610 research outputs found
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 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
Periodic Orbits and Escapes in Dynamical Systems
We study the periodic orbits and the escapes in two different dynamical
systems, namely (1) a classical system of two coupled oscillators, and (2) the
Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a
general relativistic system). We find their simple periodic orbits, their
characteristics and their stability. Then we find their ordered and chaotic
domains. As the energy goes beyond the escape energy, most chaotic orbits
escape. In the first case we consider escapes to infinity, while in the second
case we emphasize escapes to the central "bumpy" black hole. When the energy
reaches its escape value a particular family of periodic orbits reaches an
infinite period and then the family disappears (the orbit escapes). As this
family approaches termination it undergoes an infinity of equal period and
double period bifurcations at transitions from stability to instability and
vice versa. The bifurcating families continue to exist beyond the escape
energy. We study the forms of the phase space for various energies, and the
statistics of the chaotic and escaping orbits. The proportion of these orbits
increases abruptly as the energy goes beyond the escape energy.Comment: 28 pages, 23 figures, accepted in "Celestial Mechanics and Dynamical
Astronomy
Populating Stellar Orbits Inside a Rotating, Gaseous Bar
In an effort to better understand the formation and evolution of barred
galaxies, we have examined the properties of equatorial orbits in the effective
potential of one model of a rapidly rotating, steady-state gas-dynamical bar
that has been constructed via a self-consistent hydrodynamical simulation.
Using a ``Restriction Hypothesis'' to determine initial conditions, we find
that a significant fraction of orbits in this potential are quasi-ergodic and
that regular orbits have a ``bowtie'' shape in contrast to the more typical x1
orbits. This bowtie orbit should give a boxy-peanut shape to such systems.Comment: Accepted for publication in The Astrophysical Journal; 29 pages, 29
gif figure
The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation
We study the orbital behavior at the neighborhood of complex unstable
periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a
transition of a family of periodic orbits from stability to complex instability
(also known as Hamiltonian Hopf Bifurcation) the four eigenvalues of the stable
periodic orbits move out of the unit circle. Then the periodic orbits become
complex unstable. In this paper we first integrate initial conditions close to
the ones of a complex unstable periodic orbit, which is close to the transition
point. Then, we plot the consequents of the corresponding orbit in a 4D surface
of section. To visualize this surface of section we use the method of color and
rotation [Patsis and Zachilas 1994]. We find that the consequents are contained
in 2D "confined tori". Then, we investigate the structure of the phase space in
the neighborhood of complex unstable periodic orbits, which are further away
from the transition point. In these cases we observe clouds of points in the 4D
surfaces of section. The transition between the two types of orbital behavior
is abrupt.Comment: 10 pages, 14 figures, accepted for publication in the International
Journal of Bifurcation and Chao
The Potential-Density Phase Shift Method for Determining the Corotation Radii in Spiral and Barred Galaxies
We have developed a new method for determining the corotation radii of
density waves in disk galaxies, which makes use of the radial distribution of
an azimuthal phase shift between the potential and density wave patterns. The
approach originated from improved theoretical understandings of the relation
between the morphology and kinematics of galaxies, and on the dynamical
interaction between density waves and the basic-state disk stars which results
in the secular evolution of disk galaxies. In this paper, we present the
rationales behind the method, and the first application of it to several
representative barred and grand-design spiral galaxies, using near-infrared
images to trace the mass distributions, as well as to calculate the potential
distributions used in the phase shift calculations. We compare our results with
those from other existing methods for locating the corotations, and show that
the new method both confirms the previously-established trends of bar-length
dependence on galaxy morphological types, as well as provides new insights into
the possible extent of bars in disk galaxies. Application of the method to a
larger sample and the preliminary analysis of which show that the phase shift
method is likely to be a generally-applicable, accurate, and essentially
model-independent method for determining the pattern speeds and corotation
radii of single or nested density wave patterns in galaxies. Other implications
of this work are: most of the nearby bright disk galaxies appear to possess
quasi-stationary spiral modes; that these density wave modes and the associated
basic state of the galactic disk slowly transform over time; and that
self-consistent N-particle systems contain physics not revealed by the passive
orbit analysis approaches.Comment: 48 pages, 16 figures. Accepted for publication in the Astronomical
Journa
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
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
Revised research about chaotic dynamics in Manko et al. spacetime
A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that
chaos phenomenon of test particles in gravitational field of rotating neutron
stars which are described by Manko, Sanabria-Gomez, and Manko (Manko et al.)
metric can only occur when the stars have oblate deformation. But the chaotic
motions they found are limited in a very narrow zone which is very close to the
center of the massive bodies. This paper argues that this is impossible because
the region is actually inside of the stars, so the motions cannot exist at this
place. In this paper, we scan all parameters space and find chaos and unstable
fixed points outside of stars with big mass-quadrupole moments. The
calculations show that chaos can only occur when the stars have prolate
deformation. Because real deformation of stars should be oblate, all orbits of
test particles around the rotating neutron stars described by Manko et al.
solutions are regular. The case of nonzero dipolar magnetic moment has also
been taken into account in this study.Comment: 6 pages, 5 figure
Stability of axial orbits in galactic potentials
We investigate the dynamics in a galactic potential with two reflection
symmetries. The phase-space structure of the real system is approximated with a
resonant detuned normal form constructed with the method based on the Lie
transform. Attention is focused on the stability properties of the axial
periodic orbits that play an important role in galactic models. Using energy
and ellipticity as parameters, we find analytical expressions of bifurcations
and compare them with numerical results available in the literature.Comment: 20 pages, accepted for publication on Celestial Mechanics and
Dynamical Astronom
Revised Pulsar Spindown
We address the issue of electromagnetic pulsar spindown by combining our
experience from the two limiting idealized cases which have been studied in
great extent in the past: that of an aligned rotator where ideal MHD conditions
apply, and that of a misaligned rotator in vacuum. We construct a spindown
formula that takes into account the misalignment of the magnetic and rotation
axes, and the magnetospheric particle acceleration gaps. We show that near the
death line aligned rotators spin down much slower than orthogonal ones. In
order to test this approach, we use a simple Monte Carlo method to simulate the
evolution of pulsars and find a good fit to the observed pulsar distribution in
the P-Pdot diagram without invoking magnetic field decay. Our model may also
account for individual pulsars spinning down with braking index n < 3, by
allowing the corotating part of the magnetosphere to end inside the light
cylinder. We discuss the role of magnetic reconnection in determining the
pulsar braking index. We show, however, that n ~ 3 remains a good approximation
for the pulsar population as a whole. Moreover, we predict that pulsars near
the death line have braking index values n > 3, and that the older pulsar
population has preferentially smaller magnetic inclination angles. We discuss
possible signatures of such alignment in the existing pulsar data.Comment: 8 pages, 7 figures; accepted to Ap
- …