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1.
M. Harsoula C. Kalapotharakos 《Monthly notices of the Royal Astronomical Society》2009,394(3):1605-1619
We study the orbital structure in a series of self-consistent N -body configurations simulating rotating barred galaxies with spiral and ring structures. We perform frequency analysis in order to measure the angular and the radial frequencies of the orbits at two different time snapshots during the evolution of each N -body system. The analysis is done separately for the regular and the chaotic orbits. We thereby identify the various types of orbits, determine the shape and percentages of the orbits supporting the bar and the ring/spiral structures, and study how the latter quantities change during the secular evolution of each system. Although the frequency maps of the chaotic orbits are scattered, we can still identify concentrations around resonances. We give the distributions of frequencies of the most important populations of orbits. We explore the phase-space structure of each system using projections of the 4D surfaces of section. These are obtained via the numerical integration not only of the orbits of test particles, but also of the real N -body particles. We thus identify which domains of the phase space are preferred and which are avoided by the real particles. The chaotic orbits are found to play a major role in supporting the shape of the outer envelope of the bar as well as the rings and the spiral arms formed outside corotation. 相似文献
2.
G. Contopoulos N. Voglis C. Kalapotharakos 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):191-204
We construct and compare two different self-consistent N-body equilibrium configurations of galactic models. The two systems have their origin in cosmological initial conditions selected so that the radial orbit instability appears in one model and gives an E5 type elliptical galaxy, but not in the other that gives an E1 type. We examine their phase spaces using uniformly distributed orbits of test particles in the resulting potential and compare with the distribution of the orbits of the real particles in the two systems. The main types of orbits in both cases are box, tube and chaotic orbits. One main conclusion is that the orbits of the test particles in the 3-dimensional potential are foliated in a way quite close to the foliation of invariant tori in a 2-dimensional potential. The real particles describe orbits having similar foliation. However, their distribution is far from being uniform. The difference between the two models of equilibrium is realized mainly by different balances of the populations of real particles in box and tube orbits. 相似文献
3.
4.
We introduce a new class of 2D mass models, whose potentials are of Stäckel form in elliptic coordinates. Our model galaxies have two separate strong cusps that form double nuclei. The potential and surface density distributions are locally axisymmetric near the nuclei and become highly non-axisymmetric outside the nucleus. The surface density diverges toward the cuspy nuclei with the law Our model is sustained by four general types of regular orbits: butterfly , nucleophilic banana , horseshoe and aligned loop orbits. Horseshoes and nucleophilic bananas support the existence of cuspy regions. Butterflies and aligned loops control the non-axisymmetric shape of outer regions. Without any need for central black holes, our distributed mass models resemble the nuclei of M31 and NGC 4486B. It is also shown that the self-gravity of the stellar disc can prevent the double nucleus to collapse. 相似文献
5.
P. A. Patsis 《Monthly notices of the Royal Astronomical Society》2005,358(2):305-315
We investigate the morphological relation between the orbits of the central family of periodic orbits ( x 1 family) and the bar itself using models of test particles moving in a barred potential. We show that different bar morphologies may have as a backbone the same set of x 1 periodic orbits. We point out that by populating initially axisymmetric stellar discs exponentially with test particles in circular, or almost circular motion, we may end up with a response bar which reveals a shape different in crucial details from that of the individual stable x 1 orbits. For example, a bar model in which the x 1 orbits are pure ellipses may have a much more complicated response morphology. This depends on the particular invariant curves around x 1 , which are populated in each model. 相似文献
6.
Edo Noordermeer † Linda S. Sparke Stephen E. Levine 《Monthly notices of the Royal Astronomical Society》2001,328(4):1064-1080
Lopsidedness is a common feature in galaxies, both in the distribution of light and in the kinematics. We investigate the kinematics of a model for lopsided galaxies that consists of a disc lying off-centre in a dark halo, and circling around the halo centre. We search for families of stable, closed, non-crossing orbits, and assume that gas in our galaxies moves on these orbits. Several of our models show strong lopsided gas kinematics, especially those in which the disc spins around its axis in a retrograde sense compared with its motion around the halo centre. We are able to reproduce the H i velocity map of the kinematically lopsided galaxy NGC 4395.
The lopsidedness in our models is most pronounced in the models where the halo provides a relatively large fraction of the total mass at small radii. This may explain why the gas shows lopsidedness more frequently in late-type galaxies, which are dominated by dark matter. Surfaces of section show large regions of irregular orbits in the models where the halo density is low. This may indicate that these models are unstable. 相似文献
The lopsidedness in our models is most pronounced in the models where the halo provides a relatively large fraction of the total mass at small radii. This may explain why the gas shows lopsidedness more frequently in late-type galaxies, which are dominated by dark matter. Surfaces of section show large regions of irregular orbits in the models where the halo density is low. This may indicate that these models are unstable. 相似文献
7.
We present a general scheme for constructing Monte Carlo realizations of equilibrium, collisionless galaxy models with known distribution function (DF) f 0 . Our method uses importance sampling to find the sampling DF f s that minimizes the mean-square formal errors in a given set of projections of the DF f 0 . The result is a multimass N -body realization of the galaxy model in which 'interesting' regions of phase space are densely populated by lots of low-mass particles, increasing the effective N there, and less interesting regions by fewer, higher mass particles.
As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N -body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor of ∼100 reduction in the variance at the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N -body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N -body simulations closer to the collisionless ideal. 相似文献
As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N -body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor of ∼100 reduction in the variance at the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N -body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N -body simulations closer to the collisionless ideal. 相似文献
8.
P. Tsoutsis C. Efthymiopoulos N. Voglis † 《Monthly notices of the Royal Astronomical Society》2008,387(3):1264-1280
In a previous paper (Voglis et al., Paper I), we demonstrated that, in a rotating galaxy with a strong bar, the unstable asymptotic manifolds of the short-period family of unstable periodic orbits around the Lagrangian points L 1 or L 2 create correlations among the apocentric positions of many chaotic orbits, thus supporting a spiral structure beyond the bar. In this paper, we present evidence that the unstable manifolds of all the families of unstable periodic orbits near and beyond corotation contribute to the same phenomenon. Our results refer to a N -body simulation, a number of drawbacks of which, as well as the reasons why these do not significantly affect the main results, are discussed. We explain the dynamical importance of the invariant manifolds as due to the fact that they produce a phenomenon of 'stickiness' slowing down the rate of chaotic escape in an otherwise non-compact region of the phase space. We find a stickiness time of the order of 100 dynamical periods, which is sufficient to support a long-living spiral structure. Manifolds of different families become important at different ranges of values of the Jacobi constant. The projections of the manifolds of all the different families in the configuration space produce a pattern due to the 'coalescence' of the invariant manifolds. This follows closely the maxima of the observed m = 2 component near and beyond corotation. Thus, the manifolds support both the outer edge of the bar and the spiral arms. 相似文献
9.
Ch. Skokos P. A. Patsis E. Athanassoula 《Monthly notices of the Royal Astronomical Society》2002,333(4):861-870
We investigate the orbital structure in a class of three-dimensional (3D) models of barred galaxies. We consider different values of the pattern speed, of the strength of the bar and of the parameters of the central bulge of the galactic model. The morphology of the stable orbits in the bar region is associated with the degree of folding of the x1 characteristic. This folding is larger for lower values of the pattern speed. The elongation of rectangular-like orbits belonging to x1 and to x1-originated families depends mainly on the pattern speed. A detailed investigation of the trees of bifurcating families in the various models shows that major building blocks of 3D bars can be supplied by families initially introduced as unstable in the system, but becoming stable at another energy interval. In some models without radial and vertical 2:1 resonances we find, except for the x1 and x1-originated families, also families related to the z -axis orbits, which support the bar. Bifurcations of the x2 family can build a secondary 3D bar along the minor axis of the main bar. This is favoured in the slowly rotating bar case. 相似文献
10.
Jeannette M. Myers Dieter H. Hartmann Lih-Sin The 《Astrophysics and Space Science》2003,284(2):787-790
In an effort to study the halo globular clusters we perform a simulation of inhomogeneous halo collapse using a SPH/N-body
code. We include dark matter particles, (cooling) gas, and stars. Supernova feedback is included as a heat source for the
gas in the local environment of star forming regions. We find this model cannot reproduce the age distribution and spatial
distribution of halo globular clusters.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
11.
N. Voglis P. Tsoutsis C. Efthymiopoulos 《Monthly notices of the Royal Astronomical Society》2006,373(1):280-294
In the presence of a strong m = 2 component in a rotating galaxy, the phase-space structure near corotation is shaped to a large extent by the invariant manifolds of the short-period family of unstable periodic orbits terminating at L 1 or L 2 . The main effect of these manifolds is to create robust phase correlations among a number of chaotic orbits large enough to support a spiral density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine–Gordon equation. Numerical examples are given in an N -body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar–spiral pattern. 相似文献
12.
The Kuzmin–Toomre family of discs is used to construct potential–density pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a ring with a centre of attraction are also presented. The circular velocity of test particles and the epicyclic frequency of small oscillations about circular orbits are calculated for these structures. A few examples of three-dimensional potential–density pairs of 'inflated' flat rings (toroidal mass distributions) are presented. 相似文献
13.
We study the role of asymptotic curves in supporting the spiral structure of a N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions on the unstable asymptotic manifolds of the main unstable periodic orbits follow the shape of the periodic orbits for an initial interval of time and then they are diffused outwards along the spiral structure of the galaxy. Chaotic orbits having small deviations from the unstable periodic orbits, stay close and along the corresponding unstable asymptotic manifolds, supporting the spiral structure for more than 10 rotations of the bar. Chaotic orbits of different Jacobi constants support different parts of the spiral structure. We also study the diffusion rate of chaotic orbits outwards and find that the orbits that support the outer parts of the galaxy are diffused outwards more slowly than the orbits supporting the inner parts of the spiral structure. 相似文献
14.
R. Brasser 《Monthly notices of the Royal Astronomical Society》2001,324(4):1109-1116
In this paper the effect of the Galactic tidal field on a Sun–comet pair will be considered when the comet is situated in the Oort cloud and planetary perturbations can be neglected. First, two averaged models were created, one of which can be solved analytically in terms of Jacobi elliptic functions. In the latter system, switching between libration and circulation of the argument of perihelion is prohibited. The non-averaged equations of motion are integrated numerically in order to determine the regions of the ( e , i ) phase space in which chaotic orbits can be found, and an effort is made to explain why the chaotic orbits manifest in these regions only. It is evident that for moderate values of semimajor axis, a ∼50 000 au , chaotic orbits are found for ( e <0.15 , 40°≤ i ≤140°) as determined by integrating the evolution of the comet over a period of 104 orbits. These regions of chaos increase in size with increasing semimajor axis. The typical e-folding times for these orbits range from around 600 Myr to 1 Gyr and thus are of little practical interest, as the time-scales for chaos arising from passing stars are much shorter. As a result of Galactic rotation, the chaotic regions in ( e , i ) phase space are not symmetric for prograde and retrograde orbits. 相似文献
15.
R. Capuzzo-Dolcetta A. Vicari 《Monthly notices of the Royal Astronomical Society》2005,356(3):899-912
The present work extends and deepens previous examinations of the evolution of globular cluster orbits in elliptical galaxies, by means of numerical integrations of a wide set of orbits in five self-consistent triaxial galactic models characterized by a central core and different axial ratios. These models are valid and complete in the representation of regular orbits in elliptical galaxies. Dynamical friction is definitely shown to be an efficient cause of evolution for the globular cluster systems in elliptical galaxies of any mass or axial ratio. Moreover, our statistically significant sample of computed orbits confirms that the globular cluster orbital decay times are, at least for clusters moving on box orbits, much shorter than the age of the galaxies. Consequently, the mass carried into the innermost galactic region in the form of decayed globular clusters may have contributed significantly to feeding and accreting a compact object therein. 相似文献
16.
V. Dury S. De Rijcke Victor P. Debattista † H. Dejonghe 《Monthly notices of the Royal Astronomical Society》2008,387(1):2-12
Lopsidedness is common in spiral galaxies. Often, there is no obvious external cause, such as an interaction with a nearby galaxy, for such features. Alternatively, the lopsidedness may have an internal cause, such as a dynamical instability. In order to explore this idea, we have developed a computer code that searches for self-consistent perturbations in razor-thin disc galaxies and performed a thorough mode-analysis of a suite of dynamical models for disc galaxies embedded in an inert dark matter halo with varying amounts of rotation and radial anisotropy.
Models with two equal-mass counter-rotating discs and fully rotating models both show growing lopsided modes. For the counter-rotating models, this is the well-known counter-rotating instability, becoming weaker as the net rotation increases. The m = 1 mode of the maximally rotating models, on the other hand, becomes stronger with increasing net rotation. This rotating m = 1 mode is reminiscent of the eccentricity instability in near-Keplerian discs.
To unravel the physical origin of these two different m = 1 instabilities, we studied the individual stellar orbits in the perturbed potential and found that the presence of the perturbation gives rise to a very rich orbital behaviour. In the linear regime, both instabilities are supported by aligned loop orbits. In the non-linear regime, other orbit families exist that can help support the modes. In terms of density waves, the counter-rotating m = 1 mode is due to a purely growing Jeans-type instability. The rotating m = 1 mode, on the other hand, grows as a result of the swing amplifier working inside the resonance cavity that extends from the disc centre out to the radius where non-rotating waves are stabilized by the model's outwardly rising Q profile. 相似文献
Models with two equal-mass counter-rotating discs and fully rotating models both show growing lopsided modes. For the counter-rotating models, this is the well-known counter-rotating instability, becoming weaker as the net rotation increases. The m = 1 mode of the maximally rotating models, on the other hand, becomes stronger with increasing net rotation. This rotating m = 1 mode is reminiscent of the eccentricity instability in near-Keplerian discs.
To unravel the physical origin of these two different m = 1 instabilities, we studied the individual stellar orbits in the perturbed potential and found that the presence of the perturbation gives rise to a very rich orbital behaviour. In the linear regime, both instabilities are supported by aligned loop orbits. In the non-linear regime, other orbit families exist that can help support the modes. In terms of density waves, the counter-rotating m = 1 mode is due to a purely growing Jeans-type instability. The rotating m = 1 mode, on the other hand, grows as a result of the swing amplifier working inside the resonance cavity that extends from the disc centre out to the radius where non-rotating waves are stabilized by the model's outwardly rising Q profile. 相似文献
17.
18.
J. C. Muzzio H. D. Navone A. F. Zorzi 《Celestial Mechanics and Dynamical Astronomy》2009,105(4):379-395
We used a multipolar code to create, through dissipationless collapses of systems of 106 particles, two cuspy self-consistent triaxial stellar systems with γ ≈ 1. One of the systems has an axial ratio similar to that of an E4 galaxy and it is only mildly triaxial (T = 0.914), while the other one is strongly triaxial (T = 0.593) and its axial ratio lies in between those of Hubble types E5 and E6. Both models rotate although their total angular
momenta are zero, i.e., they exhibit figure rotation. The angular velocity is very small for the less triaxial model and,
while it is larger for the more triaxial one, it is still comparable to that found by Muzzio (Celest Mech Dynam Astron 96(2):85–97,
2006) to affect only slightly the dynamics of a similar model. Except for minor evolution, probably caused by unavoidable
relaxation effects of the N-body code, the systems are highly stable. The potential of each system was subsequently approximated
with interpolating formulae yielding smooth potentials, stationary in frames that rotate with the models. The Lyapunov exponents
could then be computed for randomly selected samples of the bodies that make up the two systems, allowing the recognition
of regular and of partially and fully chaotic orbits. Finally, the regular orbits were Fourier analyzed and classified using
their locations on the frequency map. Most of the orbits are chaotic, and by a wide margin: less than 30% of the orbits are
regular in our most triaxial model. Regular orbits are dominated by tubes, long axis ones in the less triaxial model and short
axis tubes in the more triaxial one. Most of the boxes are resonant (i.e., they are boxlets), as could be expected from cuspy
systems. 相似文献
19.
Witold Maciejewski Linda S. Sparke 《Monthly notices of the Royal Astronomical Society》2000,313(4):745-760
High-resolution observations of the inner regions of barred disc galaxies have revealed many asymmetrical, small-scale central features, some of which are best described as secondary bars. Because orbital time-scales in the galaxy centre are short, secondary bars are likely to be dynamically decoupled from the main kiloparsec-scale bars. Here we show that regular orbits exist in such doubly barred potentials, and that they can support the bars in their motion. We find orbits in which particles remain on loops : closed curves which return to their original positions after two bars have come back to the same relative orientation. Stars trapped around stable loops could form the building blocks for a long-lived, doubly barred galaxy. Using the loop representation, we can find which orbits support the bars in their motion, and the constraints on the sizes and shapes of self-consistent double bars. In particular, it appears that a long-lived secondary bar may exist only when an inner Lindblad resonance is present in the primary bar, and that it would not extend beyond this resonance. 相似文献
20.
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 massMn. 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) 相似文献