Motion in a double nucleus galactic dynamical model

We construct a 2D-dynamical model in order to study the motion in a galaxy with a double nucleus. Numerical calculations show that the majority of high energy stars, near the double nuclear region, are on chaotic orbits. On the contrary, low energy stars are on chaotic orbits only near massive nuclei while, for less massive nuclei, the motion is regular. Using a semi-numerical approach we explain the chaotic scattering of orbits near each nucleus. The high values of the velocities near the dense nuclei are also explained. Computation of the LCEs indicates a very high degree of chaos. The results derived from our double nucleus dynamical model are compared with models with single ones. Our outcomes are in satisfactory agreement with observational data for the double nucleus system $\mathit{NGC}6240$.     

Chaos in a quasar model with a disk and a massive nucleus

We present a quasar model with a rotating disk and a massive nucleus. We use this model in order to characterize the motion in the model (regular or chaotic) and to connect the extent of the chaotic regions to the physical parameters of the model. Numerical experiments suggest that, there are connections between the extent of the chaotic areas and the parameters of the system. Furthermore, it is shown that the form of numerically found relationships can be expressed analytically. Comparison to previous work is also made. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Escape regions of a quartic potential

We investigate the escape regions of a quartic potential and the main types of irregular periodic orbits. Because of the symmetry of the model the zero velocity curve consists of four summetric arcs forming four open channels around the lines y = ± x through which an orbit can escape. Four unstable Lyapunov periodic orbits bridge these openings.We have found an infinite sequence of families of periodic orbits which is the outer boundary of one of the escape regions and several infinite sequences of periodic orbits inside this region that tend to homoclinic and heteroclinic orbits. Some of these sequences of periodic orbits tend to homoclinic orbits starting perpendicularly and ending asymptotically at the x-axis. The other sequences tend to heteroclinic orbits which intersect the x-axis perpendicularly for x > 0 and make infinite oscillations almost parallel to each of the two Lyapunov orbits which correspond to x > 0 or x < 0.     

A dynamical condition for a relativistic galaxy cluster model

In an attempt to give a coherent interpretation of the secondary maximum in the density distribution of clusters of galaxies we use an approximate metric tensor proposed by other authors, with the purpose of building a relativistic generalization of the isothermal models of galaxy clusters.Although such a generalization gives rise to oscillations in the density distribution, the quantitative agreement with the observational data is unsatisfactory.The analysis of the metric tensor we have used brings us to point out that (i) the approximation on which the metric is based is not suitable for describing an actual galaxy cluster and (ii) the dynamical conditions of clusters require inclusion of a cosmological expansion, and of anisotropic distribution function in the phase-space.     

The stochastic behaviour of a galactic model dynamical system

We study the stochastic behaviour of a time-independent dynamical system that has closed zero velocity curves for arbitrarily large energies. Thus no escapes appear in such a system and we can study the stochasticity of the system for any value of the energy. The numerical results show that the degree of stochasticity grows as the energy increases from zero, but then it reaches a maximum and for still larger energies it decreases slowly.     

A dynamical model of the corona

The hydrodynamic equations for an ideal, inviscid, fully ionized hydrogen gas in a gravitational, but not magnetic, field are solved by an explicit Lax-Wendroff two-step technique using a one-dimensional slab symmetry. Radiation and thermal conductivity are included. The model spans 100000 km starting from the chromosphere-corona transition region. An initially isothermal gas is seen to evolve coronal properties in 4000 s, by which time it settles into dynamic equilibrium characterized by a 2000 km transition region, a temperature maximum of 1.6 × 10⁶ K at a height of 60000 km, and a solar wind mass flux of 10^-9 g cm^-2 s^-1.     

A dynamical model of prominence loops

A dynamical model of prominence loops is constructed on the basis of the theory of hydromagnetic buoyancy force. A prominence loop is regarded as a flux rope immersed in the solar atmosphere above a bipolar region of the photospheric magnetic field. The motion of a loop is partitioned into a translational motion, which accounts for the displacement of the centroidal axis of the loop, and an expansional motion, which accounts for the displacement of the periphery of the loop relative to the axis. The translational motion is driven by the hydromagnetic buoyancy force exerted by the surrounding medium of the solar atmosphere and the gravitational force exerted by the Sun. The expansional motion is driven by the pressure gradient that sustains the pressure difference between internal and external gas pressures and the self-induced Lorentz force that results from interactions among internal currents. The main constituent of the hydromagnetic buoyancy force on a prominence loop is the diamagnetic force exerted on the internal currents by the external currents that sustain the pre-existing magnetic field. By spatial transformation between magnetic and mechanical stresses, the diamagnetic force is manifested through a mechanical force acting at various mass elements of the prominence. For a prominence loop in equilibrium, the gravitational force is balanced by the hydromagnetic buoyancy force and the Lorentz force of helical magnetic field is balanced by a gradient force of gas pressure.     

Chaos in cuspy triaxial galaxies with a supermassive black hole: a simple toy model

This paper summarises an investigation of chaos in a toy potential which mimics much of the behaviour observed for the more realistic triaxial generalisations of the Dehnen potentials, which have been used to model cuspy triaxial galaxies both with and without a supermassive black hole. The potential is the sum of an anisotropic harmonic oscillator potential, ${\text{V}}_{\text{0}} = \frac{1}{2}\left( {a^2 x^2 + b^2 y^2 + c^2 z^2 } \right)$ , and aspherical Plummer potential, ${\text{V}}_{\text{P}} = M_{BH} /\sqrt {r^2 + \varepsilon ^2 } $ , with $r^2 = x^2 + y^2 + z^2$ . Attention focuses on three issues related tothe properties of ensembles of chaotic orbits which impact on chaotic mixing and the possibility of constructing self-consistent equilibria:(1) What fraction of the orbits are chaotic? (2) How sensitive are the chaotic orbits, that is, how large are their largest (short time) Lyapunov exponents? (3) To what extent is the motion of chaotic orbits impeded by Arnold webs, that is, how 'sticky' are the chaotic orbits? These questions are explored as functions of the axis ratio a: b: c, black hole mass M _BH, softening length ε, and energy E with the aims of understanding how the manifestations of chaos depend onthe shape of the system and why the black hole generates chaos. The simplicity of the model makes it amenable to a perturbative analysis. That it mimics the behaviour of more complicated potentials suggests that much of this behaviour should be generic.     

A Map for a Group of Resonant Cases in a quartic Galactic Hamiltonian

We present a map for the study of resonant motion in a potential made up of two harmonic oscillators with quartic perturbing terms. This potential can be considered to describe motion in the central parts of non-rotating elliptical galaxies. The map is based on the averaged Hamiltonian. Adding on a semi-empirical basis suitable terms in the unperturbed averaged Hamiltonian, corresponding to the 1:1 resonant case, we are able to construct a map describing motion in several resonant cases. The map is used in order to find thex − p _x Poincare phase plane for each resonance. Comparing the results of the map, with those obtained by numerical integration of the equation of motion, we observe, that the map describes satisfactorily the broad features of orbits in all studied cases for regular motion. There are cases where the map describes satisfactorily the properties of the chaotic orbits as well.     

A dynamical model for the extraplanar gas in spiral galaxies

Recent H  i observations reveal that the discs of spiral galaxies are surrounded by extended gaseous haloes. This extraplanar gas reaches large distances (several kiloparsecs) from the disc and shows peculiar kinematics (low rotation and inflow). We have modelled the extraplanar gas as a continuous flow of material from the disc of a spiral galaxy into its halo region. The output of our models is pseudo data cubes that can be directly compared to the H  i data. We have applied these models to two spiral galaxies (NGC 891 and NGC 2403) known to have a substantial amount of extraplanar gas. Our models are able to reproduce accurately the vertical distribution of extraplanar gas for an energy input corresponding to a small fraction (<4 per cent) of the energy released by supernovae. However, they fail in two important aspects: (1) they do not reproduce the right gradient in rotation velocity; (2) they predict a general outflow of the extraplanar gas, contrary to what is observed. We show that neither of these difficulties can be removed if clouds are ionized and invisible at 21 cm as they leave the disc but become visible at some point on their orbits. We speculate that these failures indicate the need for accreted material from the intergalactic medium that could provide the low angular momentum and inflow required.     

A generic dynamical model of gamma-ray burst remnants

The conventional generic model is considered to explain the dynamics of gamma-ray burst remnants very well, no matter whether they are adiabatic or highly radiative. However, we find that, for adiabatic expansion, the model cannot reproduce the Sedov solution in the non-relativistic phase, and thus it needs to be revised. In this paper a new differential equation is derived. The generic model based on this equation is shown to be correct for both radiative and adiabatic fireballs, and in both ultrarelativistic and non-relativistic phases.     

A new dynamical model for the Uranian satellites

We have developed a new dynamical model of the main Uranian satellites, based on numerical integration and fitted to astrometric observations. Old observations, as well as modern and Voyager observations have been included. This model has provided ephemerides that have already been used for predicting the mutual events during the PHE-URA campaign. It is updated here to improve the prediction of these events. We also tried to assess the real accuracy of our ephemerides by checking the distance differences of the Uranian satellites, using simultaneously our former and new model. It appears that both solutions are very close to each other (within few tens of kilometers), and most probably accurate at the level of few hundred of kilometers. Using new available meridian observations of the Uranian satellites, we have checked the Uranian ephemeris accuracy using DE406. An error of more than 0.1 arcsec on the Uranian position is observed.     

A dynamical model for the chromosphere-corona transition region

A dynamical, homogeneous model of the chromosphere-corona transition region and of the lower corona is presented, based on the hydrodynamical equations and on a semi-empirical relation deduced from radio observations. The model is shown to be in agreement with radio and UV observations and with the particle flux given by solar wind measurements. A comparison with the analogous static model shows that dynamical effects are very small. From the model it is possible to give an estimate of the energy dissipated at each level by the waves that propagate in the solar atmosphere. It is shown that this energy source cannot be neglected with comparison to the usual conductive, convective and radiative sources. The importance of the kinetic energy flux connected with the spicules is also discussed.     

A dynamical model of the sporadic meteoroid complex

Sporadic meteoroids are the most abundant yet least understood component of the Earth's meteoroid complex. This paper aims to build a physics-based model of this complex calibrated with five years of radar observations. The model of the sporadic meteoroid complex presented here includes the effects of the Sun and all eight planets, radiation forces and collisions. The model uses the observed meteor patrol radar strengths of the sporadic meteors to solve for the dust production rates of the populations of comets modeled, as well as the mass index. The model can explain some of the differences between the meteor velocity distributions seen by transverse versus radial scatter radars. The different ionization limits of the two techniques result in their looking at different populations with different velocity distributions. Radial scatter radars see primarily meteors from 55P/Tempel-Tuttle (or an orbitally similar lost comet), while transverse scatter radars are dominated by larger meteoroids from the Jupiter-family comets. In fact, our results suggest that the sporadic complex is better understood as originating from a small number of comets which transfer material to near-Earth space quite efficiently, rather than as a product of the cometary population as a whole. The model also sheds light on variations in the mass index reported by different radars, revealing it to be a result of their sampling different portions of the meteoroid population. In addition, we find that a mass index of s=2.34 as observed at Earth requires a shallower index (s=2.2) at the time of meteoroid production because of size-dependent processes in the evolution of meteoroids. The model also reveals the origin of the 55° radius ring seen centered on the Earth's apex (a result of high-inclination meteoroids undergoing Kozai oscillation) and the central condensations seen in the apex sources, as well as providing insight into the strength asymmetry of the helion and anti-helion sources.     

A model for binary-binary close encounters and collisions from a dynamical point of view

The goal of this paper is to provide a model for binary-binary interactions in star clusters, which is based on simultaneous binary collision of a special case of the one-dimensional 4-body problem where four masses move symmetrically about the center of mass. From the theoretical point of view, the singularity due to binary collisions between point masses can be handled by means of regularization theory. Our main tool is a change of coordinates due to McGehee by which we blow-up the singular set associated to total collision and replace it with an invariant manifold which includes binary and simultaneous binary collisions, and then gain a complete picture of the local behavior of the solutions near to total collision via the homothetic orbit.     

Relativistic dynamical friction in a collisional fluid

The dynamical friction force experienced by a body moving at relativistic speed in a gaseous medium is examined. This force, which arises due to the gravitational interaction of the body with its own gravitationally-induced wake, is calculated for straight-line motion and circular motion, generalizing previous results by several authors. Possible applications to the study of extreme mass-ratio inspirals around strongly accreting supermassive black holes are suggested.     

Periodic orbits in a resonant dynamical system

We study the periodic orbits in a two dimensional dynamical system, symmetric with respect to both axes, with two equal or nearly equal frequencies. It is shown that the periodic orbits can be found directly from the equations of motion. The form of these orbits depends on the value of the coupling parameter . We verify the theoretical results by numerical calculations.     

Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model

We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotation of the star. An illustrative application to the case of an F-type main-sequence star hosting a hot Jupiter is presented. The general relevance of our model to test more sophisticated numerical dynamical models and to study the internal rotation profile of exoplanet hosts, submitted to the combined effects of tides and stellar winds, by means of asteroseismology are discussed.