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T. Manos

Publications and source records attributed to T. Manos.

At least 19 recordsLinked to original sources
arXiv2024

The response of the inner dark matter halo to stellar bars

Barred galaxies constitute about two thirds of observed disc galaxies. Bars affect not only the mass distribution of gas and stars, but also that of the dark matter. An elongation of the inner dark matter halo is known as the halo bar. We aim to characterise the structure of the halo bars, with the goal of correlating them with the properties of the stellar bars. We use a suite of simulated galaxies with various bar strengths, including gas and star formation. We quantify strengths, shapes, and densities of these simulated stellar bars. We carry out numerical experiments with frozen and analytic potentials in order to understand the role played by a live responsive stellar bar. We find that the halo bar generally follows the trends of the disc bar. The strengths of the halo and stellar bars are tightly correlated. Stronger bars induce a slight increase of dark matter density within the inner halo. Numerical experiments show that a non-responsive frozen stellar bar would be capable of inducing a dark matter bar, but it would be weaker than the live case by a factor of roughly two.

astro-ph.GA↗
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↗
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.

astro-ph.GA↗
arXiv2016

Chaotic motion and the evolution of morphological components in a time-dependent model of a barred galaxy within a dark matter halo

Studies of dynamical stability (chaotic versus regular motion) in galactic dynamics often rely on static analytical models of the total gravitational potential. Potentials based upon self-consistent N-body simulations offer more realistic models, fully incorporating the time-dependent nature of the systems. Here we aim at analysing the fractions of chaotic motion within different morphological components of the galaxy. We wish to investigate how the presence of chaotic orbits evolves with time, and how their spatial distribution is associated with morphological features of the galaxy. We employ a time-dependent analytical potential model that was derived from an N-body simulation of a strongly barred galaxy. With this analytical potential we may follow the dynamical evolution of ensembles of orbits. Using the Generalized Alignment Index (GALI) chaos detection method, we study the fraction of chaotic orbits, sampling the dynamics of both the stellar disc and of the dark matter halo. Within the stellar disc, the global trend is for chaotic motion to decrease in time, specially in the region of the bar. We scrutinized the different changes of regime during the evolution (orbits that are permanently chaotic, permanently regular, those that begin regular and end chaotic, and those that begin chaotic and end regular), tracing the types of orbits back to their common origins. Within the dark matter halo, chaotic motion also decreases globally in time. The inner halo (r < 5 kpc) is where most chaotic orbits are found and it is the only region where chaotic orbits outnumber regular orbits, in the early evolution.

astro-ph.GA↗
arXiv2015

The Smaller (SALI) and the Generalized (GALI) Alignment Indices: Efficient Methods of Chaos Detection

We provide a concise presentation of the Smaller (SALI) and the Generalized Alignment Index (GALI) methods of chaos detection. These are efficient chaos indicators based on the evolution of two or more, initially distinct, deviation vectors from the studied orbit. After explaining the motivation behind the introduction of these indices, we sum up the behaviors they exhibit for regular and chaotic motion, as well as for stable and unstable periodic orbits, focusing mainly on finite-dimensional conservative systems: autonomous Hamiltonian models and symplectic maps. We emphasize the advantages of these methods in studying the global dynamics of a system, as well as their ability to identify regular motion on low dimensional tori. Finally we discuss several applications of these indices to problems originating from different scientific fields like celestial mechanics, galactic dynamics, accelerator physics and condensed matter physics.

nlin.CD↗
arXiv2015

Statistical properties of the localization measure in a finite-dimensional model of the quantum kicked rotator

We study the quantum kicked rotator in the classically fully chaotic regime $K=10$ and for various values of the quantum parameter $k$ using Izrailev's $N$-dimensional model for various $N \le 3000$, which in the limit $N \rightarrow \infty$ tends to the exact quantized kicked rotator. By numerically calculating the eigenfunctions in the basis of the angular momentum we find that the localization length ${\cal L}$ for fixed parameter values has a certain distribution, in fact its inverse is Gaussian distributed, in analogy and in connection with the distribution of finite time Lyapunov exponents of Hamilton systems. However, unlike the case of the finite time Lyapunov exponents, this distribution is found to be independent of $N$, and thus survives the limit $N=\infty$. This is different from the tight-binding model of Anderson localization. The reason is that the finite bandwidth approximation of the underlying Hamilton dynamical system in the Shepelyansky picture (D.L. Shepelyansky, {\em Phys. Rev. Lett.} {\bf 56}, 677 (1986)) does not apply rigorously. This observation explains the strong fluctuations in the scaling laws of the kicked rotator, such as e.g. the entropy localization measure as a function of the scaling parameter $\Lambda={\cal L}/N$, where $\cal L$ is the theoretical value of the localization length in the semiclassical approximation. These results call for a more refined theory of the localization length in the quantum kicked rotator and in similar Floquet systems, where we must predict not only the mean value of the inverse of the localization length $\cal L$ but also its (Gaussian) distribution, in particular the variance. In order to complete our studies we numerically analyze the related behavior of finite time Lyapunov exponents in the standard map and of the 2$\times$2 transfer matrix formalism. This paper is extending our recent work.

nlin.CD↗
arXiv2015

Accelerator modes and their effect in the diffusion properties in the kicked rotator

We highlight a few recent results on the effect of the diffusion process in deterministic area preserving maps with noncompact phase space, namely the standard map. In more detail, we focus on the anomalous diffusion arising due to the accelerator modes, i.e. resonant-like features of the phase space which are transported in a super-diffusive (ballistic) manner. Their presence affects also the trajectories lying in the immediate neighborhood resulting in anomalous (non-Gaussian) diffusion. We aim to shed some light on these special properties of the phase space by utilizing the diffusion exponent (rate of diffusion) and the momentum distribution in terms of the Lévy stable distributions, with the goal to reach an understanding of the global behaviour. To this end we consider a rather large interval for the kick parameter ($0\le K \le 70$) of the standard map where accelerator modes of different periodicity exist.

nlin.CD↗
arXiv2013

Chaos and dynamical trends in barred galaxies: bridging the gap between N-body simulations and time-dependent analytical models

Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global phase space properties, which are the underlying cause of observed structures. The potentials needed to describe self-consistent models are time-dependent. Here, we aim to investigate dynamical properties (regular/chaotic motion) of a non-autonomous galactic system, whose time-dependent potential adequately mimics certain realistic trends arising from N-body barred galaxy simulations. We construct a fully time-dependent analytical potential, modeling the gravitational potentials of disc, bar and dark matter halo, whose time-dependent parameters are derived from a simulation. We study the dynamical stability of its reduced time-independent 2-degrees of freedom model, charting the different islands of stability associated with certain orbital morphologies and detecting the chaotic and regular regions. In the full 3-degrees of freedom time-dependent case, we show representative trajectories experiencing typical dynamical behaviours, i.e., interplay between regular and chaotic motion for different epochs. Finally, we study its underlying global dynamical transitions, estimating fractions of (un)stable motion of an ensemble of initial conditions taken from the simulation. For such an ensemble, the fraction of regular motion increases with time.

astro-ph.GA↗
arXiv2012

Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model

We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.

nlin.CD↗
arXiv2012

Explicit Construction of First Integrals by Singularity Analysis in Nonlinear Dynamical Systems

The Painleve and weak Painleve conjectures have been used widely to identify new integrable nonlinear dynamical systems. The calculation of the integrals relies though on methods quite independent from Painlevé analysis. This paper proposes a new explicit algorithm to build the first integrals of a given set of nonlinear ordinary differential equations by exploiting the information provided by the Painleve - Laurent series representing the solution in the neighbourhood of a movable singularity. The algorithm is based on known theorems from the theory of singularity analysis. Examples are given of the explicit construction of the first integrals in nonlinear Hamiltonian dynamical systems with a polynomial potential, and in generalized Volterra systems.

nlin.SI↗
arXiv2011

Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method

As originally formulated, the Generalized Alignment Index (GALI) method of chaos detection has so far been applied to distinguish quasiperiodic from chaotic motion in conservative nonlinear dynamical systems. In this paper we extend its realm of applicability by using it to investigate the local dynamics of periodic orbits. We show theoretically and verify numerically that for stable periodic orbits the GALIs tend to zero following particular power laws for Hamiltonian flows, while they fluctuate around non-zero values for symplectic maps. By comparison, the GALIs of unstable periodic orbits tend exponentially to zero, both for flows and maps. We also apply the GALIs for investigating the dynamics in the neighborhood of periodic orbits, and show that for chaotic solutions influenced by the homoclinic tangle of unstable periodic orbits, the GALIs can exhibit a remarkable oscillatory behavior during which their amplitudes change by many orders of magnitude. Finally, we use the GALI method to elucidate further the connection between the dynamics of Hamiltonian flows and symplectic maps. In particular, we show that, using for the computation of GALIs the components of deviation vectors orthogonal to the direction of motion, the indices of stable periodic orbits behave for flows as they do for maps.

nlin.CD↗
arXiv2011

Regular and chaotic orbits in barred galaxies - I. Applying the SALI/GALI method to explore their distribution in several models

The distinction between chaotic and regular behavior of orbits in galactic models is an important issue and can help our understanding of galactic dynamical evolution. In this paper, we deal with this issue by applying the techniques of the Smaller (and Generalized) ALingment Indices, SALI (and GALI), to extensive samples of orbits obtained by integrating numerically the equations of motion in a barred galaxy potential. We estimate first the fraction of chaotic and regular orbits for the two-degree-of-freedom (DOF) case (where the galaxy extends only in the (x,y)-space) and show that it is a non-monotonic function of the energy. For the three DOF extension of this model (in the z-direction), we give similar estimates, both by exploring different sets of initial conditions and by varying the model parameters, like the mass, size and pattern speed of the bar. We find that regular motion is more abundant at small radial distances from the center of the galaxy, where the relative non-axisymmetric forcing is relatively weak, and at small distances from the equatorial plane, where trapping around the stable periodic orbits is important. We also find that the variation of the bar pattern speed, within a realistic range of values, does not affect much the phase space's fraction of regular and chaotic motions. Using different sets of initial conditions, we show that chaotic motion is dominant in galaxy models whose bar component is more massive, while models with a fatter or thicker bar present generally more regular behavior. Finally, we find that the fraction of orbits that are chaotic correlates strongly with the bar strength.

astro-ph.GA↗
arXiv2010

SALI: An Efficient Indicator of Chaos with Application to 2 and 3 Degrees of Freedom Hamiltonian Systems

The Smaller Alignment Index (SALI) is a very useful and efficient indicator that can distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian systems. This is based on the different behavior of the SALI in the two cases, as it fluctuates around non-zero values for ordered orbits and converges exponentially to zero for chaotic orbits. In this paper we present a detailed numerical study, comparing the advantages of the SALI to those of the Maximal Lyapunov Exponent (MLE), which is the traditional indicator of chaos detection in dynamical systems. Exploiting these advantages, we demonstrate how the SALI can be used to identify even tiny regions of order and chaos in Hamiltonian systems of 2 and 3 degrees of freedom.

nlin.CD↗
arXiv2010

Experimental perspectives for systems based on long-range interactions

The possibility of observing phenomena peculiar to long-range interactions, and more specifically in the so-called Quasi-Stationary State (QSS) regime is investigated within the framework of two devices, namely the Free-Electron Laser (FEL) and the Collective Atomic Recoil Laser (CARL). The QSS dynamics has been mostly studied using the Hamiltonian Mean-Field (HMF) toy model, demonstrating in particular the presence of first versus second order phase transitions from magnetized to unmagnetized regimes in the case of HMF. Here, we give evidence of the strong connections between the HMF model and the dynamics of the two mentioned devices, and we discuss the perspectives to observe some specific QSS features experimentally. In particular, a dynamical analog of the phase transition is present in the FEL and in the CARL in its conservative regime. Regarding the dissipative CARL, a formal link is established with the HMF model. For both FEL and CARL, calculations are performed with reference to existing experimental devices, namely the FERMI@Elettra FEL under construction at Sincrotrone Trieste (Italy) and the CARL system at LENS in Florence (Italy).

nlin.CD↗
arXiv2008

Application of the GALI Method to Localization Dynamics in Nonlinear Systems

We investigate localization phenomena and stability properties of quasiperiodic oscillations in $N$ degree of freedom Hamiltonian systems and $N$ coupled symplectic maps. In particular, we study an example of a parametrically driven Hamiltonian lattice with only quartic coupling terms and a system of $N$ coupled standard maps. We explore their dynamics using the Generalized Alignment Index (GALI), which constitutes a recently developed numerical method for detecting chaotic orbits in many dimensions, estimating the dimensionality of quasiperiodic tori and predicting slow diffusion in a way that is faster and more reliable than many other approaches known to date.

nlin.CD↗
arXiv2008

Dynamical study of 2D and 3D barred galaxy models

We study the dynamics of 2D and 3D barred galaxy analytical models, focusing on the distinction between regular and chaotic orbits with the help of the Smaller ALigment Index (SALI), a very powerful tool for this kind of problems. We present briefly the method and we calculate the fraction of chaotic and regular orbits in several cases. In the 2D model, taking initial conditions on a Poincaré $(y,p_y)$ surface of section, we determine the fraction of regular and chaotic orbits. In the 3D model, choosing initial conditions on a cartesian grid in a region of the $(x, z, p_y)$ space, which in coordinate space covers the inner disc, we find how the fraction of regular orbits changes as a function of the Jacobi constant. Finally, we outline that regions near the $(x,y)$ plane are populated mainly by regular orbits. The same is true for regions that lie either near to the galactic center, or at larger relatively distances from it.

astro-ph↗
arXiv2008

Global dynamics of coupled standard maps

Understanding the dynamics of multi--dimensional conservative dynamical systems (Hamiltonian flows or symplectic maps) is a fundamental issue of non-linear science. The Generalized ALignment Index (GALI), which was recently introduced and applied successfully for the distinction between regular and chaotic motion in Hamiltonian systems \cite{sk:6}, is an ideal tool for this purpose. In the present paper we make a first step towards the dynamical study of multi--dimensional maps, by obtaining some interesting results for a 4--dimensional (4D) symplectic map consisting of N=2 coupled standard maps \cite{Kan:1}. In particular, using the new GALI$_3$ and GALI$_4$ indices, we compute the percentages of regular and chaotic motion of the map equally reliably but much faster than previously used indices, like GALI$_2$ (known in the literature as SALI).

nlin.CD↗