The non-integrability of the Zipoy-Voorhees metric

The low frequency gravitational wave detectors like eLISA/NGO will give us the opportunity to test whether the supermassive compact objects lying at the centers of galaxies are indeed Kerr black holes. A way to do such a test is to compare the gravitational wave signals with templates of perturbed black hole spacetimes, the so-called bumpy black hole spacetimes. The Zipoy-Voorhees (ZV) spacetime (known also as the $\gamma$ spacetime) can be included in the bumpy black hole family, because it can be considered as a perturbation of the Schwarzschild spacetime background. Several authors have suggested that the ZV metric corresponds to an integrable system. Contrary to this integrability conjecture, in the present article it is shown by numerical examples that in general ZV belongs to the family of non-integrable systems.Comment: 10 pages, 13 figure

A model for nulling and mode changing in pulsars

We propose that in some pulsars the magnetosphere has different states with different geometries or/and different distributions of currents, it occasionally switches between them. These states have different spindown rates and emission beams, in some of the states no radioemission is produced at all. Switching into a different state manifests as a mode change when we see different parts of the emission beam or the beams in different states have significantly different geometries, it manifests as nulling when we either miss the new beam or no radioemission is generated in the new state. We show that modest variations in the beam shape can be accompanied by large variations in the pulsar spindown rate W - the dependence of W on the opening angle of the emission beam $\alpha$ can be as strong as W\propto\alpha^4. We speculate about physical mechanisms which may cause reconfiguration of the magnetosphere.Comment: 5 pages, 1 figure; MNRAS, in pres

The structure of invariant tori in a 3D galactic potential

We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the 4D spaces of section. We compare our results with those of previous works and we describe the morphology of the rotational, as well as of the tube tori in the 4D space. We find sticky chaotic orbits in the immediate neighborhood of sets of invariant tori surrounding 3D stable periodic orbits. Particularly useful for galactic dynamics is the behavior of chaotic orbits trapped for long time between 4D invariant tori. We find that they support during this time the same structure as the quasi-periodic orbits around the stable periodic orbits, contributing however to a local increase of the dispersion of velocities. Finally we find that the tube tori do not appear in the 3D projections of the spaces of section in the axisymmetric Hamiltonian we examined.Comment: 26 pages, 34 figures, accepted for publication in the International Journal of Bifurcation and Chao

Order in de Broglie - Bohm quantum mechanics

A usual assumption in the so-called {\it de Broglie - Bohm} approach to quantum dynamics is that the quantum trajectories subject to typical `guiding' wavefunctions turn to be quite irregular, i.e. {\it chaotic} (in the dynamical systems' sense). In the present paper, we consider mainly cases in which the quantum trajectories are {\it ordered}, i.e. they have zero Lyapunov characteristic numbers. We use perturbative methods to establish the existence of such trajectories from a theoretical point of view, while we analyze their properties via numerical experiments. Using a 2D harmonic oscillator system, we first establish conditions under which a trajectory can be shown to avoid close encounters with a moving nodal point, thus avoiding the source of chaos in this system. We then consider series expansions for trajectories both in the interior and the exterior of the domain covered by nodal lines, probing the domain of convergence as well as how successful the series are in comparison with numerical computations or regular trajectories. We then examine a H\'{e}non - Heiles system possessing regular trajectories, thus generalizing previous results. Finally, we explore a key issue of physical interest in the context of the de Broglie - Bohm formalism, namely the influence of order in the so-called {\it quantum relaxation} effect. We show that the existence of regular trajectories poses restrictions to the quantum relaxation process, and we give examples in which the relaxation is suppressed even when we consider initial ensembles of only chaotic trajectories, provided, however, that the system as a whole is characterized by a certain degree of order.Comment: 25 pages, 12 figure

Force-free magnetosphere of an aligned rotator with differential rotation of open magnetic field lines

Here we briefly report on results of self-consistent numerical modeling of a differentially rotating force-free magnetosphere of an aligned rotator. We show that differential rotation of the open field line zone is significant for adjusting of the global structure of the magnetosphere to the current density flowing through the polar cap cascades. We argue that for most pulsars stationary cascades in the polar cap can not support stationary force-free configurations of the magnetosphere.Comment: 5 pages, 4 figures. Presented at the conference "Isolated Neutron Stars: from the Interior to the Surface", London, April 24-28, 2006; to appear in Astrophysics and Space Science. Significantly revised version, a mistake found by ourselfs in the numerical code was corrected, all presented results are obtained with the correct version of the cod

A New High Resolution CO Map of the inner 2.'5 of M51 I. Streaming Motions and Spiral Structure

[Abridged] The Owens Valley mm-Array has been used to map the CO 1--0 emission in the inner 2'.5 of the grand design spiral galaxy M51 at 2''-3'' resolution. The molecular spiral arms are revealed with unprecedented clarity: supermassive cloud complexes, Giant Molecular Associations, are for the first time resolved both along and perpendicular to the arms. Major complexes occur symmetrically opposite each other in the two major arms. Streaming motions can be studied in detail along the major and minor axes of M51. The streaming velocities are very large, 60-150 km/s. For the first time, sufficient resolution to resolve the structure in the molecular streaming motions is obtained. Our data support the presence of galactic shocks in the arms of M51. In general, velocity gradients across arms are higher by a factor of 2-10 than previously found. They vary in steepness along the spiral arms, becoming particularly steep in between GMAs. The steep gradients cause conditions of strong reverse shear in several regions in the arms, and thus the notion that shear is generally reduced by streaming motions in spiral arms will have to be modified. Of the three GMAs studied on the SW arm, only one shows reduced shear. We find an expansion in the NE molecular arm at 25'' radius SE of the center. This broadening occurs right after the end of the NE arm at the Inner Lindblad Resonance. Bifurcations in the molecular spiral arm structure, at a radius of 73'', may be evidence of a secondary compression of the gas caused by the 4/1 ultraharmonic resonance. Inside the radius of the ILR, we detect narrow (~ 5'') molecular spiral arms possibly related to the K-band arms found in the same region. We find evidence of non-circular motions in the inner 20'' which are consistent with gas on elliptical orbits in a bar.Comment: 29 pages, 15 figures, uses latex macros for ApJ; accepted for publication in Ap

Quantum vortices and trajectories in particle diffraction

We investigate the phenomenon of the diffraction of charged particles by thin material targets using the method of the de Broglie-Bohm quantum trajectories. The particle wave function can be modeled as a sum of two terms $\psi=\psi_{ingoing}+\psi_{outgoing}$. A thin separator exists between the domains of prevalence of the ingoing and outgoing wavefunction terms. The structure of the quantum-mechanical currents in the neighborhood of the separator implies the formation of an array of \emph{quantum vortices}. The flow structure around each vortex displays a characteristic pattern called `nodal point - X point complex'. The X point gives rise to stable and unstable manifolds. We find the scaling laws characterizing a nodal point-X point complex by a local perturbation theory around the nodal point. We then analyze the dynamical role of vortices in the emergence of the diffraction pattern. In particular, we demonstrate the abrupt deflections, along the direction of the unstable manifold, of the quantum trajectories approaching an X-point along its stable manifold. Theoretical results are compared to numerical simulations of quantum trajectories. We finally calculate the {\it times of flight} of particles following quantum trajectories from the source to detectors placed at various scattering angles $\theta$, and thereby propose an experimental test of the de Broglie - Bohm formalism.Comment: 17 pages, 7 figures, accepted by IJB

Density Waves Inside Inner Lindblad Resonance: Nuclear Spirals in Disk Galaxies

We analyze formation of grand-design two-arm spiral structure in the nuclear regions of disk galaxies. Such morphology has been recently detected in a number of objects using high-resolution near-infrared observations. Motivated by the observed (1) continuity between the nuclear and kpc-scale spiral structures, and by (2) low arm-interarm contrast, we apply the density wave theory to explain the basic properties of the spiral nuclear morphology. In particular, we address the mechanism for the formation, maintenance and the detailed shape of nuclear spirals. We find, that the latter depends mostly on the shape of the underlying gravitational potential and the sound speed in the gas. Detection of nuclear spiral arms provides diagnostics of mass distribution within the central kpc of disk galaxies. Our results are supported by 2D numerical simulations of gas response to the background gravitational potential of a barred stellar disk. We investigate the parameter space allowed for the formation of nuclear spirals using a new method for constructing a gravitational potential in a barred galaxy, where positions of resonances are prescribed.Comment: 18 pages, 9 figures, higher resolution available at http://www.pa.uky.edu/~ppe/papers/nucsp.ps.g

Bar Diagnostics in Edge-On Spiral Galaxies. I. The Periodic Orbits Approach

We develop diagnostics to detect the presence and orientation of a bar in an edge-on disk, using its kinematical signature in the position-velocity diagram (PVD) of a spiral galaxy observed edge-on. Using a well-studied barred spiral galaxy mass model, we briefly review the orbital properties of two-dimensional non-axisymmetric disks and identify the main families of periodic orbits. We use those families as building blocks to model real galaxies and calculate the PVDs obtained for various realistic combinations of periodic orbit families and for a number of viewing angles with respect to the bar. We show that the global structure of the PVD is a reliable bar diagnostic in edge-on disks. Specifically, the presence of a gap between the signatures of the families of periodic orbits in the PVD follows directly from the non-homogeneous distribution of the orbits in a barred galaxy. Similarly, material in the two so-called forbidden quadrants of the PVD results from the elongated shape of the orbits. We show how the shape of the signatures of the dominant x1 and x2 families of periodic orbits in the PVD can be used efficiently to determine the viewing angle with respect to the bar and, to a lesser extent, to constrain the mass distribution of an observed galaxy. We also address the limitations of the models when interpreting observational data.Comment: 22 pages, 9 figures (AASTeX, aaspp4.sty). Accepted for publication in The Astrophysical Journa

The tale of two centres

We study motion in the field of two fixed centres described by a family of Einstein-dilaton-Maxwell theories. Transitions between regular and chaotic motion are observed as the dilaton coupling is varied.Comment: 20 pages, RevTeX, 7 figures included, TeX format change