Relative chaos in stellar systems

Statistical properties of many-dimensional dynamical systems-stellar systems of different types, are investigated by means of new definition of relative chaos based on the estimation of the Ricci curvature in the direction of the velocity of geodesics. Numerical experiment is performed to calculate the Ricci and scalar curvatures for systems with equal total energy. The results of calculations enable one to obtain schematic classification of stellar systems by increasing degree of chaos.     

Fluctuations in finite-N equilibrium stellar systems

Gravitational amplification of Poisson noise in stellar systems is important on large scales. For example, it increases the dipole noise power by roughly a factor of 6 and the quadrupole noise by 50 per cent for a King model profile. The dipole noise is amplified by a factor of 15 for the core-free Hernquist model. The predictions are computed by summing over the wakes caused by each star in the system — the dressed-particle formalism of Rostoker & Rosenbluth — and are demonstrated by N -body simulation.   This result implies that a collisionless N -body simulation is impossible; the fluctuation noise which causes relaxation is an intrinic part of self-gravity. In other words, eliminating two-body scattering at interparticle scales does not eliminate relaxation altogether.   Applied to dark matter haloes of disc galaxies, particle numbers of at least 10⁶ will be necessary to suppress this noise at a level that does not dominate or significantly affect the disc response. Conversely, haloes are most likely far from phase-mixed equilibrium and the resulting noise spectrum may seed or excite observed structure such as warps, spiral arms and bars. For example, discreteness noise in the halo, similar to that caused by a population of 10⁶-M⊙ black holes, can produce observable warping and possibly excite or seed other disc structure.     

Tidal interactions in binary stellar systems

The tidal interactions in binary stellar systems are studied under the assumption that the orbital motion of the binary is negligible in comparison with the stellar motion. By integrating over time the tidal forces acting on the stars, the energy changes are derived. These are used to obtain simple analytical expressions for the rates of disruption and merging. This method gives appropriate value for the Roche density ρ_r and it is found that the disruption rate of a satellite of density ρ changes drastically at ρ ρ_R A comparison is made with earlier results obtained under the simplifying assumption that stellar motion is negligible in comparison with the orbital motion of the binary and its implications are discussed.     

Color functions of stellar systems

Model calculations of the photometric evolution of rather dense stellar systems, such as globular clusters, are presented. On “luminosity-effective temperature” diagrams of these systems, low-mass stars are concentrated near the minimum and maximum temperatures for a given luminosity and are deficient in the intermediate region. This sort of double-peaked distribution of the stars can be avoided in open models with ejection of excess metals into the surrounding medium. The distributions of the stars with respect to effective temperature on a “ luminosity-effective temperature” diagram are sensitive to the history of star formation in the system and to possible time variations in the initial mass function. In open systems with a single-peak distribution function, the asymmetry in the distribution varies over wide limits with the lower bound for the initial mass function and this can be used to establish whether the first generations of stars might have been more massive than in the present epoch. __________ Translated from Astrofizika, Vol. 49, No. 1, pp. 139–150 (February 2006).     

Dynamics of plance stellar systems

The evolution of initially balanced rotating disks of stars is investigated with a computer model for isolated disks of stars. An isolated, initially cold balanced disk is found to be violently unstable. Adding a sufficient amount of velocity dispersion will stabilize all small-scale disturbances. However, the disks are still unstable against slowly growing long wave-length modes and after about two rotations most disks tend to assume a bar-shaped structure. It is found that the final mass distribution over most of the disk can be closely approximated by an exponential variation, irrespective of the initial mass distribution. The gravitational two-stream instability is investigated by means of a modified computer model for infinite doubly periodic stellar systems.     

Tomography of collisionless stellar systems

In this paper the concept of tomography of a collisionless stellar system of general shape is introduced, and a generalization of the Projected Virial Theorem is obtained. Applying the tomographic procedure we then derive a new family of virial equations which coincides with the already known ones for spherically symmetric systems. This result is obtained without any use of explicit expressions for the line-of-sight velocity dispersion, or spherical coordinate system.     

Kinematic constraints between stellar systems in superposition

Some kinematic consequences of a superposition of two stellar systems are studied. Chandrasekhar's axially-symmetric model has been adopted for each one of the subsystems. The solution of Chandrasekhar's equations provides us with a potential function, which must be shared by both stellar subsystems and, thus, some relationships between the kinematic parameters of both, subsystems are obtained. In the case of a stationary potential function the whole set of second-order centred moments may be explained.Gotta serve somebody... (Bob Dylan) may be U may be ₂.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Simple distribution functions for stellar systems

We use two elementary solutions of the integral equation connecting the density of a stellar system with its two-integral distribution function in order to construct simple distribution functions. Applications for axisymmetric, disk-like and spherical systems are given.     

Periodic orbits of stars in axisymmetrical stellar systems

Periodic orbits of stars in axisymmetrical nearly spherical stellar systems have been investigated. Generating orbits have been found among periodic ones relating to the spherically-symmetrical field. The linear approximation appears to be insufficient for constructing periodic trajectories. Possible variants of the generating periodic solutions have been found, which give rise to disturbed periodic orbits in the second approximation.

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The distinctive feature of relativistic stellar systems

In this paper we adopt the method of relativistic fluid dynamics to examine the number density distribution of stars around a massive black hole in the core of stellar clusters. We obtain extensive results,n(r) r ^–a, 3/2a9/2, which include, respectively, then(r) r ^–7/4 power law obtained by Bahcall and Wolf and then(r) r ^–9/4 power law by Peebles. Sincen(r) is not an observable quantity for star clusters, we also consider general relativity effects, i.e., the consequence of the bending of light, in calculating the projected density of stars in such a system. As an example we employ a massive black hole 10³ M inlaid in the center of a globular cluster and calculate various projected densities of stars. The results show that cusp construction occurs in all cases unless the central black hole massM=0, and the polytropic index does not affect at all the position of the capture radiusr _a. The obvious differences in the surface density is only embodied in the interior of the capture radius. At the outer regions of the core, the surface density of stars declines rapidly with ar ^–5 power law in all cases. These results can be applied to cases of unequal-mass and non-steady state.     

Orbital structure of self-consistent triaxial stellar systems

We used a multipolar code to create, through the dissipationless collapses of systems of 1,000,000 particles, three self-consistent triaxial stellar systems with axial ratios corresponding to those of E4, E5 and E6 galaxies. The E5 and E6 models have small, but significant, rotational velocities although their total angular momenta are zero, that is, they exhibit figure rotation; the rotational velocity decreases with decreasing flattening of the models and for the E4 model it is essentially zero. Except for minor changes, probably caused by unavoidable relaxation effects, the systems are highly stable. The potential of each system was subsequently approximated with interpolating formulae yielding smooth potentials, stationary for the non-rotating model and stationary in the rotating frame for the rotating ones. The Lyapunov exponents could then be computed for randomly selected samples of the bodies that make up the different systems, allowing the recognition of regular and partially and fully chaotic orbits. Finally, the regular orbits were Fourier analyzed and classified using their locations on the frequency map. As it could be expected, the percentages of chaotic orbits increase with the flattening of the system. As one goes from E6 through E4, the fraction of partially chaotic orbits relative to that of fully chaotic ones increases, with the former surpassing the latter in model E4; the likely cause of this behavior is that triaxiality diminishes from E6 through E4, the latter system being almost axially symmetric. We especulate that some of the partially chaotic orbits may obey a global integral akin to the long axis component of angular momentum. Our results show that is perfectly possible to have highly stable triaxial models with large fractions of chaotic orbits, but such systems cannot have constant axial ratios from center to border: a slightly flattened reservoir of highly chaotic orbits seems to be mandatory for those systems.     

Compact stellar systems around NGC 1399

We have obtained spectroscopic redshifts of colour-selected point sources in four wide area VLT-FLAMES (Very Large Telescope-Fibre Large Array Multi Element Spectrograph) fields around the Fornax cluster giant elliptical galaxy NGC 1399, identifying as cluster members 27 previously unknown faint     compact stellar systems (CSS), and improving redshift accuracy for 23 previously catalogued CSS.
By amalgamating our results with CSS from previous 2dF observations and excluding CSS dynamically associated with prominent (non-dwarf) galaxies surrounding NGC 1399, we have isolated 80 'unbound' systems that are either part of NGC  1399's globular cluster (GC) system or intracluster GCs. For these unbound systems, we find (i) they are mostly located off the main stellar locus in colour–colour space; (ii) their projected distribution about NGC  1399 is anisotropic, following the Fornax cluster galaxy distribution, and there is weak evidence for group rotation about NGC  1399; (iii) their completeness-adjusted radial surface density profile has a slope similar to that of NGC  1399's inner GC system; (iv) their mean heliocentric recessional velocity is between that of NGC  1399's inner GCs and that of the surrounding dwarf galaxies, but their velocity dispersion is significantly lower; (v) bright CSS  ( M _V < −11)  are slightly redder than the fainter systems, suggesting they have higher metallicity; (vi) CSS show no significant trend in   g '− i '  colour index with radial distance from NGC  1399.