the bar and spiral arms starting tangential to the ring. This is a morphology resembling barred-spiral systems with inner rings. However, the dynamics associated with this structure in the case we study is different from that of a typical bar ending close to corotation. The ring of our model is round, or rather elongated perpendicular to the bar. It is associated with a folding (an "S" shaped feature) of the characteristic of the central family, which is typical in bistable bifurcations. Along the "S" part of the characteristic we have a change in the orientation of the periodic orbits from a x1-type to a x2-type morphology. The orbits populated in the response model change rather abruptly their orientation when reaching the lowest energy of the "S". The spirals of the model follow a standard "precessing ellipses flow" and the orbits building them have energies beyond the "S" region. The bar is structured mainly by sticky orbits from regions around the stability islands of the central family. This leads to the appearance of X-features in the bars \textit{on} the galactic plane. Such a bar morphology appears in the unsharp-masked images of some moderately inclined galaxies.

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arXiv2014

The phase-space of boxy-peanut and X-shaped bulges in galaxies II. The relation between face-on and edge-on boxiness

We study the dynamical mechanisms that reinforce the formation of boxy structures in the \textit{inner} regions, roughly in the middle, of bars observed nearly \textit{face-on}. Outer boxiness, at the ends of the bars, is usually associated with orbits at the inner, radial 4:1 resonance region and can be studied with 2D dynamics. However, in the middle of the bar dominate 3D orbits that give boxy/peanut bulges in the edge-on views of the models. In the present paper we show that 3D quasi-periodic, as well as 3D chaotic orbits sticky to the x1v1 and x1v1$^{\prime}$ tori, especially from the Inner Lindblad Resonance (ILR) region, have boxy projections on the equatorial plane of the bar. The majority of vertically perturbed 2D orbits, initially on the equatorial plane in the ILR resonance region, enhance boxy features in face-on bars. Orbits that build a bar by supporting sharp "{\sf X}" features in their side-on views at energies \textit{beyond} the ILR, may also have a double boxy character. If populated, the extent of the inner boxiness along the major axis is about the same with that of the peanut supporting orbits in the side-on views. At any rate these orbits do not obscure the observation of the boxy orbits of the ILR region in the face-on views, as they contribute more to the surface density at the sides of the bar than to their central parts.

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arXiv2014

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

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 "{\sf X}-shaped" structures in rotating potentials of galactic type. We underline the significance of the rotational tori around the 3D families x1v1 and x1v1$^{\prime}$ 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$^{\prime}$). Their unstable asymptotic curves wind around the x1v1 and x1v1$^{\prime}$ 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. 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$^{\prime}$ periodic orbits are pronounced only in side-on or nearly end-on views of the bar.

nlin.CD↗

arXiv2014

The structure of phase space close to fixed points in a 4D symplectic map

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.

nlin.CD↗

arXiv2013

The structure of invariant tori in a 3D galactic potential

We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the 4D spaces of section. We compare our results with those of previous works and we describe the morphology of the rotational, as well as of the tube tori in the 4D space. We find sticky chaotic orbits in the immediate neighborhood of sets of invariant tori surrounding 3D stable periodic orbits. Particularly useful for galactic dynamics is the behavior of chaotic orbits trapped for long time between 4D invariant tori. We find that they support during this time the same structure as the quasi-periodic orbits around the stable periodic orbits, contributing however to a local increase of the dispersion of velocities. Finally we find that the tube tori do not appear in the 3D projections of the spaces of section in the axisymmetric Hamiltonian we examined.

nlin.CD↗

arXiv2013

Instabilities and stickiness in a 3D rotating galactic potential

We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color and rotation. We investigate the structure of the invariant manifolds that we found in the neighborhood of simple and double unstable periodic orbits in the 4D spaces of section. We consider orbits in the neighborhood of the families x1v2, belonging to the x1 tree, and the z-axis (the rotational axis of our system). Close to the transition points from stability to simple instability, in the neighborhood of the bifurcated simple unstable x1v2 periodic orbits we encounter the phenomenon of stickiness as the asymptotic curves of the unstable manifold surround regions of the phase space occupied by rotational tori existing in the region. For larger energies, away from the bifurcating point, the consequents of the chaotic orbits form clouds of points with mixing of color in their 4D representations. In the case of double instability, close to x1v2 orbits, we find clouds of points in the four dimensional spaces of section. However, in some cases of double unstable periodic orbits belonging to the z-axis family we can visualize the associated unstable eigensurface. Chaotic orbits close to the periodic orbit remain sticky to this surface for long times (of the order of a Hubble time or more). Among the orbits we studied we found those close to the double unstable orbits of the x1v2 family having the largest diffusion speed.

nlin.CD↗

arXiv2011

Chains of rotational tori and filamentary structures close to high multiplicity periodic orbits in a 3D galactic potential

This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use the method of color and rotation [Patsis and Zachilas 1994] in order to visualize them. As examples we use the case of two orbits, one 2-periodic and one 7-periodic. We investigate the structure of multiple tori around them in the 4D surface of section and in addition we study the orbital behavior in the neighborhood of the corresponding simple unstable periodic orbits. By considering initially a few consequents in the neighborhood of the orbits in both cases we find a structure in the space of section, which is in direct correspondence with what is observed in a resonance zone of a 2D autonomous Hamiltonian system. However, in our 3D case we have instead of stability islands rotational tori, while the chaotic zone connecting the points of the unstable periodic orbit is replaced by filaments extending in 4D following a smooth color variation. For more intersections, the consequents of the orbit which started in the neighborhood of the unstable periodic orbit, diffuse in phase space and form a cloud that occupies a large volume surrounding the region containing the rotational tori. In this cloud the colors of the points are mixed. The same structures have been observed in the neighborhood of all m-periodic orbits we have examined in the system. This indicates a generic behavior.

nlin.CD↗

arXiv2011

The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation

We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known as Hamiltonian Hopf Bifurcation) the four eigenvalues of the stable periodic orbits move out of the unit circle. Then the periodic orbits become complex unstable. In this paper we first integrate initial conditions close to the ones of a complex unstable periodic orbit, which is close to the transition point. Then, we plot the consequents of the corresponding orbit in a 4D surface of section. To visualize this surface of section we use the method of color and rotation [Patsis and Zachilas 1994]. We find that the consequents are contained in 2D "confined tori". Then, we investigate the structure of the phase space in the neighborhood of complex unstable periodic orbits, which are further away from the transition point. In these cases we observe clouds of points in the 4D surfaces of section. The transition between the two types of orbital behavior is abrupt.

nlin.CD↗

arXiv2010

NGC 1300 Dynamics: I. The gravitational potential as a tool for detailed stellar dynamics

In a series of papers we study the stellar dynamics of the grand design barred-spiral galaxy NGC~1300. In the first paper of this series we estimate the gravitational potential and we give it in a form suitable to be used in dynamical studies. The estimation is done directly from near-infrared observations. Since the 3D distribution of the luminous matter is unknown, we construct three different general models for the potential corresponding to three different assumptions for the geometry of the system, representing limiting cases. A pure 2D disc, a cylindrical geometry (thick disc) and a third case, where a spherical geometry is assumed to apply for the major part of the bar. For the potential of the disc component on the galactic plane a Fourier decomposition method is used, that allows us to express it as a sum of trigonometric terms. Both even and odd components are considered, so that the estimated potential accounts also for the observed asymmetries in the morphology. For the amplitudes of the trigonometric terms a smoothed cubic interpolation scheme is used. The total potential in each model may include two additional terms (Plummer spheres) representing a central mass concentration and a dark halo component, respectively. In all examined models, the relative force perturbation points to a strongly nonlinear gravitational field, which ranges from 0.45 to 0.8 of the axisymmetric background with the pure 2D being the most nonlinear one. We present the topological distributions of the stable and unstable Lagrangian points as a function of the pattern speed $(Ω_p)$. In all three models there is a range of $Ω_p$ values, where we find multiple stationary points whose stability affects the overall dynamics of the system.

astro-ph.CO↗

arXiv2010

NGC 1300 Dynamics: II. The response models

We study the stellar response in a spectrum of potentials describing the barred spiral galaxy NGC 1300. These potentials have been presented in a previous paper and correspond to three different assumptions as regards the geometry of the galaxy. For each potential we consider a wide range of $Ω_p$ pattern speed values. Our goal is to discover the geometries and the $Ω_p$ supporting specific morphological features of NGC 1300. For this purpose we use the method of response models. In order to compare the images of NGC 1300 with the density maps of our models, we define a new index which is a generalization of the Hausdorff distance. This index helps us to find out quantitatively which cases reproduce specific features of NGC 1300 in an objective way. Furthermore, we construct alternative models following a Schwarzschild type technique. By this method we vary the weights of the various energy levels, and thus the orbital contribution of each energy, in order to minimize the differences between the response density and that deduced from the surface density of the galaxy, under certain assumptions. We find that the models corresponding to $Ω_p\approx16$\ksk and $Ω_p\approx22$\ksk are able to reproduce efficiently certain morphological features of NGC 1300, with each one having its advantages and drawbacks.

astro-ph.CO↗

arXiv2010

NGC 1300 Dynamics: III. Orbital analysis

We present the orbital analysis of four response models, that succeed in reproducing morphological features of NGC 1300. Two of them assume a planar (2D) geometry with $Ω_p$=22 and 16 \ksk respectively. The two others assume a cylindrical (thick) disc and rotate with the same pattern speeds as the 2D models. These response models reproduce most successfully main morphological features of NGC 1300 among a large number of models, as became evident in a previous study. Our main result is the discovery of three new dynamical mechanisms that can support structures in a barred-spiral grand design system. These mechanisms are presented in characteristic cases, where these dynamical phenomena take place. They refer firstly to the support of a strong bar, of ansae type, almost solely by chaotic orbits, then to the support of spirals by chaotic orbits that for a certain number of pat tern revolutions follow an n:1 (n=7,8) morphology, and finally to the support of spiral arms by a combination of orbits trapped around L$_{4,5}$ and sticky chaotic orbits with the same Jacobi constant. We have encountered these dynamical phenomena in a large fraction of the cases we studied as we varied the parameters of our general models, without forcing in some way their appearance. This suggests that they could be responsible for the observed morphologies of many barred-spiral galaxies. Comparing our response models among themselves we find that the NGC 130 0 morphology is best described by a thick disc model for the bar region and a 2D disc model for the spirals, with both components rotating with the same pattern speed $Ω_p$=16 \ksk !. In such a case, the whole structure is included inside the corotation of the system. The bar is supported mainly by regular orbits, while the spirals are supported by chaotic orbits.

astro-ph.CO↗

arXiv2010

Ordered and chaotic spirals in disk galaxies

The pattern speeds of spiral galaxies are closely related to the flow of material in their disks. Flows that follow the `precessing ellipses' paradigm (see e.g., Kalnajs 1973) are likely associated with slowly rotating spirals, which have corotation beyond their end. Such a flow can be secured by material trapped around stable, elliptical, x_1 periodic orbits precessing as their Jacobi constant varies. Contrarily, if part of the spiral arms is located at a corotation region then the spiral structure has to `survive' in chaotic regions. Barred-spiral systems with a single pattern speed and a bar ending before, but close to, corotation are candidates for having spirals supported by stars in chaotic motion. In this work we review the flows we have found in response models for various types of spiral potentials and indicate the cases, where order or chaos shapes the observed morphologies.

astro-ph.GA↗

arXiv2005

Boxy/peanut "bulges": comparing the structure of galaxies with the underlying families of periodic orbits

The vertical profiles of disc galaxies are built by the material trapped around stable periodic orbits, which form their "skeletons". According to this, the knowledge of the stability of the main families of periodic orbits in appropriate 3D models, can predict possible morphologies for edge-on disc galaxies. In a pilot survey we compare the orbital structures which lead to the appearance of "peanuts" and "X"-like features with the edge-on profiles of three disc galaxies (IC 2531, NGC 4013 and UGC 2048). The subtraction from the images of a model representing the axisymmetric component of the galaxies reveals the contribution of the non-axisymmetric terms. We find a direct correspondence between the orbital profiles of 3D bars in models and the observed main morphological features of the residuals. We also apply a simple unsharp masking technique in order to study the sharpest features of the images. Our basic conclusion is that the morphology of the boxy "bulges" of these galaxies can be explained by considering disc material trapped around stable 3D periodic orbits. In most models these building-blocks periodic orbits are bifurcated from the planar central family of a non-axisymmetric component, usually a bar, at low order vertical resonances. In such a case the boxy "bulges" are parts of bars seen edge-on. For the three galaxies we study the families associated with the "peanut" or "X"-shape morphology are most probably bifurcations at the vertical 2/1 or 4/1 resonance.

astro-ph↗

arXiv2005

Particle Swarm Optimization: An efficient method for tracing periodic orbits in 3D galactic potentials

We propose the Particle Swarm Optimization (PSO) as an alternative method for locating periodic orbits in a three--dimensional (3D) model of barred galaxies. We develop an appropriate scheme that transforms the problem of finding periodic orbits into the problem of detecting global minimizers of a function, which is defined on the Poincaré Surface of Section (PSS) of the Hamiltonian system. By combining the PSO method with deflection techniques, we succeeded in tracing systematically several periodic orbits of the system. The method succeeded in tracing the initial conditions of periodic orbits in cases where Newton iterative techniques had difficulties. In particular, we found families of 2D and 3D periodic orbits associated with the inner 8:1 to 12:1 resonances, between the radial 4:1 and corotation resonances of our 3D Ferrers bar model. The main advantages of the proposed algorithm is its simplicity, its ability to work using function values solely, as well as its ability to locate many periodic orbits per run at a given Jacobian constant.

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