116 research outputs found
Effective power-law dependence of Lyapunov exponents on the central mass in galaxies
Using both numerical and analytical approaches, we demonstrate the existence
of an effective power-law relation between the mean Lyapunov
exponent of stellar orbits chaotically scattered by a supermassive black
hole in the center of a galaxy and the mass parameter , i.e. ratio of the
mass of the black hole over the mass of the galaxy. The exponent is found
numerically to obtain values in the range --. We propose a
theoretical interpretation of these exponents, based on estimates of local
`stretching numbers', i.e. local Lyapunov exponents at successive transits of
the orbits through the black hole's sphere of influence. We thus predict
with --. Our basic model refers to elliptical
galaxy models with a central core. However, we find numerically that an
effective power law scaling of with holds also in models with central
cusp, beyond a mass scale up to which chaos is dominated by the influence of
the cusp itself. We finally show numerically that an analogous law exists also
in disc galaxies with rotating bars. In the latter case, chaotic scattering by
the black hole affects mainly populations of thick tube-like orbits surrounding
some low-order branches of the family of periodic orbits, as well as its
bifurcations at low-order resonances, mainly the Inner Lindbland resonance and
the 4/1 resonance. Implications of the correlations between and to
determining the rate of secular evolution of galaxies are discussed.Comment: 27 pages, 19 figure
NGC 1300 Dynamics: III. Orbital analysis
We present the orbital analysis of four response models, that succeed in
reproducing morphological features of NGC 1300. Two of them assume a planar
(2D) geometry with =22 and 16 \ksk respectively. The two others
assume a cylindrical (thick) disc and rotate with the same pattern speeds as
the 2D models. These response models reproduce most successfully main
morphological features of NGC 1300 among a large number of models, as became
evident in a previous study. Our main result is the discovery of three new
dynamical mechanisms that can support structures in a barred-spiral grand
design system. These mechanisms are presented in characteristic cases, where
these dynamical phenomena take place. They refer firstly to the support of a
strong bar, of ansae type, almost solely by chaotic orbits, then to the support
of spirals by chaotic orbits that for a certain number of pat tern revolutions
follow an n:1 (n=7,8) morphology, and finally to the support of spiral arms by
a combination of orbits trapped around L and sticky chaotic orbits with
the same Jacobi constant. We have encountered these dynamical phenomena in a
large fraction of the cases we studied as we varied the parameters of our
general models, without forcing in some way their appearance. This suggests
that they could be responsible for the observed morphologies of many
barred-spiral galaxies. Comparing our response models among themselves we find
that the NGC 130 0 morphology is best described by a thick disc model for the
bar region and a 2D disc model for the spirals, with both components rotating
with the same pattern speed =16 \ksk !. In such a case, the whole
structure is included inside the corotation of the system. The bar is supported
mainly by regular orbits, while the spirals are supported by chaotic orbits.Comment: 18 pages, 32 figures, accepted for publication in MNRA
Particle Acceleration in Dissipative Pulsar Magnetospheres
Pulsar magnetospheres represent unipolar inductor-type electrical circuits at which an EM potential across the polar cap (due to the rotation of their magnetic field) drives currents that run in and out of the polar cap and close at infinity. An estimate ofthe magnitude of this current can be obtained by dividing the potential induced across the polar cap V approx = B(sub O) R(sub O)(Omega R(sub O)/c)(exp 2) by the impedance of free space Z approx eq 4 pi/c; the resulting polar cap current density is close to where is the Goldreich-Julian (GJ) charge density. This argument suggests that even at current densities close to the GJ one, pulsar magnetospheres have a significant component of electric field , parallel to the magnetic field, a condition necessary for particle acceleration and the production of radiation. We present the magnetic and electric field structures as well as the currents, charge densities, spin down rates and potential drops along the magnetic field lines of pulsar magnetospheres which do not obey the ideal MHD condition . By relating the current density along the poloidal field lines to the parallel electric field via a kind of Ohm's law we study the structure of these magnetospheres as a function of the conductivity . We find that for sigma 11 OmegaS. Finally, we present dissipative magnetospheric solutions with spatially variable that supports various microphysical properties and are compatible with the observations
NGC 1300 Dynamics: II. The response models
We study the stellar response in a spectrum of potentials describing the
barred spiral galaxy NGC 1300. These potentials have been presented in a
previous paper and correspond to three different assumptions as regards the
geometry of the galaxy. For each potential we consider a wide range of
pattern speed values. Our goal is to discover the geometries and the
supporting specific morphological features of NGC 1300. For this
purpose we use the method of response models. In order to compare the images of
NGC 1300 with the density maps of our models, we define a new index which is a
generalization of the Hausdorff distance. This index helps us to find out
quantitatively which cases reproduce specific features of NGC 1300 in an
objective way. Furthermore, we construct alternative models following a
Schwarzschild type technique. By this method we vary the weights of the various
energy levels, and thus the orbital contribution of each energy, in order to
minimize the differences between the response density and that deduced from the
surface density of the galaxy, under certain assumptions. We find that the
models corresponding to \ksk and \ksk are
able to reproduce efficiently certain morphological features of NGC 1300, with
each one having its advantages and drawbacks.Comment: 13 pages, 10 figures, accepted for publication in MNRA
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 are near the value
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 () compared with the
fraction of mass in chaotic motion in the non-rotating iso-energetic model
(). 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 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]
Modeling magnetic disk wind state transitions in black hole X-Ray binaries
We analyze three prototypical black hole X-ray binaries, 4U 1630-472, GRO J1655-40, and H1743-322, in an effort to systematically understand the intrinsic state transition of the observed accretion disk winds between wind-on and wind-off states by utilizing state-of-the-art Chandra/HETGS archival data from multi-epoch observations. We apply our magnetically driven wind models in the context of magnetohydrodynamic (MHD) calculations to constrain (1) their global density slope (p), (2) their density (n (17)) at the foot point of the innermost launching radius, and (3) the abundances of heavier elements (A (Fe,S,Si)). Incorporating the MHD winds into xstar photoionization calculations in a self-consistent manner, we create a library of synthetic absorption spectra given the observed X-ray continua. Our analysis clearly indicates a characteristic bimodal transition of multi-ion X-ray winds; i.e., the wind density gradient is found to steepen (from p similar to 1.2-1.4 to similar to 1.4-1.5) while its density normalization declines as the source transitions from the wind-on to the wind-off state. The model implies that the ionized wind remains physically present even in the wind-off state, despite its apparent absence in the observed spectra. Supersolar abundances for heavier elements are also favored. Our global multi-ion wind models, taking into account soft X-ray ions as well as Fe K absorbers, show that the internal wind condition plays an important role in wind transitions besides photoionization changes. Simulated XRISM/Resolve and Athena/X-IFU spectra are presented to demonstrate a high fidelity of the multi-ion wind model for a better understanding of these powerful ionized winds in the coming decades
Nodal points and the transition from ordered to chaotic Bohmian trajectories
We explore the transition from order to chaos for the Bohmian trajectories of
a simple quantum system corresponding to the superposition of three stationary
states in a 2D harmonic well with incommensurable frequencies. We study in
particular the role of nodal points in the transition to chaos. Our main
findings are: a) A proof of the existence of bounded domains in configuration
space which are devoid of nodal points, b) An analytical construction of formal
series representing regular orbits in the central domain as well as a numerical
investigation of its limits of applicability. c) A detailed exploration of the
phase-space structure near the nodal point. In this exploration we use an
adiabatic approximation and we draw the flow chart in a moving frame of
reference centered at the nodal point. We demonstrate the existence of a saddle
point (called X-point) in the vicinity of the nodal point which plays a key
role in the manifestation of exponential sensitivity of the orbits. One of the
invariant manifolds of the X-point continues as a spiral terminating at the
nodal point. We find cases of Hopf bifurcation at the nodal point and explore
the associated phase space structure of the nodal point - X-point complex. We
finally demonstrate the mechanism by which this complex generates chaos.
Numerical examples of this mechanism are given for particular chaotic orbits,
and a comparison is made with previous related works in the literature.Comment: 32 pages, 13 figures, Accepted for publication in Journal of Physics
Nonlinear force-free reconstruction of the global solar magnetic field: methodology
We present a novel numerical method that allows the calculation of nonlinear
force-free magnetostatic solutions above a boundary surface on which only the
distribution of the normal magnetic field component is given. The method relies
on the theory of force-free electrodynamics and applies directly to the
reconstruction of the solar coronal magnetic field for a given distribution of
the photospheric radial field component. The method works as follows: we start
with any initial magnetostatic global field configuration (e.g. zero, dipole),
and along the boundary surface we create an evolving distribution of tangential
(horizontal) electric fields that, via Faraday's equation, give rise to a
respective normal field distribution approaching asymptotically the target
distribution. At the same time, these electric fields are used as boundary
condition to numerically evolve the resulting electromagnetic field above the
boundary surface, modelled as a thin ideal plasma with non-reflecting,
perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear
force-free configuration that satisfies the given normal field distribution on
the boundary. This is different from existing methods relying on a fixed
boundary condition - the boundary evolves toward the a priori given one, at the
same time evolving the three-dimensional field solution above it. Moreover,
this is the first time a nonlinear force-free solution is reached by using only
the normal field component on the boundary. This solution is not unique, but
depends on the initial magnetic field configuration and on the evolutionary
course along the boundary surface. To our knowledge, this is the first time
that the formalism of force-free electrodynamics, used very successfully in
other astrophysical contexts, is applied to the global solar magnetic field.Comment: 18 pages, 5 figures, Solar Physic
Invariant manifolds and the response of spiral arms in barred galaxies
The unstable invariant manifolds of the short-period family of periodic
orbits around the unstable Lagrangian points and of a barred galaxy
define loci in the configuration space which take the form of a trailing spiral
pattern. In the present paper we investigate this association in the case of
the self-consistent models of Kaufmann & Contopoulos (1996) which provide an
approximation of real barred-spiral galaxies. We also examine the relation of
`response' models of barred-spiral galaxies with the theory of the invariant
manifolds. Our main results are the following: The invariant manifolds yield
the correct form of the imposed spiral pattern provided that their calculation
is done with the spiral potential term turned on. We provide a theoretical
model explaining the form of the invariant manifolds that supports the spiral
structure. The azimuthal displacement of the Lagrangian points with respect to
the bar's major axis is a crucial parameter in this modeling. When this is
taken into account, the manifolds necessarily develop in a spiral-like domain
of the configuration space, delimited from below by the boundary of a
banana-like non-permitted domain, and from above either by rotational KAM tori
or by cantori forming a stickiness zone. We construct `spiral response' models
on the basis of the theory of the invariant manifolds and examine the
connection of the latter to the `response' models (Patsis 2006) used to fit
real barred-spiral galaxies, explaining how are the manifolds related to a
number of morphological features seen in such models.Comment: 16 Page
- âŚ