Dynamical evolution of galactic disks driven by interaction with a satellite

Dynamical evolution of galactic disks driven by interaction with satellite galaxies, particularly the problem of the disk warping and thickening is studied numerically. One of the main purpose of the study is to resolve the long standing problem of the origin of the disk warping. A possible cause of the warp is interaction with a satellite galaxy. In the case of the Milky Way, the LMC has been considered as the candidate. Some linear analysis have already given a positive result, but one had to wait for a fully self-consistent simulation as a proof. I have accomplished the numerical simulations with a million particles, by introducing a hybrid algorithm, SCF-TREE. Those simulations give us quantitative estimates for the Milky Way system. We have found an example in which large warp amplitudes are developed. We also found that the warp amplitudes depend on the halo distribution. Among our three models, the most massive and spherical halo is preferable for the observable warp excitation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Time evolution of galactic warps in prolate haloes

A recent observation with the Hipparcos satellite and some numerical simulations imply that the interaction between an oblate halo and a disc is inappropriate for the persistence of galactic warps. Following on from this , we have compared the time evolution of galactic warps in a prolate halo with that in an oblate halo. The haloes were approximated as fixed potentials, while the discs were represented by N -body particles. We have found that the warping in the oblate halo continues to wind up, and finally disappears. On the other hand, for the prolate halo model, the precession rate of the outer disc increases when the precession of the outer disc recedes from that of the inner disc, and vice versa. Consequently, the warping in the prolate halo persisted to the end of the simulation by retaining the alignment of the line of nodes of the warped disc. Therefore, our results suggest that prolate haloes could sustain galactic warps. The physical mechanism of the persistence of warp is discussed on the basis of the torque between a halo and a disc and that between the inner and outer regions of the disc.     

Dynamical stability and evolution of the discs of Sc galaxies

We examine the local stability of galactic discs against axisymmetric density perturbations with special attention to the different dynamics of the stellar and gaseous components. In particular, the discs of the Milky Way and of NGC 6946 are studied. The Milky Way is shown to be stable, whereas the inner parts of NGC 6946, a typical Sc galaxy from the Kennicutt sample, are dynamically unstable. The ensuing dynamical evolution of the composite disc is studied by numerical simulations. The evolution is so fierce that the stellar disc heats up dynamically on a short time-scale to such a high degree, which seems to contradict the morphological appearance of the galaxy. The star formation rate required to cool the disc dynamically is estimated. Even if the star formation rate in NGC 6946 is at present high enough to meet this requirement, it is argued that the discs of Sc galaxies cannot sustain such a high star formation rate for extended periods.     

Three-integral models for axisymmetric galactic discs

We present new equilibrium component distribution functions that depend on three analytic integrals in a Stäckel potential, and that can be used to model stellar discs of galaxies. These components are generalizations of two-integral ones and can thus provide thin discs in the two-integral approximation. Their most important properties are the partly analytical expression for their moments, the disc-like features of their configuration space densities (exponential decline in the galactic plane and finite extent in the vertical direction) and the anisotropy of their velocity dispersions. We further show that a linear combination of such components can fit a van der Kruit disc.     

From kinematics to dynamics in thin galactic discs

We present a method for recovering the distribution functions of edge-on thin axisymmetric discs directly from their observable kinematic properties. The most generally observable properties of such a stellar system are the line-of-sight velocity distributions of the stars at different projected radii along the galaxy. If the gravitational potential is known, then the general two-integral distribution function can be reconstructed using the shapes of the high-velocity tails of these line-of-sight distributions. If the wrong gravitational potential is adopted, then a distribution function can still be constructed using this technique, but the low-velocity parts of the observed velocity distributions will not be reproduced by the derived dynamical model. Thus, the gravitational potential is also tightly constrained by the observed kinematics.     

Orbits supporting bars within bars

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.     

Orbital dynamics of three-dimensional bars – I. The backbone of three-dimensional bars. A fiducial case

In this series of papers we investigate the orbital structure of three-dimensional (3D) models representing barred galaxies. In the present introductory paper we use a fiducial case to describe all families of periodic orbits that may play a role in the morphology of three-dimensional bars. We show that, in a 3D bar, the backbone of the orbital structure is not just the x1 family, as in two-dimensional (2D) models, but a tree of 2D and 3D families bifurcating from x1. Besides the main tree we have also found another group of families of lesser importance around the radial 3:1 resonance. The families of this group bifurcate from x1 and influence the dynamics of the system only locally. We also find that 3D orbits elongated along the bar minor axis can be formed by bifurcations of the planar x2 family. They can support 3D bar-like structures along the minor axis of the main bar. Banana-like orbits around the stable Lagrangian points build a forest of 2D and 3D families as well. The importance of the 3D x1-tree families at the outer parts of the bar depends critically on whether they are introduced in the system as bifurcations in z or in   z˙   .     

Self-consistent response of a galactic disc to vertical perturbations

We study the self-consistent, linear response of a galactic disc to vertical perturbations, as induced, say, by a tidal interaction. We calculate the self-gravitational potential corresponding to a non-axisymmetric, self-consistent density response of the disc using the Green's function method. The response potential is shown to oppose the perturbation potential because the self-gravity of the disc resists the imposed potential, and this resistance is stronger in the inner parts of a galactic disc. For the   m = 1  azimuthal wavenumber, the disc response opposes the imposed perturbation up to a radius that spans a range of 4–6 disc scalelengths, so that the disc shows a net warp only beyond this region. This physically explains the well known but so far unexplained observation that warps typically set in beyond this range of radii. We show that the inclusion of a dark matter halo in the calculation only marginally changes (by ∼10 per cent) the radius for the onset of warps. For perturbations with higher azimuthal wavenumbers, the net signature of the vertical perturbations can only be seen at larger radii – for example, beyond 7 exponential disc scalelengths for   m = 10  . Also, for the high- m cases, the magnitude of the negative disc response due to the disc self-gravity is much smaller. This is shown to result in corrugations of the mid-plane density, which explains the puzzling scalloping with   m = 10  detected in H  i in the outermost regions ∼30 kpc in the Galaxy.     

A new dynamical spectrum for galactic potentials

We investigate the properties of motion, using the distribution of the values of a new dynamical parameter, in two different galactic potentials. The first is a potential made up of harmonic oscillators while the second is a logarithmic potential. We call the distribution functions of the new parameter the S(r) dynamical spectrum. A comparison between the spectrum of stretching numbers S(α) and the new spectrum is made. The results of our numerical calculations suggest that the S(r) spectrum is a better discriminant between different types of orbits while requiring considerable less computation time. An application of the new dynamical spectrum to barred galaxy models is also presented.     

Fast detection of chaotic behavior in galactic potentials

In the present paper we apply a new method of distinction between ordered and chaotic motion in galactic potentials. The method uses the Fourier Transform of a series of time intervals each one representing the time that elapsed between two successive points on the Poincaré surface of section. Examples of the methods ability to achieve an early and clear detection of an orbit's behavior are provided using two galactic potentials. The new method can also be applied in order to have an early distinction between ordered and sticky orbits. The method is generalized in order to be used in models with more than two dimensions. Finally we have tried to find an one‐number index to give us the nature of the orbit instead of checking by eye the whole spectrum. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Orbital dynamics of three-dimensional bars – II. Investigation of the parameter space

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.     

Integrable models of galactic discs with double nuclei

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.     

Analytical galactic models with mild stellar cusps

In the past two decades, it has been established by high-resolution observations of early-type galaxies that their nuclear surface brightness and corresponding stellar mass densities are characterized by cusps. In this paper, we present a new spherical analytical model family describing mild cuspy centres. We study isotropic and anisotropic models of Osipkov–Merritt type. It is shown that the associated distribution functions and intrinsic velocity dispersions can be represented analytically in a unified way in terms of hypergeometric series, allowing thus a straightforward comparison of these important global quantities for galaxies having underlying mass densities which may differ significantly in their degree of central cuspiness or radial falloff.