The structure of motion in a 4-component galaxy mass model

We use a composite galaxy model consisting of a disk-halo, bulge, nucleus and dark-halo components in order to investigate the motion of stars in ther-z plane. It is observed that high angular momentum stars move in regular orbits. The majority of orbits are box orbits. There are also banana-like orbits. For a given value of energy, only a fraction of the low angular momentum stars — those going near the nucleus — show chaotic motion while the rest move in regular orbits. Again one observes the above two kinds of orbits. In addition to the above one can also see orbits with the characteristics of the 2/3 and 3/4 resonance. It is also shown that, in the absence of the bulge component, the area of chaotic motion in the surface of section increases, significantly. This suggests that a larger number of low angular momentum stars are in chaotic orbits in galaxies with massive nuclei and no bulge components.     

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

In the present article, we use an axially symmetric galactic gravitational model with a disk–halo and a spherical nucleus, in order to investigate the transition from regular to chaotic motion for stars moving in the meridian (r,z) plane. We study in detail the transition from regular to chaotic motion, in two different cases: the time independent model and the time evolving model. In both cases, we explored all the available range regarding the values of the main involved parameters of the dynamical system. In the time dependent model, we follow the evolution of orbits as the galaxy develops a dense and massive nucleus in its core, as mass is transported exponentially from the disk to the galactic center. We apply the classical method of the Poincaré (r,p_r) phase plane, in order to distinguish between ordered and chaotic motion. The Lyapunov Characteristic Exponent is used, to make an estimation of the degree of chaos in our galactic model and also to help us to study the time dependent model. In addition, we construct some numerical diagrams in which we present the correlations between the main parameters of our galactic model. Our numerical calculations indicate, that stars with values of angular momentum L_z less than or equal to a critical value L_zc, moving near to the galactic plane, are scattered to the halo upon encountering the nuclear region and subsequently display chaotic motion. A linear relationship exists between the critical value of the angular momentum L_zc and the mass of the nucleus M_n. Furthermore, the extent of the chaotic region increases as the value of the mass of the nucleus increases. Moreover, our simulations indicate that the degree of chaos increases linearly, as the mass of the nucleus increases. A comparison is made between the critical value L_zc and the circular angular momentum L_z0 at different distances from the galactic center. In the time dependent model, 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 orbits, depends on the presence of massive objects in the galactic cores of the galaxies. Our results suggest, that for disk galaxies with massive and prominent nuclei, the low angular momentum stars in the associated central regions of the galaxy, must be in predominantly chaotic orbits. Some theoretical arguments to support the numerically derived outcomes are presented. Comparison with similar previous works is also made.     

Chaos in Barred Galaxy Models

We investigate the regular and chaotic motion in a model potential found using the recent developments of the Inverse Problem of Dynamics. The potential describes the motion in the central parts of a barred galaxy. In the absence of rotation chaotic motion is observed when the perturbation strength is near the escape perturbation for a fixed value of the energy. In the rotating cases one observes that the area of chaotic motion on the surface of section decreases as the angular velocity Ω increases and finally all orbits become regular. The character of motion is also checked by computing the Liapunov characteristic exponents in all cases. This revised version was published online in July 2006 with corrections to the Cover Date.     

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 cb 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. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dark halos acting as chaos controllers in asymmetric triaxial galaxy models

We study the regular or chaotic character of orbits in a 3D dynamical model,describing a triaxial galaxy surrounded by a spherical dark halo component.Our numerical experiments suggest that the percentage of chaotic orbits decreases exponentially as the mass of the dark halo increases.A linear increase of the percentage of the chaotic orbits was observed as the scale length of the halo component increases. In order to distinguish between regular and chaotic motion,we chose to use the total angular momentum ...     

The S(c) spectrum machine to visualize the motion in galaxies

The behavior of the orbits in a galaxy model composed of an harmonic core and a strong bar potential is studied. Numerical calculations show that a large number of orbits display chaotic motion. These orbits are low angular momentun orbits. The percentage of chaotic orbits increases as the angular velocity of the system increases or the strength of the harmonic term decreases. A new dynamical parameter, the S(c) spectrum, is introduced and used to detect the island motion and the evolution of the sticky regions. Comparison to previously obtained results reveals the leading role of the new spectrum. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Galactic chaos driven by an oscillating massive particle

The effect of an oscillating massive particle on the motion of stars in a spherical Plummer gravitational system is examined for chaotic behaviour for ratios of satellite to parent galaxy masses ranging from .001 to .15. Thee-folding times for chaos are calculated for non-zero angular momentum orbits and discussed in relation to the time-scales for dynamical friction.     

Determining the character of motion in quiet and active galaxies with a satellite companion

A galaxy model with a satellite companion is used to study the character of motion for stars moving in the x ‐y plane. It is observed that a large part of the phase plane is covered by chaotic orbits. The percentage of chaotic orbits increases when the galaxy has a dense nucleus of massM_n. The presence of the dense nucleus also increases the stellar velocities near the center of the galaxy. For small values of the distance R between the two bodies, low energy stars display a chaotic region near the centre of the galaxy, when the dense nucleus is present, while for larger values of R the motion in active galaxies is regular for low energy stars. Our results suggest that in galaxies with a satellite companion, the chaotic character of motion is not only a result of galactic interaction but also a result caused by the dense nucleus. Theoretical arguments are used to support the numerical outcomes. We follow the evolution of the galaxy, as mass is transported adiabatically from the disk to the nucleus. Our numerical results are in satisfactory agreement with observational data from M51‐type binary galaxies (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

振动Kuzmin盘中恒星的运动性质

本文研究振动盘中恒星的运动性质．所采用的势模型为它由一种具简单径向振动模态的Kuzmin盘和一种对数晕共同产生．得到的主要结论是：（1）恒星存在稳定且有序的近圆轨道；（2）盘振动对角动量较小的恒星及远离近圆轨道的恒星影响较大；（3）盘中大部分恒星的运动是有序的；（4）远离近圆轨道的恒星一般作混沌运动，并且最终可能逃逸，但在一个Hubble时间内实际逃逸的恒星比例较小；（5）盘振动可能是振动Kurmin盘中某些星团形成并长期维持的机制之一，盘振动幅度越大，盘中星团数目可能越多；在同一个星系盘中，角动量越大的星团数目可能越少．     

The kinematic properties of stars in an oscillating Kuzmin disk

We study the kinematic properties of stars under the combined potential of a Kuzmin disk with a simple radial oscillation and a logarithmic halo. The results are: 1) There exist stable, ordered and near-circular orbits. 2) The effect of the oscillating disk is greater on orbits with smaller angular momenta and on that departly greatly from the near-circular orbits. 3) Most of the motion in the disk is ordered motion. 4) Orbits that depart greatly from the near-circular orbits generally have chaotic motion and may eventually escape. But the actual fraction escaped in one Hubble time is small. 5) Disk oscillation may be one of the mechanisms for the formation and long-term maintenance of some star clusters; the larger the amplitude, the greater may be the number of clusters; for a given disk galaxy, there may be more clusters with small than with large angular momenta.     

Do active galaxies have a massive halo component?

We present a dynamical model for an active galaxy. Our model is a mass model with a disk, nucleus, and halo components. Numerical calculations and theoretical evidence show, that for a fixed value of mass of the galaxy the stellar velocities in the central region decrease as the mass of halo increases. Furthermore, the motion tends to be regular while, when the halo component is absent, the majority of orbits are chaotic. The dynamical evolution of the system is also studied when mass is transported from the halo to the disk and the nucleus. Our results are compared to the recently obtained observation data for active galaxies.     

Formation of massive galaxies at the centre of a cluster

The formation of massive galaxies at the centre of a cluster is discussed here. The protogalaxies move with both rotation and random velocities through the gaseous medium pervading the cluster. Each galaxy is supposed to move through a resisting medium under the general gravitational field produced by the cluster as a whole. Also, the mass of the galaxy increases by accretion all the time as it moves through the medium. Using plausible laws for density of the medium and accretion of matter and solving equation of motion, we find that the galaxy loses angular momentum in the course of the time. The loss of angular momentum drives the galaxy towards the centre of the cluster. Thus over a sufficiently long time-scale several galaxies may merge in the central region of the cluster resulting in a single massive galaxy. The process can drive rise to several massive galaxies in the central region of the cluster.     

A dynamical interpretation of the Hubble sequence of galaxies

Brosche (1970) has proposed a theory in which the energy loss due to collisions among gas clouds contained in a galaxy constitutes the driving mechanism for its evolution, through virial equilibrium states which, from an initial spherical shape, makes it to contract towards an elongated form; moreover, the value of the total angular momentum, assumed as given by uniform rotation, is assumed to determine the galaxy type on the Hubble sequence and to strongly influence the contraction time from the initial spherical to the final flat configuration.We have modified Brosche's scheme by assuming as models the rotating polytropes of Chandrasekhar and Lebovitz with variable density from centre to border. As a consequence of this change, centrifugal shedding of matter is attained at the equator of the contracting ellipsoid for a configuration with an axial ratio different from zero, so that, hereafter, a flat disk is formed surrounding the internal bulge, with a decreasing overall eccentricity; the rotation curve assumes then an aspect qualitatively similar to the one observed for spiral galaxies.We have further considered the feedback of star formation which, by exhausting the material of the gas clouds, is able to stop the driving mechanism of evolution before the final flat stage is attained at several positions according to the value of the angular momentum.Numerical calculations seem to indicate that one can obtain in this way, by varying the angular momentum and the initial number of clouds, different galaxy types (elliptical, lenticular, spiral) resembling those of the Hubble sequence.     

Complex statistics in Hamiltonian barred galaxy models

We use probability density functions (pdfs) of sums of orbit coordinates, over time intervals of the order of one Hubble time, to distinguish weakly from strongly chaotic orbits in a barred galaxy model. We find that, in the weakly chaotic case, quasi-stationary states arise, whose pdfs are well approximated by q-Gaussian functions (with 1 <?q < 3), while strong chaos is identified by pdfs which quickly tend to Gaussians (q =?1). Typical examples of weakly chaotic orbits are those that ??stick?? to islands of ordered motion. Their presence in rotating galaxy models has been investigated thoroughly in recent years due to their ability to support galaxy structures for relatively long time scales. In this paper, we demonstrate, on specific orbits of 2 and 3 degree of freedom barred galaxy models, that the proposed statistical approach can distinguish weakly from strongly chaotic motion accurately and efficiently, especially in cases where Lyapunov exponents and other local dynamic indicators appear to be inconclusive.     

The evolution of chaos in active galaxy models with an oblate or a prolate dark halo component

The evolution of chaotic motion in a galactic dynamical model with a disk, a dense nucleus and a flat biaxial dark halo component is investigated. Two cases are studied: (i) the case where the halo component is oblate and (ii) the case where a prolate halo is present. In both cases, numerical calculations show that the extent of the chaotic regions decreases exponentially as the scale‐length of the dark halo increases. On the other hand, a linear relationship exists between the extent of the chaotic regions and the flatness parameter of the halo component. A linear relationship between the critical value of the angular momentum and the flatness parameter is also found. Some theoretical arguments to support the numerical outcomes are presented. An estimation of the degree of chaos is made by computing the Lyapunov Characteristic Exponents. Comparison with earlier work is also made (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dissipationless mergers of elliptical galaxies and the evolution of the fundamental plane

We carry out numerical simulations of dissipationless major mergers of elliptical galaxies using initial galaxy models that consist of a dark matter haloes and a stellar bulge with properties consistent with the observed fundamental plane. By varying the density profile of the dark matter haloes [standard Navarro, Frenk & White (NFW) profile versus adiabatically contracted NFW profile], the global stellar to dark matter mass ratio and the orbit of the merging galaxies, we are able to assess the impact of each of these factors on the structure of the merger remnant. Our results indicate that the properties of the remnant bulge depend primarily on the angular momentum and energy of the orbit; for a cosmologically motivated orbit, the effective radius and velocity dispersion of the remnant bulge remain approximately on the fundamental plane. This indicates that the observed properties of elliptical galaxies are consistent with significant growth via late dissipationless mergers. We also find that the dark matter fraction within the effective radius of our remnants increases after the merger, consistent with the hypothesis that the tilt of the fundamental plane from the virial theorem is due to a varying dark matter fraction as a function of galaxy mass.     

Modeling the dynamical profile of a BL Lacertae object

A simple dynamical model for a BL Lacertae active galaxy is presented. The model consists of a logarithmic potential with an additional term representing internal perturbations. The time independent and the evolving model are investigated. In both cases we search for regular and chaotic motion and study the velocity distribution near the centre of the system. Numerical calculations suggest that responsible for the chaotic phenomena is the internal perturbation, the flattening parameter and the dense nucleus. The radius of the nucleus also affects the maximum velocity in the central regions of the galaxy. Our numerical outcomes are supported by theoretical arguments and analytical calculations. A linking of our numerical outcomes to observational data is also presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The formation of a disk galaxy within a slowly growing dark halo

The formation of a disk galaxy within a slowly growing dark halo is simulated with a new chemo-dynamical model. The model describes the evolution of the stellar populations, the multi-phase ISM and all important interaction. I find, that the galaxy forms radially from inside-out and vertically from top-to-bottom. The derived stellar age distributions show that the inner halo is the oldest component, followed by the outer halo, the triaxial bulge, the halo-disk transition region and the disk. Despite the still idealized model, the final galaxy resembles present-day disk galaxies in many aspects. In particular, the stellar metallicity distribution in the halo of the model resembles the one of M31. The bulge in the model shows, at least two stellar subpopulations, an early collapse population and a population that formed later out of accreted disk mass. In the stellar metallicity distribution of the disk, I find a pronounced ‘G-dwarf problem’ which is the result of a pre-enrichment of the disk ISM with metal-rich gas from the bulge. This revised version was published online in September 2006 with corrections to the Cover Date.     

The Disruption of a Small Disc Galaxy by a Massive Elliptical

N-body simulations of the capture of a small disc galaxy by a massive elliptical primary show that tidal forces destroy the inner part of the disc in a brief episode at some critical distance from the centre of the primary. We suggest that this phase may be characterised by chaotic motions in the disc material causing a burst of star formation. Such an event would offer a natural explanation of the colour differences between stars in shells around an elliptical galaxy and those in the galaxy itself. We report a study of orbits in the disc prior to and during its disruption, designed to test this hypothesis. This revised version was published online in July 2006 with corrections to the Cover Date.     

Evolution of the Galactic Halo and Disk

Correlations between stellar kinematics and chemical abundances are fossil evidence for evolutionary connections between Galactic structural components. Extensive stellar surveys show that the only tolerably clear distinction between galactic components appears in the distributions of specific angular momentum. Here the stellar metal-poor halo and the metal-rich bulge are indistinguishable from each other, as are the thick disk and the old disk. Each pair is very distinct from the other. This leads to an evolutionary model in which the metal-poor stellar halo evolves into the inner bulge, while the thick disk is a precursor to the thin disk. These evolutionary sequences are distinct. The galaxy is made of two discrete 'populations', one of low and one of high angular momentum. Some (minor?) complexity is added to this picture by the debris of late and continuing mergers, which will be especially important in the outer stellar halo.