Exploring the nature of orbits in a galactic model with a massive nucleus

Zotos, Euaggelos E.

doi:10.1016/j.newast.2012.02.002

Cited by 27 publications

(33 citation statements)

References 46 publications

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“…The above discussion strongly indicates that in the centers of active galaxies, chaotic motion and high velocities are expected. This fact, combined with outcomes from previous works, shows that the majority of orbits in galaxies with dense and massive nuclei are in chaotic orbits (see Caranicolas & Innanen 1991;Caranicolas & Papadopoulos 2003;Zotos 2012a). This seems reasonable because theoretical results show that the nuclear force near the center increases linearly as M n increases.…”

Section: Discussionsupporting

confidence: 68%

Revealing the Character of Orbits in a Binary System Consisting of a Primary Galaxy and a Satellite Companion

Zotos

2013

Publ. Astron. Soc. Aust.

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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 behaviour 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. For the description of the structure of the 2D system, we use the classical method of the Poincaré (x, p x ), y = 0, p y < 0 phase plane. In order to study the structure of the phase space of the 3D system, we take sections in the plane y = 0 of the 3D orbits, whose initial conditions differ from the plane parent periodic orbits, only by the z component. The set of the four-dimensional points in the (x, p x , z, p z ) phase space is projected on the (z, p z ) plane. The maximum Lyapunov characteristic exponent is used in order to make an estimation of the chaoticity of our galactic system, in both 2D and 3D dynamical models. 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.

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Section: Discussionsupporting

confidence: 68%

Revealing the Character of Orbits in a Binary System Consisting of a Primary Galaxy and a Satellite Companion

Zotos

2013

Publ. Astron. Soc. Aust.

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“…In [45] the case of a cosmological model is discussed, where orbits may experience regular and/or chaotic motion during their time evolution, while in [46] the effects of a black hole, friction, noise and periodic driving are studied on a triaxial elliptic galaxy model, in which a type of transient chaos was found caused by a damped, oscillatory component [47,48]. Finally, in [49] the so-called "pattern method" was used to study a Hénon-Heiles potential to which an exponential function of time is added, while the dynamics of some simple TD galactic models was investigated in [50,51].…”

Section: Introductionmentioning

confidence: 99%

Interplay between chaotic and regular motion in a time-dependent barred galaxy model

Manos¹,

Bountis²,

Skokos³

2013

J. Phys. A: Math. Theor.

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Abstract. 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.PACS numbers: 95.10. Fh, 05.45.Ac, 05.45.Pq, 98.62.Ck, 98.62.Dm, 98.62.Hr

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“…The horizontal red dashed line at L z = 53.44 marks the last indication of chaos; for L z > 53.44 the motion of stars is entirely regular and there is no evidence of chaotic motion whatsoever. In fact, L z = 53.44 is the maximum value of the angular momentum for which the orbits can display chaotic motion and it is called the critical value of the angular momentum L zc (e.g., Zotos, 2011Zotos, , 2012Zotos & Carpintero, 2013).…”

Section: An Overview Analysismentioning

confidence: 99%

Orbit classification of low and high angular momentum stars

Zotos

2014

Mechanics Research Communications

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We determine the character of orbits of stars moving in the meridional plane (R, z) of an axially symmetric timeindependent 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,Ṙ) 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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Exploring the nature of orbits in a galactic model with a massive nucleus

Cited by 27 publications

References 46 publications

Revealing the Character of Orbits in a Binary System Consisting of a Primary Galaxy and a Satellite Companion

Revealing the Character of Orbits in a Binary System Consisting of a Primary Galaxy and a Satellite Companion

Interplay between chaotic and regular motion in a time-dependent barred galaxy model

Orbit classification of low and high angular momentum stars

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