Chaotic motion and spiral structure in self-consistent models of rotating galaxies

Dissipationless N-body models of rotating galaxies, iso-energetic to a non-rotating model, are examined as regards the mass in regular and in chaotic motion. The values of their spin parameters $\lambda$ are near the value $\lambda=0.22$ of our Galaxy. We obtain the distinction between the sets of particles moving in regular and in chaotic orbits and we show that the spatial distribution of these two sets of particles is much different. The rotating models are characterized by larger fractions of mass in chaotic motion ($\thickapprox 65$) compared with the fraction of mass in chaotic motion in the non-rotating iso-energetic model ($\thickapprox 32$). Furthermore, the Lyapunov numbers of the chaotic orbits in the rotating models become by about one order of magnitude larger than in the non-rotating model. Chaotic orbits are concentrated preferably in values of the Jacobi integral around the value of the effective potential at the corotation radius. We find that density waves form a central rotating bar embedded in a thin and a thick disc with exponential surface density profile. A surprising new result is that long living spiral arms are exited on the disc, composed almost completely by chaotic orbits. The bar excites an $m=2$ mode of spiral waves on the surface density of the disc, emanating from the corotation radius. These spiral waves are deformed, fade, or disappear temporarily, but they grow again re-forming a well developed spiral pattern. Spiral arms are discernible up to 20 or 30 rotations of the bar (lasting for about a Hubble time).Comment: 30 pages, 17 figures (low resolution). Revised version. Accepted for publication in MNRAS. For high resolution figures please send email to [email protected]

Large scale structure in the HI Parkes All-Sky Survey: Filling the Voids with HI galaxies?

We estimate the two-point correlation function in redshift space of the recently compiled HIPASS neutral hydrogen (HI) sources catalogue, which if modeled as a power law, $\xi(r)=(r_{0}/r)^{\gamma}$, the best-fitting parameters for the HI selected galaxies are found to be $r_{0}=3.3 \pm 0.3 h^{-1}$ Mpc with $\gamma=1.38 \pm 0.24$. Fixing the slope to its universal value $\gamma=1.8$, we obtain $r_{0}= 3.2\pm 0.2 h^{-1}$ Mpc. Comparing the measured two point correlation function with the predictions of the concordance cosmological model, we find that at the present epoch the HI selected galaxies are anti-biased with respect to the underlying matter fluctuation field with their bias value being $b_{0}\simeq 0.68$. Furthermore, dividing the HI galaxies into two richness subsamples we find that the low mass HI galaxies have a very low present bias factor ($b_{0}\simeq 0.48$), while the high mass HI galaxies trace the underlying matter distribution as the optical galaxies ($b_{0}\simeq 1$). Using our derived present-day HI galaxy bias we estimate their redshift space distortion parameter, and correct accordingly the correlation function for peculiar motions. The resulting real-space correlation length is $r^{\rm re}_{0}=1.8 \pm 0.2 h^{-1}$Mpc and $r^{\rm re}_{0}=3.9 \pm 0.6 h^{-1}$Mpc for the low and high mass HI galaxies, respectively. The low-mass HI galaxies appear to have the lowest correlation length among all extragalactic populations studied to-date. Also, we have correlated the IRAS-PSCz reconstructed density field, smoothed over scales of 5$h^{-1}$ Mpc, with the positions of the HI galaxies, to find that indeed the HI galaxies are typically found in negative overdensity regions (\delta\rho/\rho_{\rm PSCz} \mincir 0).Comment: 9 pages, 8 figures, MNRAS in pres

The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity

We study the connection between the appearance of a `metastable' behavior of weakly chaotic orbits, characterized by a constant rate of increase of the Tsallis q-entropy (Tsallis 1988), and the solutions of the variational equations of motion for the same orbits. We demonstrate that the variational equations yield transient solutions, lasting for long time intervals, during which the length of deviation vectors of nearby orbits grows in time almost as a power-law. The associated power exponent can be simply related to the entropic exponent for which the q-entropy exhibits a constant rate of increase. This analysis leads to the definition of a new sensitive indicator distinguishing regular from weakly chaotic orbits, that we call `Average Power Law Exponent' (APLE). We compare the APLE with other established indicators of the literature. In particular, we give examples of application of the APLE in a) a thin separatrix layer of the standard map, b) the stickiness region around an island of stability in the same map, and c) the web of resonances of a 4D symplectic map. In all these cases we identify weakly chaotic orbits exhibiting the `metastable' behavior associated with the Tsallis q-entropy.Comment: 19 pages, 12 figures, accepted for publication by Physica

Stickiness in Chaos

We distinguish two types of stickiness in systems of two degrees of freedom (a) stickiness around an island of stability and (b) stickiness in chaos, along the unstable asymptotic curves of unstable periodic orbits. We studied these effects in the standard map with a rather large nonlinearity K=5, and we emphasized the role of the asymptotic curves U, S from the central orbit O and the asymptotic curves U+U-S+S- from the simplest unstable orbit around the island O1. We calculated the escape times (initial stickiness times) for many initial points outside but close to the island O1. The lines that separate the regions of the fast from the slow escape time follow the shape of the asymptotic curves S+,S-. We explained this phenomenon by noting that lines close to S+ on its inner side (closer to O1) approach a point of the orbit 4/9, say P1, and then follow the oscillations of the asymptotic curve U+, and escape after a rather long time, while the curves outside S+ after their approach to P1 follow the shape of the asymptotic curves U- and escape fast into the chaotic sea. All these curves return near the original arcs of U+,U- and contribute to the overall stickiness close to U+,U-. The isodensity curves follow the shape of the curves U+,U- and the maxima of density are along U+,U-. For a rather long time the stickiness effects along U+,U- are very pronounced. However after much longer times (about 1000 iterations) the overall stickiness effects are reduced and the distribution of points in the chaotic sea outside the islands tends to be uniform.Comment: 28 pages, 12 figure

Acoustics of early universe. I. Flat versus open universe models

A simple perturbation description unique for all signs of curvature, and based on the gauge-invariant formalisms is proposed to demonstrate that: (1) The density perturbations propagate in the flat radiation-dominated universe in exactly the same way as electromagnetic or gravitational waves propagate in the epoch of the matter domination. (2) In the open universe, sounds are dispersed by curvature. The space curvature defines the minimal frequency $\omega_{\rm c}$ below which the propagation of perturbations is forbidden. Gaussian acoustic fields are considered and the curvature imprint in the perturbations spectrum is discussed.Comment: The new version extended by 2 sections. Changes in notation. Some important comments adde

Application of new dynamical spectra of orbits in Hamiltonian systems

In the present article, we investigate the properties of motion in Hamiltonian systems of two and three degrees of freedom, using the distribution of the values of two new dynamical parameters. The distribution functions of the new parameters, define the S(g) and the S(w) dynamical spectra. The first spectrum definition, that is the S(g) spectrum, will be applied in a Hamiltonian system of two degrees of freedom (2D), while the S(w) dynamical spectrum will be deployed in a Hamiltonian system of three degrees of freedom (3D). Both Hamiltonian systems, describe a very interesting dynamical system which displays a large variety of resonant orbits, different chaotic components and also several sticky regions. We test and prove the efficiency and the reliability of these new dynamical spectra, in detecting tiny ordered domains embedded in the chaotic sea, corresponding to complicated resonant orbits of higher multiplicity. The results of our extensive numerical calculations, suggest that both dynamical spectra are fast and reliable discriminants between different types of orbits in Hamiltonian systems, while requiring very short computation time in order to provide solid and conclusive evidence regarding the nature of an orbit. Furthermore, we establish numerical criteria in order to quantify the results obtained from our new dynamical spectra. A comparison to other previously used dynamical indicators, reveals the leading role of the new spectra.Comment: Published in Nonlinear Dynamics (NODY) journal. arXiv admin note: text overlap with arXiv:1009.1993 by other author

Investigating the nature of motion in 3D perturbed elliptic oscillators displaying exact periodic orbits

We study the nature of motion in a 3D potential composed of perturbed elliptic oscillators. Our technique is to use the results obtained from the 2D potential in order to find the initial conditions generating regular or chaotic orbits in the 3D potential. Both 2D and 3D potentials display exact periodic orbits together with extended chaotic regions. Numerical experiments suggest, that the degree of chaos increases rapidly, as the energy of the test particle increases. About 97% of the phase plane of the 2D system is covered by chaotic orbits for large energies. The regular or chaotic character of the 2D orbits is checked using the S(c) dynamical spectrum, while for the 3D potential we use the S(c) spectrum, along with the P(f) spectral method. Comparison with other dynamical indicators shows that the S(c) spectrum gives fast and reliable information about the character of motion.Comment: Published in Nonlinear Dynamics (NODY) journa