arXiv subjects

Euaggelos E. Zotos

Publications and source records attributed to Euaggelos E. Zotos.

At least 73 records · Page 4Linked to original sources

arXiv2016

Fugitive stars in active galaxies

We investigate in detail the escape dynamics in an analytical gravitational model which describes the motion of stars in a quasar galaxy with a disk and a massive nucleus. 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. In order to distinguish safely and with certainty between ordered and chaotic motion we apply the Smaller ALingment Index (SALI) method. It is of particular interest to locate the escape basins through the openings around the collinear Lagrangian points $L_1$ and $L_2$ and relate them with the corresponding spatial distribution of the escape times of the orbits. Our exploration takes place both in the configuration $(x,y)$ and in the phase $(x,\dot{x})$ space in order to elucidate the escape process as well as the overall orbital properties of the galactic system. Our numerical analysis reveals the strong dependence of the properties of the considered escape basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the escape regimes. We hope our outcomes to be useful for a further understanding of the escape mechanism in active galaxy models.

astro-ph.GA↗

arXiv2016

Escape dynamics in a binary system of interacting galaxies

The escape dynamics in an analytical gravitational model which describes the motion of stars in a binary system of interacting dwarf spheroidal galaxies is investigated in detail. We conduct a numerical analysis distinguishing between regular and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels. In order to distinguish safely and with certainty between ordered and chaotic motion, we apply the Smaller ALingment Index (SALI) method. It is of particular interest to locate the escape basins through the openings around the collinear Lagrangian points $L_1$ and $L_2$ and relate them with the corresponding spatial distribution of the escape times of the orbits. Our exploration takes place both in the configuration $(x,y)$ and in the phase $(x,\dot{x})$ space in order to elucidate the escape process as well as the overall orbital properties of the galactic system. Our numerical analysis reveals the strong dependence of the properties of the considered escape basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the escape regimes. 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 escape mechanism in binary galaxy models.

astro-ph.GA↗

arXiv2016

Determining the type of orbits in the central regions of barred galaxies

We use a simple dynamical model which consists of a harmonic oscillator and a spherical component, in order to investigate the regular or chaotic character of orbits in a barred galaxy with a central spherically symmetric nucleus. Our aim is to explore how the basic parameters of the galactic system influence the nature of orbits, by computing in each case the percentage of chaotic orbits, as well as the percentages of different types of regular orbits. We also give emphasis to the types of regular orbits that support either the formation of nuclear rings or the barred structure of the galaxy. We provide evidence that the traditional x1 orbital family does not always dominate in barred galaxy models since we found several other types of resonant orbits which can also support the barred structure. We also found that sparse enough nuclei, fast rotating bars and high energy models can support the galactic bars. On the other hand, weak bars, dense central nuclei, slowly rotating bars and low energy models favor the formation of nuclear rings. We also compare our results with previous related work.

astro-ph.GA↗

arXiv2016

Orbital and escape dynamics in barred galaxies - I. The 2D system

In this paper we use the two-dimensional (2D) version of a new analytical gravitational model in order to explore the orbital as well as the escape dynamics of the stars in a barred galaxy composed of a spherically symmetric central nucleus, a bar, a flat disk and a dark matter halo component. A thorough numerical investigation is conducted for distinguishing between bounded and escaping motion. Furthermore bounded orbits are further classified into non-escaping regular and trapped chaotic using the Smaller ALingment Index (SALI) method. Our aim is to determine the basins of escape through the two symmetrical escape channels around the Lagrange points $L_2$ and $L_3$ and also to relate them with the corresponding distribution of the escape rates of the orbits. We integrate initial conditions of orbits in several types of planes so as to obtain a more complete view of the overall orbital properties of the dynamical system. We also present evidence that the unstable manifolds which guide the orbits in and out the interior region are directly related with the formation of spiral and ring stellar structures observed in barred galaxies. In particular, we examine how the bar's semi-major axis determines the resulting morphologies. Our numerical simulations indicate that weak barred structures favour the formation of $R_1$ rings or $R_1'$ pseudo-rings, while strong bars on the other hand, give rise to $R_1R_2$ and open spiral morphologies. Our results are compared with earlier related work. The escape dynamics and the properties of the manifolds of the full three-dimensional (3D) galactic system will be given in an accompanying paper.

astro-ph.GA↗

arXiv2015

Unveiling the influence of the radiation pressure in nature of orbits in the photogravitational restricted three-body problem

The case of the planar circular photogravitational restricted three-body problem where the more massive primary is an emitter of radiation is numerically investigated. A thorough numerical analysis takes place in the configuration $(x,y)$ and the $(x,C)$ space in which we classify initial conditions of orbits into three main categories: (i) bounded, (ii) escaping and (iii) collisional. Our results reveal that the radiation pressure factor has a huge impact on the character of orbits. Interpreting the collisional motion as leaking in the phase space we related our results to both chaotic scattering and the theory of leaking Hamiltonian systems. We successfully located the escape as well as the collisional basins and we managed to correlate them with the corresponding escape and collision times. We hope our contribution to be useful for a further understanding of the escape and collision properties of motion in this interesting version of the restricted three-body problem.

astro-ph.EP↗

arXiv2015

Orbit classification in the planar circular Pluto-Charon system

We numerically investigate the orbital dynamics of a spacecraft, or a comet, or an asteroid in the Pluto-Charon system in a scattering region around Charon using the planar circular restricted three-body problem. The test particle can move in bounded orbits around Charon or escape through the necks around the Lagrangian points $L_1$ and $L_2$ or even collide with the surface of Charon. We explore four of the five possible Hill's regions configurations depending on the value of the Jacobi constant which is of course related with the total orbital energy. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits and distinguishing between three types of motion: (i) bounded, (ii) escaping and (iii) collisional. In particular, we locate the different basins and we relate them with the corresponding spatial distributions of the escape and collision times. Our results reveal the high complexity of this planetary system. Furthermore, the numerical analysis shows a strong dependence of the properties of the considered basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the regimes. Our results are compared with earlier ones regarding the Saturn-Titan planetary system.

astro-ph.EP↗

arXiv2015

Escape dynamics in a Hamiltonian system with four exit channels

We reveal the escape mechanism of orbits in a Hamiltonian system with four exit channels composed of two-dimensional perturbed harmonic oscillators. We distinguish between trapped chaotic, non-escaping regular and escaping orbits by conducting a thorough and systematic numerical investigation in both the configuration and the phase space. We locate the different basins of escape and we relate them withe the corresponding escape times of orbits. The SALI method is used for determining the ordered or chaotic nature of the orbits. It was observed that trapped and non-escaping orbits coexist with several escape basins. When the energy is very close to the escape energy the escape rate of orbits is huge, while as the value of the energy increases the orbits escape more quickly to infinity. Furthermore, initial conditions of orbits located near the boundaries of the basins of escape and also in the vicinity of the fractal domains were found to posses the largest escape rates. The degree of the fractality of the phase space was calculated as a function of the value of the energy. Our results were compared with earlier related work.

nlin.CD↗

arXiv2015

Escapes in Hamiltonian systems with multiple exit channels: Part II

We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and escaping orbits. The determination of the location of the basins of escape towards the different escape channels and their correlations with the corresponding escape periods of the orbits is undoubtedly an issue of paramount importance. We consider four different cases depending on the perturbation function which controls the number of escape channels on the configuration space. In every case, we computed extensive samples of orbits in both the configuration and the phase space by numerically integrating the equations of motion as well as the variational equations. It was found that in all examined cases regions of non-escaping motion coexist with several basins of escape. The larger escape periods have been measured for orbits with initial conditions in the vicinity of the fractal structure, while the lowest escape rates belong to orbits with initial conditions inside the basins of escape. In addition, we related the model potential with applications in the field of reactive multichannel scattering. We hope that our numerical analysis will be useful for a further understanding of the escape mechanism of orbits in open Hamiltonian systems with two degrees of freedom.

nlin.CD↗

arXiv2015

Classifying orbits in the restricted three-body problem

The case of the planar circular restricted three-body problem is used as a test field in order to determine the character of the orbits of a small body which moves under the gravitational influence of the two heavy primary bodies. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits and distinguishing between three types of motion: (i) bounded, (ii) escape and (iii) collisional. The presented outcomes reveal the high complexity of this dynamical system. Furthermore, our numerical analysis shows a remarkable presence of fractal basin boundaries along all the escape regimes. Interpreting the collisional motion as leaking in the phase space we related our results to both chaotic scattering and the theory of leaking Hamiltonian systems. We also determined the escape and collisional basins and computed the corresponding escape/collisional times. We hope our contribution to be useful for a further understanding of the escape and collisional mechanism of orbits in the restricted three-body problem.

physics.space-ph↗

arXiv2015

Order and chaos in a three dimensional galaxy model

We explore the orbital dynamics of a realistic three dimensional model describing the properties of a disk galaxy with a spherically symmetric central dense nucleus and a triaxial dark matter halo component. Regions of phase space with regular and chaotic motion are identified depending on the parameter values for triaxiality of the dark matter halo and for breaking the rotational symmetry. The four dimensional Poincaré map of the three degrees of freedom system is analyzed by a study of its restriction to various two dimensional invariant subsets of its domain.

astro-ph.GA↗

arXiv2015

Introducing a new 3D dynamical model for barred galaxies

The regular or chaotic dynamics of an analytical realistic three dimensional model composed of a spherically symmetric central nucleus, a bar and a flat disk is investigated. For describing the properties of the bar we introduce a new simple dynamical model and we explore the influence on the character of orbits of all the involved parameters of it, such as the mass and the scale length of the bar, the major semi-axis and the angular velocity of the bar as well as the energy. Regions of phase space with ordered and chaotic motion are identified in dependence on these parameters and for breaking the rotational symmetry. First we study in detail the dynamics in the invariant plane $z = p_z = 0$ using the Poincaré map as a basic tool and then we study the full 3 dimensional case using the SALI method as principal tool for distinguishing between order and chaos. We also present strong evidence obtained through the numerical simulations that our new bar model can realistically describe the formation and the evolution of the observed twin spiral structure in barred galaxies.

astro-ph.GA↗

arXiv2015

Orbital dynamics in the planar Saturn-Titan system

We use the planar circular restricted three-body problem in order to numerically investigate the orbital dynamics of orbits of a spacecraft, or a comet, or an asteroid in the Saturn-Titan system in a scattering region around the Titan. The orbits can escape through the necks around the Lagrangian points $L_1$ and $L_2$ or collide with the surface of the Titan. We explore all the four possible Hill's regions depending on the value of the Jacobi constant. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits and distinguishing between three types of motion: (i) bounded, (ii) escaping and (iii) collisional. In particular, we locate the different basins and we relate them with the corresponding spatial distributions of the escape and crash times. Our results reveal the high complexity of this planetary system. Furthermore, the numerical analysis shows a strong dependence of the properties of the considered basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the regimes. We hope our contribution to be useful in both space mission design and study of planetary systems.

astro-ph.EP↗

arXiv2015

How does the oblateness coefficient influence the nature of orbits in the restricted three-body problem?

We numerically investigate the case of the planar circular restricted three-body problem where the more massive primary is an oblate spheroid. A thorough numerical analysis takes place in the configuration $(x,y)$ and the $(x,E)$ space in which we classify initial conditions of orbits into three categories: (i) bounded, (ii) escaping and (iii) collisional. Our results reveal that the oblateness coefficient has a huge impact on the character of orbits. Interpreting the collisional motion as leaking in the phase space we related our results to both chaotic scattering and the theory of leaking Hamiltonian systems. We successfully located the escape as well as the collisional basins and we managed to correlate them with the corresponding escape and collision times. We hope our contribution to be useful for a further understanding of the escape and collision properties of motion in this interesting version of the restricted three-body problem.

astro-ph.EP↗

arXiv2015

Comparing the escape dynamics in tidally limited star cluster models

The aim of this work is to compare the orbital dynamics in three different models describing the properties of a star cluster rotating around its parent galaxy in a circular orbit. In particular, we use the isochrone and the Hernquist potentials to model the spherically symmetric star cluster and we compare our results with the corresponding ones of a previous work in which the Plummer model was applied for the same purpose. Our analysis takes place both in the configuration $(x,y)$ and in the phase $(x,\dot{x})$ space in order to elucidate the escape process as well as the overall orbital properties of the tidally limited star cluster. We restrict our investigation into two dimensions and we conduct a thorough numerical analysis distinguishing between ordered and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels above the critical escape energy. It is of particular interest to determine the escape basins towards the two exit channels (near the Lagrangian points $L_1$ and $L_2$) and relate them with the corresponding escape times of the orbits.

astro-ph.GA↗

arXiv2015

Classifying orbits in a new dynamical model describing motion in a prolate or an oblate elliptical galaxy

The regular or chaotic character of orbits of stars moving in the meridional plane (R,z) of an axially symmetric elliptical galaxy with a dense, massive spherical nucleus and a dark matter halo component is under investigation. In particular, we explore how the flattening of an elliptical galaxy influences the overall orbital structure of the system, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits composing the main regular families. In an attempt to discriminate safely and with certainty between regular and chaotic motion, we use the Smaller ALingment Index (SALI) method to extensive samples of orbits obtained by integrating numerically the basic equations of motion as well as the variational equations. In addition, 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 classifying the regular orbits into different families and also to recognize the secondary resonances that usually bifurcate from them. Three cases are considered in our work: (i) the case where the elliptical galaxy is prolate (ii) the case where a spherically symmetric elliptical galaxy is present and (iii) the case where the elliptical galaxy has an oblate shape. Comparison between the current results and early related work is also made.

astro-ph.GA↗

arXiv2015

Crash test for the Copenhagen problem with oblateness

The case of the planar circular restricted three-body problem where one of the two primaries is an oblate spheroid is investigated. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits and distinguishing between three types of motion: (i) bounded, (ii) escape and (iii) collisional. The presented outcomes reveal the high complexity of this dynamical system. Furthermore, our numerical analysis shows a strong dependence of the properties of the considered escape basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the escape regimes. Interpreting the collisional motion as leaking in the phase space we related our results to both chaotic scattering and the theory of leaking Hamiltonian systems. We also determined the escape and collisional basins and computed the corresponding escape/crash times. The highly fractal basin boundaries observed are related with high sensitivity to initial conditions thus implying an uncertainty between escape solutions which evolve to different regions of the phase space. We hope our contribution to be useful for a further understanding of the escape and crash mechanism of orbits in this version of the restricted three-body problem.

physics.space-ph↗

arXiv2015

Escape dynamics and fractal basin boundaries in Seyfert galaxies

The escape dynamics in a simple analytical gravitational model which describes the motion of stars in a Seyfert galaxy is investigated in detail. 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. In order to distinguish safely and with certainty between ordered and chaotic motion, we apply the Smaller ALingment Index (SALI) method. It is of particular interest to locate the escape basins through the openings around the collinear Lagrangian points $L_1$ and $L_2$ and relate them with the corresponding spatial distribution of the escape times of the orbits. Our exploration takes place both in the physical $(x,y)$ and in the phase $(x,\dot{x})$ space in order to elucidate the escape process as well as the overall orbital properties of the galactic system. Our numerical analysis reveals the strong dependence of the properties of the considered escape basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the escape regimes. 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 also present evidence obtained through numerical simulations that our model can describe the formation and the evolution of the observed spiral structure in Seyfert galaxies. We hope our outcomes to be useful for a further understanding of the escape mechanism in galaxies with active nuclei.

astro-ph.GA↗

arXiv2015

Escapes in Hamiltonian systems with multiple exit channels: Part I

The aim of this work is to review and also explore even further the escape properties of orbits in a dynamical system of a two-dimensional perturbed harmonic oscillator, which is a characteristic example of open Hamiltonian systems. In particular, we conduct a thorough numerical investigation distinguishing between trapped (ordered and chaotic) and escaping orbits, considering only unbounded motion for several energy levels. It is of particular interest, 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 examination into three different cases depending on the function of the perturbation term which determines the number of escape channels on the physical space. In every case, we computed extensive samples of orbits in both the physical and the phase space by integrating numerically the equations of motion as well as the variational equations. In an attempt to determine the regular or chaotic nature of trapped motion, we applied the SALI method as a chaos detector. It was found, that in all studied cases regions of trapped orbits coexist with several basins of escape. It was also observed, that for energy levels very close to the escape value the escape times of orbits are large, while for values of energy much higher than the escape energy the vast majority of orbits escape very quickly or even immediately to infinity. The larger escape periods have been measured for orbits with initial conditions in the boundaries of the escape basins and also in the vicinity of the fractal structure. Most of the current outcomes have been compared with previous related work. We hope that our results will be useful for a further understanding of the escape mechanism of orbits in open Hamiltonian systems with two degrees of freedom.

nlin.CD↗