New biorthogonal potential–density basis functions

We use the weighted integral form of spherical Bessel functions and introduce a new analytical set of complete and biorthogonal potential–density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to   r ^{−(1+ l )}  and   r ^{−(4+ l )}  at large radii, where l is the latitudinal quantum number of spherical harmonics. The lowest order term associated with   l = 0  is the perfect sphere of de Zeeuw. Our basis functions are intrinsically suitable for the modelling of three-dimensional, soft-centred stellar systems and they complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the performance of our functions by expanding the density and potential profiles of some spherical and oblate galaxy models.     

On the least action principle in cosmology

Given the present distribution of mass tracing objects in an expanding universe, we develop and test a fast method for recovering their past orbits using the least action principle. In this method, termed FAM for fast action minimization, the orbits are expanded in a set of orthogonal time basis functions satisfying the appropriate boundary conditions at the initial and final times. The conjugate gradient method is applied to locate the extremum of the action in the space of the expansion coefficients of the orbits. The treecode gravity solver routine is used for computing the gravitational field appearing in the action and the potential field appearing in the gradient of the action. The time integration of the Lagrangian is done using Gaussian quadratures. FAM allows us to increase the number of galaxies over previous numerical action principle implementations by more than one order of magnitude. For example, orbits for the 15 000 IRAS PSC z galaxies can be recovered in 12 000 CPU seconds on a 400-MHz DEC-Alpha machine. FAM can recover the present peculiar velocities of particles and the initial fluctuations field. It successfully recovers the flow field down to cluster scales, where deviations of the flow from the Zel'dovich solution are significant. We also show how to recover orbits from the present distribution of objects in redshift space by direct minimization of a modified action, without iterating the solution between real and redshift spaces.     

Dynamical friction on globular clusters in core-triaxial galaxies: is it a cause of massive black hole accretion?

The present work extends and deepens previous examinations of the evolution of globular cluster orbits in elliptical galaxies, by means of numerical integrations of a wide set of orbits in five self-consistent triaxial galactic models characterized by a central core and different axial ratios. These models are valid and complete in the representation of regular orbits in elliptical galaxies. Dynamical friction is definitely shown to be an efficient cause of evolution for the globular cluster systems in elliptical galaxies of any mass or axial ratio. Moreover, our statistically significant sample of computed orbits confirms that the globular cluster orbital decay times are, at least for clusters moving on box orbits, much shorter than the age of the galaxies. Consequently, the mass carried into the innermost galactic region in the form of decayed globular clusters may have contributed significantly to feeding and accreting a compact object therein.     

Geodesics and geodesic deviation in static charged black holes

The radial motion along null geodesics in static charged black hole space–times, in particular, the Reissner–Nordström and stringy charged black holes, are studied. We analyzed the properties of the effective potential. The circular photon orbits in these space–times are investigated. We found that the radius of circular photon orbits in both charged black holes are different and differ from that given in Schwarzschild space–time. We studied the physical effects of the gravitational field between two test particles in stringy charged black hole and compared the results with that given in Schwarzschild and Reissner–Nordström black holes.     

Boxy/peanut 'bulges': comparing the structure of galaxies with the underlying families of periodic orbits

The vertical profiles of disc galaxies are built by the material trapped around stable periodic orbits, which form their 'skeletons'. Therefore, knowledge of the stability of the main families of periodic orbits in appropriate 3D models enables one to predict possible morphologies for edge-on disc galaxies. In a pilot survey we compare the orbital structures that lead to the appearance of 'peanut'- and 'X'-like features with the edge-on profiles of three disc galaxies (IC 2531, NGC 4013 and UGC 2048). The subtraction from the images of a model representing the axisymmetric component of the galaxies reveals the contribution of the non-axisymmetric terms. We find a direct correspondence between the orbital profiles of 3D bars in models and the observed main morphological features of the residuals. We also apply a simple unsharp masking technique in order to study the sharpest features of the images. Our basic conclusion is that the morphology of the boxy 'bulges' of these galaxies can be explained by considering disc material trapped around stable 3D periodic orbits. In most models, these building-block periodic orbits are bifurcated from the planar central family of a non-axisymmetric component, usually a bar, at low-order vertical resonances. In such a case, the boxy 'bulges' are parts of bars seen edge-on. For the three galaxies we study, the families associated with the 'peanut' or 'X'-shape morphology are probably bifurcations at the vertical 2/1 or 4/1 resonance.     

Isofrequency pairing of circular orbits in Schwarzschild spacetime in the presence of magnetic field

We study isofrequency pairing of the circular non-geodesic orbits in the vicinity of the Schwarzschild black hole immersed in external asymptotically uniform magnetic field. The dependence of the isofrequency pairing of non-geodesic orbits from the special quantities, such as radius of the innermost stable circular orbits (ISCO), radius of the circular orbits (r _b ) at the limit e(eccentricity)→0, and from the value of the small quantity ξ=(r _b ?r _ISCO) of the particles moving around the Schwarzschild black hole in the presence of the magnetic field has been found. It is shown that presence of the magnetic field gives rise to the r _ISCO and r _b of the particles to be slightly shifted from black hole and the contribution of the quantity ξ decreases the amount of isofrequency pairing of non-geodesic orbits due to the reduction of the surface of the region between the separatrix and circular-orbit duals (COD). We study the dependence of surface of region where particles can move and isofrequency pairing of non-geodesic orbits occur around the Schwarzschild black hole from the magnetic field. We find a decrease of nearly (7–10) % for the maximal values of the magnetic field B～10⁶–10⁷ Gauss in the surface of region where isofrequency pairing occurs around central object with compare to the one around Schwarzschild black hole without magnetic field. This result implies that it makes easier to identify signals through the astrophysical observations of compact objects in the presence of magnetic field.     

Stellar dynamics in a galactic centre surrounded by a massive accretion disc — I. Newtonian description

The long-term evolution of stellar orbits bound to a massive centre is studied in order to understand the cores of star clusters in central regions of galaxies. Stellar trajectories undergo tiny perturbations, the origins of which are twofold: (i) the gravitational field of a thin gaseous disc surrounding the galactic centre, and (ii) cumulative drag arising from successive interactions of the stars with the material of the disc. Both effects are closely related because they depend on the total mass of the disc, assumed to be a small fraction of the central mass. It is shown that, in contrast to previous works, most of the retrograde (with respect to the disc) orbits are captured by the central object, presumably a massive black hole. Initially prograde orbits are also affected, so that statistical properties of the central star cluster in quasi-equilibrium may differ significantly from those deduced in previous analyses.     

Chaos and elliptical galaxies

Recent results on chaos in triaxial galaxy models are reviewed. Central mass concentrations like those observed in early-type galaxies - either stellar cusps, or massive black holes — render most of the box orbits in a triaxial potential stochastic. Typical Liapunov times are 3–5 crossing times, and ensembles of stochastic orbits undergo mixing on timescales that are roughly an order of magnitude longer. The replacement of the regular orbits by stochastic orbits reduces the freedom to construct self-consistent equilibria, and strong triaxiality can be ruled out for galaxies with sufficiently high central mass concentrations.     

Global Dynamics in Self-Consistent Models of Elliptical Galaxies

We compare two different N-body models simulating elliptical galaxies. Namely, the first model is a non-rotating triaxial N-body equilibrium model with smooth center, called SC model. The second model, called CM model, is derived from the SC by inserting a central mass in it, so that all possible differences between the two models are due to the effect of the central mass. The central mass is assumed to be mainly due to a massive central black hole of mass about 1% of the total mass of the galaxy. By using the fundamental frequency analysis, the two systems are thoroughly investigated as regards the types of orbits described either by test particles, or by the real particles of the systems at all the energy levels. A comparison between the orbits of test particles and the orbits of real particles at various energy levels is made on the rotation number plane. We find that extensive stable regions of phase space, detected by test particles remain empty, i.e. these regions are not occupied by real particles, while many real particles move in unstable regions of phase space describing chaotic orbits. We run self-consistently the two models for more than a Hubble time. During this run, in spite of the noise due to small variations of the potential, the SC model maintains (within a small uncertainly) the number of particles moving on orbits of each particular type. In contrast, the CM model is unstable, due to the large amount of mass in chaotic motion caused by the central mass. This system undergoes a secular evolution towards an equilibrium state. During this evolution it is gradually self-organized by converting chaotic orbits to ordered orbits mainly of the short axis tube type approaching an oblate spheroidal equilibrium. This is clearly demonstrated in terms of the fundamental frequencies of the orbits on the rotation number plane and the time evolution of the triaxiality index.     

星系形态分类的研究进展

传统的哈勃星系形态分类法可以很好地对近邻的亮星系进行分类,但对低面亮度星系、矮椭球星系、矮旋涡星系以及高红移星系等都已无能为力。德沃古勒分类系统、叶凯士分类系统和范登伯分类系统是在哈勃分类法的基础上进行了发展和细化,利用光的中心聚集度或光度级等作为星系形态分类的参数。模型化分类系统试图定量地测量星系形态参数,但需要假定星系面亮度分布满足一定的形式,如r~(1/4)律、指数律等。最近几年,又有一些学者提出了非模型化分类系统,给出了若干个可以直接测量星系形态的结构参数,如:聚集度指数C、非对称指数A、簇聚指数S、基尼系数G及矩指数M_(20)。这些参数可以反映星系的形成历史、恒星形成、与其他星系的相互作用、已经发生或正在进行的并合活动等。它们不仅可以有效地给出近邻星系的分类特性,还能用于测量高红移星系的形态。该文介绍了不同的星系形态分类方法,比较了各类方法的优点和不足。在此基础上,最后介绍了基于非模型化分类系统的星系形态分类的研究进展。     

Equilibrium points and associated periodic orbits in the gravity of binary asteroid systems: (66391) 1999 KW4 as an example

The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations.     

Search for optical identifications in the 5C3-radio survey I. Observations

In this paper the search for optical identifications in the 5C-radio surveys is continued. Near the positions of 135 radio sources of the 5C3 catalogue all present optical objects up to the plate limit (about B ≈︁ 21) have been measured photometrically in UBVr and astrometrically on plates of the 134/200 cm Schmidt telescope of the Karl Schwarzschild Observatory Tautenburg. A total of 111 candidates for possible optical identifications were found. The number of real identifications will be, of course, much smaller. Among the 111 objects there are: 12 supposed QSO's, 21 galaxies or probable galaxies, 56 stellar objects the greater part of which may be main sequence stars, subdwarfs and white dwarfs, and I object may be the centre of an H II region in the OB-association OB 182. 21 objects near the plate limit could not be classified. A statistical treatment with information on the real rate of identification (it roughly will amount to about 10%) and its reliability will be given in part III.     

Critical cases of 3-dimensional systems

We study the evolution of families of periodic orbits of simple 3-dimensional models representing the central parts of deformed galaxies. In some cases the evolution is non-unique, i.e. if we follow a closed path in the parameter space we do not return with the same periodic orbit. This happens when the path surrounds a critical point. We found that critical points are generated at particular collisions of bifurcations in limiting cases when the 3-D system is separated into a 2-D system and an independent oscillation along the third axis. The regions of stability and instability of some families of periodic orbits change in remarkable ways near the various collisions of bifurcations and around the critical points.     

The formation of superdense gaseous cores in the nuclei of disk galaxies: II

In a previous paper (hereafter referred to as Paper I) we have tried to show that superdense cores in the nuclei of disk galaxies can be formed by accretion of gas ejected by the evolved stars which populate the central bulge of these galaxies. Solving the equations for radial flow of a magnetized gas, we found that the accretion of an explodable mass at the core can be achieved over a time-scale ranging from a few times 10⁷ and a few times 10⁸ yr. It was shown, however, that the accretion process is seriously inhibited if the gas possesses sufficient rotational velocity but lacks any dissipative, mechanism within the system. Since rotational velocity is an observed parameter of the stars which shed the gas to be accreted, one must consider the existence of some dissipative force in it in order that the accretion process may be efficient. In the present paper, therefore, we have solved the problem of the flow of a rotating, viscous (variable), magnetized gas. With plausible assumptions regarding some of the parameters involved, the time-scale for the accretion of an explodable mass (10⁹ M ) at the core again turns out to be ranging between a few times 10⁷ and a few times 10⁸yr. Such time-scale has been proposed by several authors as that for repeated explosions in nuclei of these galaxies. It has also been proposed by many authors that the spiral arms are generated and destroyed in disk galaxies over the same time-scale. Our solution also yields a nearly linear rotational velocity law which is usually observed in the central regions of these galaxies.     

A model for galactic centres

A rotating Supermassive Magnetized Disk is proposed as a model for all the violent phenomena occurring in the nuclei of galaxies, in the form of quasars, Lacertids, radio galaxies, Seyferts, exploding galaxies, etc. The cold disk feeds a fast-rotating supermassive core (some 10³ Schwarzschild radii in extent), which emits (1) an unsteady thermal wind of filamentary geometry, (2) Low-Frequency magnetic Waves, and (3) relativistic electrons and positrons. The latter reach high -factors by phase-riding the LFWs, emit synchro-Compton radiation on crossing scattered waves (from -ray energies down to radio frequencies), and are eventually focused into two antipodal relativistic beams by their frozen-in toroidal magnetic field. Torsional oscillations between the core and disk give rise to a pulsed injection, and a breathing double-onion shape of the LFW windzone can explain the superluminal jetlike appearance. A big nuclear explosion ends each duty cycle, but many smaller explosions prevent the settling core from collapsing. In this model, the helium production of galactic centres is comparable to the observed cosmic helium.     

Counterrotating Galaxies and Memory of Cosmological Initial Conditions

As it is known, a good number of galaxies are observed to have counterrotating cores. A popular scenario to explain the formation of such galaxies is based on a secondary process of merging of galaxies with their satellites, or gas infall, or merger events between galaxies. An alternative mechanism, proposed by Voglis et al., 1991, and by Harsoula and Voglis 1998, could also be responsible for the formation of these galaxies directly from cosmological initial conditions (direct scenario). The novel mechanism was demonstrated by using quiet cosmological initial conditions in N-body simulations. In the present paper we extend our N-body simulations using clumpy initial conditions and show that this mechanism still works to create counterrotating galaxies. Counterrotation is a result of the considerable amount of memory of initial conditions surviving for times comparable to the Hubble time, despite the large degree of instability of individual orbits and the dramatic redistribution and mixing of the particles in phase space. We show, for example, that the particles remember, in a statistical sense, not only their distance from the center of mass (memory of energy), but also the initial orientation of their position relative to the direction of an external tidal field, which determines the sign and the amount of angular momentum that is transferred to the particles of the system.     

Static properties of galaxies in the Shapley-centaurus cluster

The data of Paper I (Doddet al., 1986), representing a catalogue of parameters measured for bright galaxies in field 444 of the Southern Sky Survey, are examined in a search for non-random effects. A global trend of bimodal alignment of galaxies in this field is found. This effect is present even for galaxies of large apparent ellipticity (e0.5) and is interpreted as revealing a real physical phenomenon on the large scale in this field. Analysis of nearest neighbouring pairs of galaxies reveals evidence also for small-scale interactions. The difference in apparent ellipticities between close pairs is larger than would be expected if the galaxies were randomly distributed. Nearest neighbouring galaxies also show a strong preference to be aligned with their major axes parallel. The results are discussed with regard to theories for galaxy formation.