Stellar Dynamics

The stability of rotating isotropic spherical stellar systems is investigated by using N-body simulations. Four spherical models with realistic density profiles are studied: one of them fits the luminosity profile of globular clusters, while the remaining three models provide good approximations to the surface brightness of elliptical galaxies. The phase-space distribution function f (E) of each one of these non-rotating models satisfies the sufficient condition for stability d f /dE < 0. Different amounts of rotation are introduced in these models by changing the sign of the z-component of the angular momentum for a given fraction of the particles. Numerical simulations show that all these rotating models are stable to both radial and non-radial perturbations, irrespective of their degree of rotation. These results suggest that rotating isotropic spherical models with realistic density profiles might generally be stable. Furthermore, they show that spherical stellar systems can rotate very rapidly without becoming oblate.

We study an optimal inequality which relates potential and kinetic energies in an appropriate framework for bounded solutions of the Vlasov-Poisson (VP) system. Optimal distribution functions, which are completely characterized, minimize the total energy. From this variational approach, we deduce bounds for the kinetic and potential energies in terms of conserved quantities (mass and total energy) of the solutions of the VP system and a nonlinear stability result. Then we apply our estimates to the study of the large time asymptotics and observe two different regimes.

Astrophysical space missions deliver invaluable information about our universe, stellar dynamics of our galaxy, and motion of celestial bodies in the solar system. Astrometric space missions SIM and Gaia will determine distances to stars and cosmological objects as well as their physical characteristics and positions on the celestial sphere with microarcsecond precision. These and other space missions dedicated to exploration of the solar system are invaluable for experimental testing of general relativity. Permanently growing accuracy of space and ground-based astronomical observations require corresponding development of relativistic theory of reference frames, motion of celestial bodies, and propagation of light/radio signals from a source of light/radio to observer. Such theory must be based on Einstein's general relativity and account for various relativistic effects both in the solar system and outside of its boundary. We describe a hierarchy of the relativistic frames adopted by the International Astronomical Union in 2000, and outline directions for its theoretical and practical extentions by matching the IAU 2000 reference frames in the solar system to the cosmological Friedman-Robertson-Walker reference frame and to the frames used in the parametrized post-Newtonian formalism.

Challenging stellar dynamical problems, such as the study of gravothermal oscillations in star clusters, have in the past initiated the very successful building of GRAPE special purpose computers. It is discussed, that present day tasks such as the formation and evolution of galactic nuclei with one or more massive black holes and the coupled stellar and gas dynamical processes in

An improved transformation of the full width at half maxima (FWHM) of the [O III] 5007 line in AGNs to the stellar velocity dispersion, sigma, of the host galaxy is given. This significantly reduces the systematic errors in using the [O III] FWHM as a proxy for sigma. AGN black hole masses, M, estimated using the Dibai single epoch spectrum method, are combined with the new estimates of sigma to give a revised AGN M-sigma relationship extending up to high masses. This shows that the masses of the most massive black holes are systematically higher than predicted by extrapolation of M \propto sigma^4 to high masses. This supports recent suggestions that stellar dynamical masses of the most massive black holes have been systematically underestimated. The steepening of the M-sigma relationship is consistent with the absence of very high sigma galaxies in the local universe and with the curvature of the Faber-Jackson relationship. There appears to be significantly less intrinsic scatter ...

In a series of papers we study the stellar dynamics of the grand design barred-spiral galaxy NGC 1300. In the first paper of this series we estimate the gravitational potential and we give it in a form suitable to be used in dynamical studies. The estimation is done directly from near-infrared observations. Since the 3D distribution of the luminous matter is unknown, we construct three different general models for the potential corresponding to three different assumptions for the geometry of the system, representing limiting cases. A pure 2D disc, a cylindrical geometry (thick disc) and a third case, where a spherical geometry is assumed to apply for the major part of the bar. For the potential of the disc component on the galactic plane a Fourier decomposition method is used, that allows us to express it as a sum of trigonometric terms. Both even and odd components are considered, so that the estimated potential accounts also for the observed asymmetries in the morphology. For the amplitudes of the trigonometric terms a smoothed cubic interpolation scheme is used. The total potential in each model may include two additional terms (Plummer spheres) representing a central mass concentration and a dark halo component, respectively. In all examined models, the relative force perturbation points to a strongly nonlinear gravitational field, which ranges from 0.45 to 0.8 of the axisymmetric background with the pure 2D being the most nonlinear one. The force perturbation in each model is found being robust to small changes of the required parameter values. We present the topological distributions of the stable and unstable Lagrangian points as a function of the pattern speed (Ω p ). The topological distribution found deviates in several cases from the classical paradigm with two stable Lagrangian points at the sides of the bar and two unstable ones close to the ends of the bar. In all three models there is a range of Ω p values, where we find multiple stationary points whose stability affects the overall dynamics of the system.

Star formation in the Taurus-Auriga (TA) molecular clouds is producing binary-rich aggregates containing at most a few dozen systems within a region spanning one pc without massive stars. This environment is very different to another well-studied starforming event which produced the Orion Nebula cluster (ONC). The ONC contains a few thousand systems within a region of one pc including massive stars. Differences between these two environments have been found. Notably, the ONC has a significantly smaller binary proportion but a significantly larger number of isolated brown dwarfs (BDs) per star than TA. The aim of the present project is to investigate if these differences can be explained through stellar-dynamical evolution alone. The stellar-dynamical issue is very relevant because dense environments destroy binaries liberating BD companions, possibly leading to the observed difference between the TA and ONC populations. Here a series of high-precision N −body models of TA-like embedded aggregates are presented, assuming the standard reference star-formation model for the input populations according to which stars and BDs form with the same kinematical, spatial and binary properties. After a discussion of the general evolution of the aggregates, it is shown that the binary population indeed remains mostly unevolved. Therefore, TA-type star formation cannot have added significantly to the Galactic-field population. The standard model leads to BDs tracing the stellar distribution, apart from a high-velocity tail (v > ∼ 1 km/s) which leads to a more widely distributed spatial distribution of single BDs. The slow-moving BDs, however, retain a high binary proportion, this being an important observational diagnostic for testing against the embryo-ejection hypothesis. Inferences about the IMF and the binarystar orbital distribution functions are made in two accompanying papers with useful implications for star formation and the possible origin of BDs.

This report from Commission 30 covers the salient areas in which major progress has been made in the triennium covered by the present volume. The principal scientific areas are: The Milky Way, star clusters, spectroscopic binaries, extrasolar planets, pulsating stars and stellar oscillations. Following these, an account is given of the progress in techniques and methodology for radial velocity determinations. Finally, a summary is given of the progress made by the working groups of the Commission, followed by a list of key papers in the triennium. A more extensive report also covering extragalactic work, which due to unforeseen circumstances could not be included here, can be found at the web page of Commission 30

This paper investigates spheroidal galaxies comprising a self-interacting dark matter (SIDM) halo plus de Vaucouleurs stellar distribution. These are coupled only via their shared gravitational field, which is computed consistently from the density profiles. Assuming conservation of mass, momentum and angular momentum, perturbation analyses reveal the galaxy's response to radial disturbance. The modes depend on fundamental dark matter properties, the stellar mass, and the halo's mass and radius. The coupling of stars and dark matter stabilizes some haloes that would be unstable as one-fluid models. However the centrally densest haloes are unstable, causing radial flows of SIDM and stars (sometimes in opposite directions). Depending on the dark microphysics, some highly diffuse haloes are also unstable. Unstable galaxies might shed their outskirts or collapse. Observed elliptical galaxies appear to exist in the safe domain. Halo pulsations are possible. The innermost node of SIDM waves may occur within 10 half-light radii. Induced stellar ripples may also occur at detectable radii if higher overtones are excited. If any SIDM exists, observational skotoseismology of galaxies could probe dark matter (DM) physics, measure the sizes of specific systems, and perhaps help explain peculiar objects (e.g. some shell galaxies, and the growth of red nuggets).

Πιστεύω ακράδαντα, ότι αυτά τα δύο γεγονότα αποτελούν απόδειξη της ποιότητας του έργου του επιτελούµενου στο Εργαστήριο Αστρονοµίας, έργου που τιµά και τους δυο αγαπητούς συναδέλφους, αλλά και το Εργαστήριο Αστρονοµίας και κατ' επέκταση το Τµήµα Φυσικής και το Πανεπιστήµιό µας. Θεωρώντας ότι εκφράζω ολόκληρο το Εργαστήριο Αστρονοµίας, συγχαίρω θερµά και τους δύο συναδέλφους µου και τους εύχοµαι και εις ανώτερα.

A new empirical formulae is given for estimating the masses of black holes in AGNs from the H beta velocity dispersion and the continuum luminosity at 5100 Angstroms. It is calibrated to reverberation-mapping and stellar-dynamical estimates of black hole masses. The resulting mass estimates are as accurate as reverberation-mapping and stellar-dynamical estimates. The new mass estimates show that there is very little scatter in the M_{bh} - L_{bulge} relationship for high-luminosity galaxies, and that the scatter increases substantially in lower-mass galaxies.

Context. Stellar dynamics indicate the presence of a supermassive 3−4 × 10 6 M black hole at the Galactic Center. It is associated with the variable radio, near-infrared, and X-ray source Sagittarius A* (SgrA*). Aims. The goal is the investigation and understanding of the physical processes responsible for the variable emission from SgrA*. Methods. The observations have been carried out using the NACO adaptive optics (AO) instrument at the European Southern Observatory's Very Large Telescope (July 2005, May 2007) and the ACIS-I instrument aboard the Chandra X-ray Observatory (July 2005). Results. We find that for the July 2005 flare the variable and polarized NIR emission of SgrA* occurred synchronous with a moderately bright flare event in the X-ray domain with an excess 2−8 keV luminosity of about 8 × 10 33 erg/s. We find no time lag between the flare events in the two wavelength bands with a lower limit of ≤10 min. The May 2007 flare shows the highest sub-flare to flare contrast observed until now. It provides evidence for a variation in the profile of consecutive sub-flares. Conclusions. We confirm that highly variable and NIR polarized flare emission is non-thermal and that there exists a class of synchronous NIR/X-ray flares. We find that the flaring state can be explained via the synchrotron self-Compton (SSC) process involving up-scattered X-rays from the compact source component. The observations can be interpreted in a model involving a temporary disk with a short jet. In the disk component the flux density variations can be explained by spots on relativistic orbits around the central supermassive black hole (SMBH). The profile variations for the May 2007 flare can be interpreted as a variation of the spot structure due to differential rotation within the disk.

We present the formulation of a new infinite family of self-consistent stellar models, designed to describe axisymmetric flat galaxies. The corresponding density-potential pair is obtained as a superposition of members belonging to the generalized Kalnajs family, by imposing the condition that the density can be expressed as a regular function of the gravitational potential, in order to derive analytically the corresponding equilibrium distribution functions (DF). The resulting models are characterized by a well-behaved surface density, as in the case of generalized Kalnajs discs. Then, we present a study of the kinematical behavior which reveals, in some particular cases, a very satisfactory behavior of the rotational curves (without the assumption of a dark matter halo). We also analyze the equatorial orbit's stability and Poincaré surfaces of section are performed for the 3-dimensional orbits. Finally, we obtain the corresponding equilibrium DFs, using the approaches introduced by Kalnajs (1976) and Dejonghe (1986).

We present the results of a series of numerical simulations of gravitational collisionless N-body systems in equilibrium after a violent relaxation from cosmological initial conditions. The distribution function f of such systems has a complicated form due to the complex structure of the phase space of stellar orbits. This complexity makes hardly tractable the old problem of writing a simple model for f. However, we show that it is possible to benefit from various statistical regularities of the phase space in order to compose a heuristic approximation for f. Such regularities are revealed if we decompose a system in a number of spherical shells. For each shell we define thermodynamical quantities (e.g., temperatures) which, as we find, vary smoothly with the radius r of the shell. Using these quantities, we find a model that fits the number density function ν(E, L 2 , r) in each shell. For the greatest range of energies, this function tends to the form of the Stiavelli-Bertin (1987) model. By adding the contributions of all the spherical shells, we then find a global model for f. While our method is based on a spherical approximation, we show that it reproduces very accurately the global profiles of our triaxial N-body systems.

A quantitative description of Hamiltonian chaos, based on a Riemannian geometrization of Newtonian dynamics, is discussed here for a model, introduced by Contopoulos, describing the dynamics of a test star in a galactic potential. A statistical treatment of the geometry of dynamics, effective in the limit of a large number N of degrees of freedom, is here applied to the N = 3 case of the Contopoulos model, discussing how the statistical model has to be modified in order to quantitatively account for the chaoticity of the dynamics.

On May 9 the Minor Planet Center announced the re-discovery of the last 'lost' minor planet, (719) Albert. In this paper we study its orbital evolution. We show that Albert follows an extremely chaotic orbit, typical of near-Earth asteroids (NEAs) that are extracted from main belt resonances through close planetary encounters. It will become an Earth-crosser and, eventually, it will either be ejected from the solar system on a hyperbolic orbit or will become a Sun-grazer, most probably within the next 5 Myrs.

We investigate the kinematics of the central gas disk of the radio-loud elliptical galaxy NGC 4335, derived from HST/STIS long-slit spectroscopic observations of Hα+[N II] along 3 parallel slit positions. The observed mean velocities are consistent with a rotating thin disk. We model the gas disk in the customary way, taking into account the combined potential of the galaxy and a putative black hole with mass M • , as well as the influence on the observed kinematics of the point spread function and finite slit width. This sets a 3σ upper limit of 10 8 M ⊙ on M • . The velocity dispersion at r 0.5 ′′ is in excess of that predicted by the thin rotating disk model. This does not invalidate the model, if the excess dispersion is caused by localized turbulent motion in addition to bulk circular rotation. However, if instead the dispersion is caused by the BH potential then the thin disk model provides an underestimate of M • . A BH mass M • ∼ 6 × 10 8 M ⊙ is inferred by modeling the central gas dispersion as due to an isotropic spherical distribution of collisionless gas cloudlets. The stellar kinematics for NGC 4335 are derived from a ground-based (WHT/ISIS) long-slit observation along the galaxy major axis. A two-integral model of the stellar dynamics yields M • 3×10 9 M ⊙ . However, there is reason to believe that this model overestimates M • .

We present observations and dynamical models of the stellar nuclear clusters (NCs) at the centres of NGC 4244 and M33. We then compare these to an extensive set of simulations testing the importance of purely stellar dynamical mergers on the formation and growth of NCs. Mergers of star clusters are able to produce a wide variety of observed properties, including densities, structural scaling relations, shapes (including the presence of young discs) and even rapid rotation. None the less, difficulties remain, most notably that the secondorder kinematic moment V rms = √ V 2 + σ 2 of the models is too centrally peaked to match observations. This can be partially remedied by the merger of star clusters on to a pre-existing nuclear disc, but the line-of-sight velocity V is still more slowly rising than in NGC 4244. Our results therefore suggest that purely stellar dynamical mergers cannot form NCs and that gas dissipation is a necessary ingredient for at least ∼50 per cent of a NC's mass. The negative vertical anisotropy found in NGC 4244, however, requires at least 10 per cent of the mass to have been accreted as stars, since gas dissipation and in situ star formation leads to positive vertical anisotropy.

To be presented is a study of the secular evolution of a spherical stellar system with a central star-accreting black hole (BH) using the anisotropic gaseous model. This method solves numerically moment equations of the full Fokker-Planck equation, with Boltzmann-Vlasov terms on the left-and collisional terms on the right-hand sides. We study the growth of the central BH due to star accretion at its tidal radius and the feedback of this process on to the core collapse as well as the post-collapse evolution of the surrounding stellar cluster in a self-consistent manner. Diffusion in velocity space into the loss-cone is approximated by a simple model. The results show that the self-regulated growth of the BH reaches a certain fraction of the total mass cluster and agree with other methods. Our approach is much faster than competing ones (Monte Carlo, N -body) and provides detailed informations about the time and space dependent evolution of all relevant properties of the system. In this work we present the method and study simple models (equal stellar masses, no stellar evolution or collisions). Nonetheless, a generalisation to include such effects is conceptually simple and under way.

We study an optimal inequality which relates potential and kinetic energies in an appropriate framework for bounded solutions of the Vlasov-Poisson (VP) system. Optimal distribution functions, which are completely characterized, minimize the total energy. From this variational approach, we deduce bounds for the kinetic and potential energies in terms of conserved quantities (mass and total energy) of the solutions of the VP system and a nonlinear stability result. Then we apply our estimates to the study of the large time asymptotics and observe two different regimes.

Because of the high eccentricities (∼ 0.3) of two of the possible planets about the star Upsilon Andromeda, the stability of the system requires careful study. We present results of 1000 numerical simulations which explore the orbital parameter space as constrained by the observations. The orbital parameters of each planet are chosen from a Gaussian error distribution, and the resulting configuration is integrated for 1,000,000 years. We find that 84% of these integrations are stable. Configurations in which the eccentricity of the third planet is ∼ < 0.3 are always stable, but when the eccentricity is ∼ > 0.45 the system is always unstable, typically producing a close encounter between the second and third planets. A similar exercise with the gas giants in our own Solar System sampled with the same error distribution was performed. Approximately 81% of these simulations were stable for 10 6 years.

Finite thin disc models of four galaxies in the Ursa Major cluster are presented. The models are obtained by means of the Hunter method and the particular solutions are choosen in such a way that the circular velocities are adjusted very accurately to the observed rotation curves of some specific spiral galaxies. We present particular models for the four galaxies NGC3877, NGC3917, NGC3949 and NGC4010 with data taken from the recent paper by Verheijen & Sancici (2001). By integrating the corresponding surface mass densities, we obtain the total mass M of these four galaxies, all of them being of the order of 10 10 M ⊙. These obtained values for M may be taken as a quite accurately estimative of the mass upper bound of these galaxies, since in the model was considered that all their mass was concentrated at the galactic disc. The models can be consider as a first approximation to the obtaining of quite realistic models of spiral galaxies.

Aims. The Coma cluster is the richest and most compact of the nearby clusters, yet there is growing evidence that its formation is still ongoing. A sensitive probe of this evolution is the dynamics of intracluster stars, which are unbound from galaxies while the cluster forms, according to cosmological simulations. Methods. With a new multi-slit imaging spectroscopy technique pioneered at the 8.2 m Subaru telescope and FOCAS, we have detected and measured the line-of-sight velocities of 37 intracluster planetary nebulae associated with the diffuse stellar population of stars in the Coma cluster core, at 100 Mpc distance. Results. We detect clear velocity substructures within a 6 arcmin diameter field. A substructure is present at ∼5000 km s −1 , probably from in-fall of a galaxy group, while the main intracluster stellar component is centered around ∼6500 km s −1 , ∼700 km s −1 offset from the nearby cD galaxy NGC 4874. The kinematics and morphology of the intracluster stars show that the cluster core is in a highly dynamically evolving state. In combination with galaxy redshift and X-ray data this argues strongly that the cluster is currently in the midst of a subcluster merger, where the NGC 4874 subcluster core may still be self-bound, while the NGC 4889 subcluster core has probably dissolved. The NGC 4889 subcluster is likely to have fallen into Coma from the eastern A2199 filament, in a direction nearly in the plane of the sky, meeting the NGC 4874 subcluster arriving from the west. The two inner subcluster cores are presently beyond their first and second close passage, during which the elongated distribution of diffuse light has been created. We predict the kinematic signature expected in this scenario, and argue that the extended western X-ray arc recently discovered traces the arc shock generated by the collision between the two subcluster gas halos. Any preexisting cooling core region would have been heated by the subcluster collision.

We present a clear N-body realization of the growth of a Bahcall-Wolf f ∝ E 1/4 (ρ ∝ r −7/4 ) density cusp around a massive object ("black hole") at the center of a stellar system. Our N-body algorithm incorporates a novel implementation of Mikkola-Aarseth chain regularization to handle close interactions between star and black hole particles. Forces outside the chain were integrated on a GRAPE-6A/8 special-purpose computer with particle numbers up to N = 0.25 × 10 6 . We compare our N-body results with predictions of the isotropic Fokker-Planck equation and verify that the time dependence of the density (both configuration and phase-space) predicted by the Fokker-Planck equation is well reproduced by the N-body algorithm, for various choices of N and of the black hole mass. Our results demonstrate the feasibility of direct-force integration techniques for simulating the evolution of galactic nuclei on relaxation time scales.

We present a general-relativistic analysis that allows the stellar radial velocities to be determined from a suitable implementation of the spectroscopic data with the astrometric ones shortly to be provided by new generations of astrometric satellites at μarcsec levels of accuracy at least. This analysis leads to an enhancement of the c −1 Doppler-shift formula presently planned for the Gaia mission to an all-inclusive, general-relativistic formula at the c −3 level, consistently with the expected accuracy. From this formula, which is shown to provide relevant corrections already at the c −2 level to a previously proposed one, we are then able to derive the explicit expression for the stellar radial velocity in terms of the spectroscopic and astrometric data, thereby accounting for all the necessary relativistic corrections up to and including the c −3 level.

Recent observational constraints restrict the strict applicability of stellar dynamics in spirals to a few rotation periods. However, stellar dynamics concepts such as periodic orbits are invaluable for understanding the various dynamical processes occurring during much more periods. A distinction of two instability types in stellar systems is pointed out, the first one being well illustrated by the bar instability, and the second one by the bar bending instability. In bars the third dimension brings essential dynamical effects which modify the views about the history of bulges and the spiral secular evolution. Bars may grow, bend, thicken, and dissolve into spheroidal bulges, and spirals may evolve along the Hubble sequence in the sense Sd→Sa. This leads to a much more dynamical picture of isolated galaxies than imagined before.

An analytical model based on the maximum entropy approach is proposed to describe the eventual asymmetries of the velocity distribution, which are collected through its sample moments. If an extended set of moments is available, the current method provides a linear algorithm, associated with a Gramian system of equations, that leads to a fast and suitable estimation of the velocity distribution. In particular, it could be used to model multimodal distributions that cannot be described through Gaussian mixtures. The method is used with several samples from the HIPPARCOS and Geneva-Copenhagen survey catalogues. For the large-scale distribution, the phase density function may be obtained by fitting moments up to sixth order as a product of two exponential functions, one giving a background ellipsoidal shape of the distribution and the other accounting for the skewness and for the slight shift in the ellipsoidal isocontours in terms of the rotation velocity. The small-scale distribution can be deduced from truncated distributions, such as velocity-bounded samples with |V| ≤ 51 km s −1 , which contain a complex mixture of early-type and young disc stars. By fitting up to ten-order moments, the maximum entropy approach gives a realistic portrait of actual asymmetries, showing a clear bimodal pattern: (i) around the Hyades-Pleiades stream, with negative radial mean velocity and (ii) around the Sirius-UMa stream, with slightly positive radial mean velocity. Among metallicity, colour, and other star properties, the eccentricity of the star's orbit behaves as a very good sampling parameter to find a more detailed structure for the disc velocity distribution, allowing distinctions between different eccentricity layers. For subsamples with eccentricities e < 0.15, star velocities are approximately symmetrically distributed around the LSR in the radial direction, with a dearth of stars at the LSR. For e = 0.15, the core distribution of the thin disc is supported by two major stellar groups with opposite radial velocities. Several simulations confirm that such a double-peaked distribution comes from the lognormal distribution of the velocity amplitudes. For maximum eccentricity 0.3 and maximum distance to the Galactic plane 0.5 kpc a representative thin disc sample is obtained. The "U-anomaly" along the radial direction is estimated straightforwardly 30−35 km s −1 from the contour plots. An explanation of the apparent vertex deviation of the disc from the swinging of those major kinematic groups around the LSR is then possible, which predicts a continuously changing orientation of the disc's pseudo ellipsoid.

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor ǫ of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order ǫ, and neglecting those of order ǫ 2 , ǫ 3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when ǫ is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.

In astrophysics numerical star cluster simulations and hydrodynamical methods like SPH require computational performance in the petaflop range. The GRAPE 1 -family of ASIC-based accelerators improves the cost-performance ratio compared to general purpose parallel computers, however with limited flexibility. The AHA-GRAPE architecture adds an reconfigurable FPGA 2 -processor to accelerate the SPH computation. The basic equations of the algorithm consist of three parts each scaling with the order of O(N), O(N*Nn) and O(N 2 ) respectively, where N is in the range of 10 4 to 10 7 and Nn ~ 50. These equations can profitably be distributed across a host workstation, an FPGA processor and a GRAPEsubsystem.

Abstract.  In this article are the 5 tables for calculating the average translational velocities of all milisecond pulsars and others fast spinning bodies and shift the center of gravity due to the rotation.  Corrections theory ideal spining circle for real  bodies. Extreme values for neutron stars. Summary values  for neutron stars. A new perspective on neutronization and nuclear fusion.  Consent theory with the real Universe. From well-functioning theory for milisecond pulsars are derived estimates for raelisation new mode of transport on the principle rotation.  CNN's Larry King covered the news story in the days following the incident, and according to Steve Allen, a private pilot who witnessed the UFO, the object was travelling at a high rate of speed which supposedly reached 3,000 feet in the air.  3000 ft/s (910 m/s) velocity .

For radius UFO  r= 20m,  the estimate revolutions per second is 18 207  rps 

for  real  UFO

Keywords: stars: kinematics, pulsars: general,  stellar dynamics,  , stars: neutron, 
PACS number:  97.60.Gb, 97.60.Jd,

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A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts signi cant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied speci cally to the problem of disk shocking of star clusters.

Collisions of main sequence stars occur frequently in dense star clusters. In open and globular clusters, these collisions produce merger remnants that may be observed as blue stragglers. Detailed theoretical models of this process require lengthy hydrodynamic computations in three dimensions. However, a less computationally expensive approach, which we present here, is to approximate the

The long-term evolution of massive black hole binaries at the centers of galaxies is studied in a variety of physical regimes, with the aim of resolving the &#x27;&#x27; final parsec problem,&#x27;&#x27; ie, how black hole binaries manage to shrink to separations at which emission ...

We present MUSE, a software framework for combining existing computational tools for different astrophysical domains into a single multiphysics, multiscale application. MUSE facilitates the coupling of existing codes written in different languages by providing inter-language tools and by specifying an interface between each module and the framework that represents a balance between generality and computa

Curves in a family derived from powers of the polar coordinate formula for ellipses are found to provide good fits to bound orbits in a range of power-law potentials. This range includes the well-known 1/r (Keplerian) and logarithmic potentials. These approximate orbits, called p-ellipses, retain some of the basic geometric properties of ellipses. They satisfy and generalize Newton's apsidal precession formula, which is one of the reasons for their surprising accuracy. Because of their simplicity the p-ellipses make very useful tools for studying trends among power-law potentials, and especially the occurence of closed orbits. The occurence of closed or nearly closed orbits in different potentials highlights the possibility of period resonances between precessing, eccentric orbits and circular orbits, or between the precession period of multi-lobed closed orbits and satellite periods. These orbits and their resonances promise to help illuminate a number of problems in galaxy and accretion disk dynamics.

The following principle of minimum energy may be a powerful substitute to the dynamical perturbation method, when the latter is hard to apply. Fluid elements of self-gravitating barotropic flows, whose vortex lines extend to the boundary of the fluid, are labelled in such a way that any change of trial configurations automatically preserves mass and circulation. The velocity field is given by a mass conserving Clebsch representation. With three independent Lagrangian functions, the total energy is stationary for all small variations about a flow with fixed linear and angular momenta provided Euler's equations for steady motion are satisfied. Thus, steady flows are stable if their energy is minimum. Since energy is here minimized subject to having local and global contants of the motion fixed, stability limits obtained that way are expected to be close to limits given by dynamical perturbation methods. Moreover, the stability limits are with respect to arbitrary, not necessary small, perturbations. A weaker form of the energy principle is also given which may be easier to apply.

In this paper, we describe the architecture and performance of the GraCCA system, a graphic-card cluster for astrophysics simulations. It consists of 16 nodes, with each node equipped with two modern graphic cards, the NVIDIA GeForce 8800 GTX. This computing cluster provides a theoretical performance of 16.2 TFLOPS. To demonstrate its performance in astrophysics computation, we have implemented a parallel direct N-body simulation program with shared time-step algorithm in this system. Our system achieves a measured performance of 7.1 TFLOPS and a parallel efficiency of 90% for simulating a globular cluster of 1024 K particles. In comparing with the GRAPE-6A cluster at RIT (Rochester Institute of Technology), the GraCCA system achieves a more than twice higher measured speed and an even higher performance-per-dollar ratio. Moreover, our system can handle up to 320M particles and can serve as a general-purpose computing cluster for a wide range of astrophysics problems.

This paper deals with the inÑuence of JupiterÏs "" Great Inequality ÏÏ (GI) on the orbital evolution of 2 : 1 resonant asteroids. This perturbation of JupiterÏs motion enhances the chaotic di †usion of orbits and the depletion of asteroids in the Hecuba gap. The failure of models that adopt for Jupiter an elliptic motion with only secular perturbations is explained. We also show the dependence of the di †usion rates on the GI period, and the maximum di †usion rates that would take place if the GI period were closer to the libration period. SigniÐcant similar e †ects are absent in the 3 : 2 asteroidal resonance.

The stability of the 2:3 mean motion resonance with Neptune is systematically explored and compared to the observed resonant population. It is shown that orbits with small and moderate amplitudes of the resonant angle are stable over the age of the Solar System. The observed resonant population is distributed within the stability limits. There exists an interval of large resonant amplitudes, where orbits are marginally unstable. Resonant objects starting in this interval may leave the resonance by slow increase of their resonant amplitudes on a time scale of several billion years. These objects eventually attain Neptune-crossing trajectories and contribute to the flux of Jupiter-family comets. The number of objects leaking from the 2:3 resonance per time interval is calibrated by the number of objects needed to keep the Jupiter-family comets population in steady state. This allows us to compute the upper limit of the number of resonant objects with cometary size. The effects of collisions and mutual gravitational scattering are discussed in this context.

Binaries are not always neatly aligned. Previous observations of the DI Her system showed that the spin axes of both stars are highly inclined with respect to one another and the orbital axis. Here we report on a measurement of the spin-axis orientation of the primary star of the NY Cep system, which is similar to DI Her in many respects: it features two young early-type stars (∼ 6Myr, B0.5V+B2V), in an eccentric and relatively long-period orbit (e = 0.48, P = 15. d 3). The sky projections of the rotation vector and the spin vector are well-aligned (β p = 2 ± 4 •), in strong contrast to DI Her. Although no convincing explanation has yet been given for the misalignment of DI Her, our results show that the phenomenon is not universal, and that a successful theory will need to account for the different outcome in the case of NY Cep.

A statistical mechanical description is proposed for two-dimensional inviscid fluid turbulence. Using this description, we make predictions for turbulent flow in a rapidly rotating laboratory annulus. Measurements on this system reveal coherent vortices in a mean zonal flow. The flow is anisotropic and inhomogeneous but has low dissipation and forcing. In statistical mechanics two crucial requirements for equilibrium are statistical independence of macro-cells (subsystems) and additivity of invariants of the macro-cells. One of these invariants is energy, an extensive quantity, which should be additive; i.e. the interaction energy between a macro-cell and the rest of the system (reservoir) should be small. We use additivity to select the appropriate Casimir invariants from the infinite set available in vortex dynamics. Exchange of micro-cells within a macro-cell should not alter an invariant of a macro-cell. Statistical analyses of turbulence for several decades have considered macro-cells without explicitly considering their statistical independence. A novel feature of the present study is our choice of the macro-cells, which are continuous phase space surfaces based on mean values of the streamfunction; the surfaces can be used to define a canonical distribution. We show that this approach can describe anisotropic and inhomogeneous properties of a flow. Quantities such as energy and enstrophy can be defined on each surface. Our approach leads to the prediction that on a surface there should be a linear relation between the ensemble-averaged potential vorticity and the time-averaged streamfunction; our laboratory data are in good accord with this prediction. Further, the approach predicts that although the probability distribution function for potential vorticity in the entire system is non-Gaussian, the distribution function of micro-cells should be Gaussian on the macro-cells, i.e., for surfaces defined by mean values of the streamfunction. This prediction is also supported by the turbulence data. While our statistical mechanics approach was motivated by and applied to experiments on turbulence in a rotating annulus, the approach is quite general and is applicable to a large class of Hamiltonian systems, including drift-wave plasma models, Vlasov-Poisson dynamics, and kinetic theories of steller dynamics.