arXiv subjects

Euaggelos E. Zotos

Publications and source records attributed to Euaggelos E. Zotos.

At least 91 records · Page 5Linked to original sources

arXiv2015

Classifying orbits in the classical Henon-Heiles Hamiltonian system

The Hénon-Heiles potential is undoubtedly one of the most simple, classical and characteristic Hamiltonian systems. The aim of this work is to reveal the influence of the value of the total orbital energy, which is the only parameter of the system, on the different families of orbits, by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits composing the main regular families evolve when energy varies. In particular, we conduct a thorough numerical investigation distinguishing between ordered and chaotic orbits, considering only bounded motion for several energy levels. The smaller alignment index (SALI) was computed by numerically integrating the equations of motion as well as the variational equations to extensive samples of orbits in order to distinguish safely between ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Our exploration takes place both in the physical $(x,y)$ and the phase $(y,\dot{y})$ space for a better understanding of the orbital properties of the system. It was found, that for low energy levels the motion is entirely regular being the box orbits the most populated family, while as the value of the energy increases chaos and several resonant families appear. We also observed, that the vast majority of the resonant orbits belong in fact in bifurcated families of the main 1:1 resonant family. We have also compared our results with previous similar outcomes obtained using different chaos indicators.

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arXiv2015

How does the mass transport in disk galaxy models influence the character of orbits?

We explore the regular or chaotic nature of orbits of stars moving in the meridional (R,z) plane of an axially symmetric time-dependent disk galaxy model with a central, spherically symmetric nucleus. In particular, mass is linearly transported from the disk to the galactic nucleus, in order to mimic, in a way, the case of self-consistent interactions of an actual N-body simulation. We thus try to unveil the influence of this mass transportation on the different families of orbits of stars by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families, evolve as the galaxy develops a dense and massive nucleus in its core. The SALI method is applied to samples of orbits in order to distinguish safely between ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics is used for identifying the various families of regular orbits and also for recognizing the secondary resonances that bifurcate from them. Our computations strongly suggest that the amount of the observed chaos is substantially increased as the nucleus becomes more massive. Furthermore, extensive numerical calculations indicate that there are orbits which change their nature from regular to chaotic and vice versa and also orbits which maintain their orbital character during the galactic evolution. The present outcomes are compared to earlier related work.

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arXiv2014

Revealing the escape mechanism of three-dimensional orbits in a tidally limited star cluster

The aim of this work is to explore the escape process of three-dimensional orbits in a star cluster rotating around its parent galaxy in a circular orbit. The gravitational field of the cluster is represented by a smooth, spherically symmetric Plummer potential, while the tidal approximation was used to model the steady tidal field of the galaxy. We conduct a thorough numerical analysis distinguishing between regular and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels. It is of particular interest to locate the escape basins towards the two exit channels and relate them with the corresponding escape times of the orbits. For this purpose, we split our investigation into three cases depending on the initial value of the $z$ coordinate which was used for launching the stars. The most noticeable finding is that the majority of stars initiated very close to the primary $(x,y)$ plane move in chaotic orbits and they remain trapped for vast time intervals, while orbits with relatively high values of $z_0$ on the other hand, form well-defined basins of escape. It was also observed, that for energy levels close to the critical escape energy the escape rates of orbits are large, while for much higher values of energy most of the orbits have low escape periods or they escape immediately to infinity. We hope our outcomes to be useful for a further understanding of the dissolution process and the escape mechanism in open star clusters.

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arXiv2014

Determining the nature of orbits in a three-dimensional galaxy model hosting a BL Lacertae object

A three-dimensional dynamical model for a galaxy hosting a BL Lacertae object is constructed. The model consists of a logarithmic potential representing an elliptical host galaxy with a bulge of radius $c_b$ and a dense massive nucleus. Using numerical experiments, we try to distinguish between regular and chaotic motion in both 2D and 3D system. In particular, we investigate how the basic parameters of our model, such as the mass of the nucleus, the internal perturbation and the flattening parameters influence the amount and the degree of chaos. Interesting correlations are presented for both 2D and 3D dynamical models. Our numerical results are explained and supported using elementary theoretical arguments and analytical calculations. Of particular interest, is the local integral of motion which have been found to exist in the vicinity of stable periodic points. The obtained numerical outcomes of the present research, are linked and also compared with several data derived from observations.

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arXiv2014

Orbit classification of low and high angular momentum stars

We determine the character of orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric time-independent disk galaxy model with a spherical central nucleus. In particular, we try to reveal the influence of the value of the angular momentum on the different families of orbits of stars, by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families evolve when angular momentum varies. The smaller alignment index (SALI) was computed by numerically integrating the equations of motion as well as the variational equations to extensive samples of orbits in order to distinguish safely between ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Our investigation takes place both in the physical $(R,z)$ and the phase $(R,\dot{R})$ space for a better understanding of the orbital properties of the system. Our numerical computations reveal that low angular momentum stars are most likely to move in chaotic orbits, while on the other hand, the vast majority of high angular momentum stars perform regular orbits.

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arXiv2014

How does the Structure of Spherical Dark Matter Halos Affect the Types of Orbits in Disk Galaxies?

The main objective of this work is to determine the character of orbits of stars moving in the meridional $(R,z)$ plane of an axially symmetric time-independent disk galaxy model with a central massive nucleus and an additional spherical dark matter halo component. In particular, we try to reveal the influence of the scale length of the dark matter halo on the different families of orbits of stars, by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families evolve when this parameter varies. The smaller alignment index (SALI) was computed by numerically integrating the equations of motion as well as the variational equations to extensive samples of orbits in order to distinguish safely between ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Our numerical computations reveal that when the dark matter halo is highly concentrated, that is when the scale length has low values the vast majority of star orbits move in regular orbits, while on the other hand in less concentrated dark matter halos the percentage of chaos increases significantly. We also compared our results with early related work.

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arXiv2014

Classifying orbits in galaxy models with a prolate or an oblate dark matter halo component

We explore the nature of orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric galactic model with a disk, a spherical nucleus, and a flat biaxial dark matter halo component. In particular, we study the influence of all the involved parameters of the dynamical system, by computing both the percentage of chaotic orbits and the percentages of orbits of the main regular resonant families in each case. To distinguish between ordered and chaotic motion, we use the smaller alignment index (SALI) method to extensive samples of orbits by numerically integrating the equations of motion as well as the variational equations. Moreover, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Two cases are studied for every parameter: (i) the case where the halo component is prolate and (ii) the case where an oblate dark halo is present. Our numerical investigation indicates that all the dynamical quantities affect, more or less, the overall orbital structure. It was observed that the mass of the nucleus, the halo flattening parameter, the scale length of the halo, the angular momentum, and the orbital energy are the most influential quantities, while the effect of all the other parameters is much weaker. It was also found that all the parameters corresponding to the disk only have a minor influence on the nature of orbits. Furthermore, some other quantities, such as the minimum distance to the origin, the horizontal, and the vertical force, were tested as potential chaos detectors. Our analysis revealed that only general information can be obtained from these quantities. We also compared our results with early related work.

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arXiv2014

Determining the nature of orbits in disk galaxies with non spherical nuclei

We investigate the regular or chaotic nature of orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric galactic model with a flat disk and a central, non spherical and massive nucleus. In particular, we study the influence of the flattening parameter of the central nucleus on the nature of orbits, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular families. In an attempt to maximize the accuracy of our results upon distinguishing between regular and chaotic motion, we use both the Fast Lyapunov Indicator (FLI) and the Smaller ALingment Index (SALI) methods to extensive samples of orbits obtained by integrating numerically the equations of motion as well as the variational equations. Moreover, a technique which is based mainly on the field of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used for identifying the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Varying the value of the flattening parameter, we study three different cases: (i) the case where we have a prolate nucleus (ii) the case where the central nucleus is spherical and (iii) the case where an oblate massive nucleus is present. Furthermore, we present some additional findings regarding the reliability of short time (fast) chaos indicators, as well as a new method to define the threshold between chaos and regularity for both FLI and SALI, by using them simultaneously. Comparison with early related work is also made.

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arXiv2014

A Hamiltonian system of three degrees of freedom with eight channels of escape: The Great Escape

In this work, we try to shed some light to the nature of orbits in a three-dimensional potential of a perturbed harmonic oscillator with eight possible channels of escape, which was chosen as an interesting example of open three-dimensional Hamiltonian systems. In particular, we conduct a thorough numerical investigation distinguishing between regular and chaotic orbits as well as between trapped and escaping orbits, considering unbounded motion for several values of the energy. In an attempt to discriminate safely and with certainty between ordered and chaotic motion, we use the Smaller ALingment Index (SALI) detector, computed by integrating numerically the basic equations of motion as well as the variational equations. Of particular interest, is to locate the basins of escape towards the different escape channels and connect them with the corresponding escape periods of the orbits. We split our study into three different cases depending on the initial value of the $z$ coordinate which was used for launching the test particles. We found, that when the orbits are started very close to the primary $(x,y)$ plane the respective grids exhibit a high degree of fractalization, while on the other hand for orbits with relatively high values of $z_0$ several well-formed basins of escape emerge thus, reducing significantly the fractalization of the grids. It was also observed, that for values of energy very close to the escape energy the escape times of orbits are large, while for energy levels much higher than the escape energy the vast majority of orbits escape extremely fast or even immediately to infinity. We hope our outcomes to be useful for a further understanding of the escape process in open 3D Hamiltonian systems.

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arXiv2014

The Fast Norm Vector Indicator (FNVI) method: A new dynamical parameter for detecting order and chaos in Hamiltonian systems

In the present article, we introduce and also deploy a new, simple, very fast and efficient method, the Fast Norm Vector Indicator (FNVI) in order to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian systems. This distinction is based on the different behavior of the FNVI for the two cases: the indicator after a very short transient period of fluctuation displays a nearly constant value for regular orbits, while it continues to fluctuate significantly for chaotic orbits. In order to quantify the results obtained by the FNVI method, we establish the dFNVI, which is the quantified numerical version of the FNVI. A thorough study of the method's ability to achieve an early and clear detection of an orbit's behavior is presented both in two and three degrees of freedom (2D and 3D) Hamiltonians. Exploiting the advantages of the dFNVI method, we demonstrate how one can rapidly identify even tiny regions of order or chaos in the phase space of Hamiltonian systems. The new method can also be applied in order to follow the time evolution of sticky orbits. A detailed comparison between the new FNVI method and some other well-known dynamical methods of chaos detection reveals the great efficiency and the leading role of this new dynamical indicator.

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arXiv2014

Order and chaos in a new 3D dynamical model describing motion in non axially symmetric galaxies

We present a new dynamical model describing 3D motion in non axially symmetric galaxies. The model covers a wide range of galaxies from a disk system to an elliptical galaxy by suitably choosing the dynamical parameters. We study the regular and chaotic character of orbits in the model and try to connect the degree of chaos with the parameter describing the deviation of the system from axial symmetry. In order to obtain this, we use the Smaller ALingment Index (SALI) technique by numerically integrating the basic equations of motion, as well as the variational equations for extensive samples of orbits. Our results suggest, that the influence of the deviation parameter on the portion of chaotic orbits strongly depends on the vertical distance $z$ from the galactic plane of the orbits. Using different sets of initial conditions, we show that the chaotic motion is dominant in galaxy models with low values of $z$, while in the case of stars with large values of $z$ the regular motion is more abundant, both in elliptical and disk galaxy models.

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arXiv2014

Revealing the character of orbits in a binary system consisting of a primary galaxy and a satellite companion

In this article, we present a galactic gravitational model of three degrees of freedom (3D), in order to study and reveal the character of the orbits of the stars, in a binary stellar system composed of a primary quiet or active galaxy and a small satellite companion galaxy. Our main dynamical analysis will be focused on the behavior of the primary galaxy. We investigate in detail the regular or chaotic nature of motion, in two different cases: (i) the time-independent model in both 2D and 3D dynamical systems and (ii) the time-evolving 3D model. Our numerical calculations indicate that the percentage of the chaotic orbits increases when the primary galaxy has a dense and massive nucleus. The presence of the dense galactic core also increases the stellar velocities near the center of the galaxy. Moreover, for small values of the distance R between the two bodies, low-energy stars display chaotic motion, near the central region of the galaxy, while for larger values of the distance R, the motion in active galaxies is entirely regular for low-energy stars. Our simulations suggest that in galaxies with a satellite companion, the chaotic nature of motion is not only a result of the galactic interaction between the primary galaxy and its companion, but also a result caused by the presence of the dense nucleus in the core of the primary galaxy. Theoretical arguments are presented in order to support and interpret the numerically derived outcomes. Furthermore, we follow the 3D evolution of the primary galaxy, when mass is transported adiabatically from the disk to the nucleus. Our numerical results are in satisfactory agreement with observational data obtained from the M51-type binary stellar systems. A comparison between the present research and similar and earlier work is also made.

astro-ph.GA↗

arXiv2014

Order and Chaos in a Three-dimensional Binary System of Interacting Galaxies

In the present article, we present a galactic gravitational model of three degrees of freedom, in order to investigate and reveal the behavior of orbits in a binary quasar system. The two quasars are hosted in a pair of interacting disk galaxies. We study in detail the regular or chaotic character of motion, in two different cases: the time independent model in both 2D and 3D dynamical systems and the evolving 3D model. Our numerical calculations, indicate that a large fraction of orbits in the 2D system are chaotic in the time independent case. A careful analysis suggest that several Lindblad resonances are also responsible for the chaotic motion of stars in both hosts galaxies. In the time dependent system, we follow the evolution of 3D orbits in our dynamical model, as the two interacting host galaxies develop dense and massive quasars in their cores, by mass transportation from the disks to their nuclei. In this interesting case, there are orbits that change their orbital character from regular to chaotic and vise versa and also orbits that maintain their character during the galactic evolution. These results strongly indicate that the ordered or chaotic nature of 3D orbits depends, not only in the galactic interaction but also in the presence of the quasars in the galactic cores of the host galaxies. The outcomes derived from our dynamical model are compared with observational data. Some theoretical arguments to support the numerically derived outcomes are presented, both in 2D and 3D systems, while a comparison with similar earlier work is also made.

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arXiv2014

Exploring the origin, the nature and the dynamical behaviour of distant stars in galaxy models

We explore the regular or chaotic nature of orbits moving in the meridional plane of an axially symmetric galactic gravitational model with a disk, a dense spherical nucleus and some additional perturbing terms corresponding to influence from nearby galaxies. In order to obtain this we use the Smaller ALingment Index (SALI) technique integrating extensive samples of orbits. Of particular interest is the study of distant, remote stars moving in large galactocentric orbits. Our extensive numerical experiments indicate that the majority of the distant stars perform chaotic orbits. However, there are also distant stars displaying regular motion as well. Most distant stars are ejected into the galactic halo on approaching the dense and massive nucleus. We study the influence of some important parameters of the dynamical system, such as the mass of the nucleus and the angular momentum, by computing in each case the percentage of regular and chaotic orbits. A second order polynomial relationship connects the mass of the nucleus and the critical angular momentum of the distant star. Some heuristic semi-theoretical arguments to explain and justify the numerically derived outcomes are also given. Our numerical calculations suggest that the majority of distant stars spend their orbital time in the halo where it is easy to be observed. We present evidence that the main cause for driving stars to distant orbits is the presence of the dense nucleus combined with the perturbation caused by nearby galaxies. The origin of young O and B stars observed in the halo is also discussed.

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arXiv2013

Revealing the influence of dark matter on the nature of motion and the families of orbits in axisymmetric galaxy models

An axially symmetric galactic gravitational model composed of a dense, massive and spherical nucleus with an additional dark matter halo component was used, to distinguish between the regular and chaotic character of orbits of stars that move in the meridional plane (R,z). We investigated two different cases: (i) a flat-disk galaxy (ii) an elliptical galaxy. It is of particular interest to reveal how the portion of the dark matter inside the main body of the galaxy influences the ordered or chaotic nature of motion. Varying the ratio of dark matter to stellar mass, we monitored the evolution not only of the percentage of chaotic orbits, but also of the percentages of orbits that compose the main regular resonant families, by classifying regular orbits into different families. Moreover we tried, to reveal how the starting position of the parent periodic orbits of each regular family changes with respect to the fractional portion of dark matter. We compared our results with previous similar work.

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arXiv2013

Unveiling the Influence of Dark Matter in Axially Symmetric Galaxies

We investigate the regular or chaotic nature of orbits of stars moving in the meridional plane (R,z) of an axially symmetric galactic model with a dense, massive spherical nucleus and a dark matter halo component. In particular, we study the influence of the fractional portion of the dark matter, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families. In an attempt to distinguish between regular and chaotic motion, we use the Fast Lyapunov Indicator (FLI) method to extensive samples of orbits obtained by integrating numerically the equations of motion as well as the variational equations. Furthermore, a technique which is based mainly on the field of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used for identifying the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Two cases are studied in our work: (i) the case where we have a disk galaxy model (ii) the case where our model represents an elliptical galaxy. Comparison with early related work is also made.

astro-ph.GA↗

arXiv2013

Orbit classification in the meridional plane of a disk galaxy model with a spherical nucleus

We investigate the regular or chaotic nature of star orbits moving in the meridional plane of an axially symmetric galactic model with a disk and a spherical nucleus. We study the influence of some important parameters of the dynamical system, such as the mass and the scale length of the nucleus, the angular momentum or the energy, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families. Some heuristic arguments to explain and justify the numerically derived outcomes are also given. Furthermore, we present a new method to find the threshold between chaos and regularity for both Lyapunov Characteristic Numbers and SALI, by using them simultaneously.

astro-ph.GA↗

arXiv2013

Revealing the evolution, the stability and the escapes of families of resonant periodic orbits in Hamiltonian systems

We investigate the evolution of families of periodic orbits in a bisymmetrical potential made up of a two-dimensional harmonic oscillator with only one quartic perturbing term, in a number of resonant cases. Our main objective is to compute sufficiently and accurately the position and the period of the periodic orbits. For the derivation of the above quantities (position and period) we deploy in each resonance case semi-numerical methods. The comparison of our semi-numerical results with those obtained by the numerical integration of the equations of motion indicates that, in every case the relative error is always less than 1% and therefore, the agreement is more than sufficient. Thus, we claim that semi-numerical methods are very effective tools for computing periodic orbits. We also study in detail, the case when the energy of the orbits is larger than the escape energy. In this case, the periodic orbits in almost all resonance families become unstable and eventually escape from the system. Our target is to calculate the escape period and the escape position of the periodic orbits and also monitor their evolution with respect to the value of the energy.

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