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What have we learned about galaxies through large computations?

Numerical models permit modelling processes within galaxies that are seemingly beyond the reach of physical contact or close-up viewing from different angles. N-body equations permit simple computations of the interactions of individual stars within galaxies, but the motions of these objects feature nonlinear characteristics because of the forces exerted by the complex as a whole which are not amenable to examination with Newtonian laws of force. The models have, however, revealed that thin disk galactic are not stable forms, that barlike structures rotating end-over-end are more stable structures, and that galactic contraction occurs during collisions between galaxies. Internal effects have been successfully predicted for galaxies which are part of clusters, growth rate disturbances due to the expansion of the Universe have been quantified as 2-3 percent and dynamical friction has been shown to damage galaxies which are sliding into background material.

Miller, R. H.↗

Massive black holes in galactic halos?

In the present attempt to resolve the problems posed by the composition of dark halos and the heating of stellar disks, under the assumption that galaxy halos are composed of massive black holes, it is noted that the black holes must have masses of the order of one million solar masses. The heating mechanism proposed yields predictions for the dependence of the velocity dispersion on time, and for the shape of the velocity ellipsoid, which are in good agreement with observations. Attention is given to the constraints set by dynamical friction causing black holes to spiral to the Galactic center, by the possible presence of dark matter in dwarf spheroidal galaxies, and by the accretion of interstellar gas by the black holes that produce luminous objects in the Galaxy.

Lacey, C. G.↗

Evolution of planetesimal velocities

A self-consistent set of equations for the velocity evolution of a general planetesimal population is presented. The equations are given in a form convenient for calculations of the early stages of planetary accumulation when it is necessary to model the planetesimal swarm by methods of gas dynamics, rather than follow the orbital evolution of individual bodies. Steady state velocities of a simple planetesimal population consisting of two different sizes of bodies are calculated. Dynamical friction is found to be an important mechanism for transferring kinetic energy from the larger planetesimals to the smaller ones. When the small planetesimals are relatively abundant, gas drag and inelastic collisions among the smaller bodies are of comparable importance for dissipating energy from the population.

Stewart, Glen R.↗

The morphology of multiple-nucleus brightest cluster galaxies

The morphology of high SNR CCD images of 16 multiple-nucleus brightest cluster galaxies is studied using an algorithm that models images of the systems as the line-of-sight superposition of normal elliptical galaxies. The algorithm is applied initially to the classic multiple-nucleus cD galaxy in A2199. Evidence is found suggestive of deep interpenetrating high-speed encounters by its secondaries. The interactions effects studied include noncentric isophotes, brightness profile effects, excess light around primary galaxies, and dynamical friction wakes. The results show that in many cases multiple systems are interacting systems.

Lauer, Tod R.↗

Evolution of planetesimal velocities

The velocity evolution of a general planetesimal population is treated by means of a self-consistent set of equations whose form is tailored to those early planetary accumulation stages in which the planetesimal swarm's modeling calls for gas dynamic methods. Dynamical friction is noted to be essential to the transfer of kinetic energy from larger to smaller planetesimals, thereby furnishing an energy source comparable to those furnished by viscous stirring.

Stewart, Glen R.↗

The evolution of the system of globular clusters

The physical processes affecting the evolution of the system of globular clusters are reviewed. Aspects of internal structure evolution discussed include evaporation, core collapse, expansion, tidal shocks, and interaction with other massive components of the Galaxy such as black holes, molecular clouds, and other clusters. The evolution of orbital parameters is examined, including dynamical friction, scattering by massive subcomponents, and interactions with nearby systems. In addition, an overview of the system evolution is presented.

Ostriker, Jeremiah P.↗

The distribution of cD galaxy peculiar velocities

A modified version of a cluster evolution computer code first described in Richstone and Malumuth (1983) and Malumuth and Richstone (1984) to investigate the distributon of cD galaxy peculiar velocities and positions relative to the center, for a sample of cDs formed through mergers in a virialized cluster. This distribution is compared to an observed distribution of 19 cD galaxies to test whether cD galaxies with large peculiar velocities could have been formed in virialized clusters. At the time of their formation the cD galaxies have a distribution of peculiar velocities similar to that of the observed cD galaxies. By the end of the simulations the cD galaxies were dragged to the center of the cluster by dynamical friction, and the distribution of peculiar velocities is inconsistent with the observed distribution. The typical cD galaxy has nine mergers and is 5 solar luminosities. This is in comparison with the observed luminosity of Morgan poor clusters of 7 solar luminosities.

Malumuth, Eliot M.↗

Galactic disks, infall, and the global value of Omega

Stringent limits on the current rate of infall of satellite systems onto spiral galaxies are set on the basis of the thinness and coldness of Galactic disks. For infalling satellites on isotropically oriented circular orbits, it is shown that, due to scattering, the thermal energy gain of the disk exceeds the satellite energy loss from dynamical friction by a factor of 1.6, with 25 percent deposited in z motion and 75 percent in planar motions. It is found that no more than 4 percent of the Galactic mass inside the solar radius can have accreted within the last 5 billion years, or else its scale and its Toomre Q-parameter would exceed observed values. In standard cold-dark-matter-dominated models for the growth of structure with Omega sub tot of 1, the mass accreted in dark matter lumps rises faster than t exp 2/3 and would exceed 28 percent in the last 5 Gyr. It is proposed that heating from satellite infall accounts for a substantial fraction of the increase of velocity dispersion and scale height with age that is observed in the Galaxy.

Toth, G.↗

The warped disk of Centaurus A in the near-infrared

We present infrared images of Cen A (NGC 5128) in the J, H, and K bands. The infrared morphology is primarily determined by the presence of a thin absorptive warped disk. By integrating the light of the underlying prolate galaxy through such a disk, we construct models which we compare with infrared and X-ray data. The geometry of the warped disk needed to fit the IR data is consistent with a warped disk which has evolved as a result of differential precession in a prolate potential. The disk has an inclination, with respect to the principal axis of the underlying elliptical galaxy, that is higher at larger radii than in the inner region. A scenario is proposed where a small gas-rich galaxy infalling under the force of dynamical friction is tidally stripped. Stripping occurs at different times during its infall. The orientation of the resulting gas disk depends upon the angular momentum of the infalling galaxy. We find that the resulting precession angle of the disk is well described by the precession model, but that the inclination angle may vary as a function of radius. We propose an orbit for the infalling galaxy that is consistent with the geometry of the warped disk needed to fit our infrared data, and rotation observed in the outer part of the galaxy.

Quillen, A. C.↗

Effects of gas on the global stability of galactic disks - Radial flows

We study numerically the effect of gas on the global stability of a two-component self-gravitating galactic disk embedded in a live halo. The stars are evolved by using a 3D collisionless N-body code, and the gas is represented by an ensemble of finite size inelastic particles. The gravitational interaction of stars and gas is calculated using a TREE method. We find that the evolution of the gaseous distribution in the globally unstable disks can be described by two different regimes. When the gas mass fraction is less than about 10 percent, the gas is channeled toward the galactic center by a growing stellar bar. For higher gas fractions, the gas becomes highly inhomogeneous, and the bar instability in the disk is heavily damped. The gas falls toward the inner kpc due to dynamical friction. Domains of both regimes depend on the efficiency of dissipation in the gas. We also discuss the relevance of the Jeans instability and give an empirical criterion for the global bar instability in a two-component self-gravitating disk.

Shlosman, Isaac↗

Indications for common origin and gravitational interaction in three binary LMC clusters

Three close pair clusters of the LMC, NGC 2006/SL 538, NGC 2011 a/b, and NGC 2042 a/b, have been studied in order to establish their binarity. The stellar content in the outer region of each cluster has been investigated by means of low resolution objective UK Schmidt prism spectra, the cores of the clusters have been examined using low resolution integrated IUE spectra, whereas their density profiles and their observed dynamical parameters have been derived by means of star counts. The integrated spectra of their cores and the stellar content of their outer cluster regions have shown a common origin and a very young age (less than 2 x 10 exp 7 yr) for each member of the pairs, whereas their dynamical study has shown that they are gravitationally interacting. Comparing the age of their stellar content with their dynamical and relaxation times, it has been found that these clusters are physically associated and had no time to relax by stellar encounters, no time to merge, and no time to be destroyed by dynamical friction.

Kontizas, E.↗

Gas flow in a two component galactic disk

Numerical simulations of two-component (stars + gas) self-gravitating galactic disks show that the interstellar gas can significantly affect the dynamical evolution of the disk even if its mass fraction (relative to the total galaxy mass) is as low as several percent. Aided by efficient energy dissipation, the gas becomes gravitationally unstable on local scale and forms massive clumps. Gravitational scattering of stars by these clumps leads to suppression of bar instability usually seen in heavy stellar disks. In this case, gas inflow towards the galactic center is driven by dynamical friction which gas clumps suffer instead of bar forcing.

Noguchi, M.↗

Improved models for the evolution of the Coma cluster of galaxies

The analysis by Fitchett & Webster of the observations of the Coma cluster of galaxies has demonstrated that the center of the Coma Cluster consists of two subclusters. Therefore, it is important to construct realistic dynamical models of a galaxy cluster with two mass centers. Our previous N-body models for the Coma Cluster consisted of point masses or particles with simple interaction properties. In the current paper, we employ a more sophisticated N-body code, which includes dynamical friction, mass exchange, and mergers between galaxies.

Dark↗

Dynamic sensitivity analysis of frictional contact/impact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic frictional contact/impact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response to variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the nodal displacements, and the Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. Temporal integration is performed by using Newmark method. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented from the frictional contact/impact response of a composite spherical cap impacting on a rigid plate.

Karaoglan, Levent↗

Notes on implementation of Coulomb friction in coupled dynamical simulations

A coupled dynamical system is defined as an assembly of rigid/flexible bodies that may be coupled by kinematic connections. The interfaces between bodies are modeled using hinges having 0 to 6 degrees of freedom. The equations of motion are presented for a mechanical system of n flexible bodies in a topological tree configuration. The Lagrange form of the D'Alembert principle was employed to derive the equations. The equations of motion are augmented by the kinematic constraint equations. This augmentation is accomplished via the method of singular value decomposition.

Vandervoort, R. J.↗

Dynamic-scanning-electron-microscope study of friction and wear

A friction and wear apparatus was built into a real time scanning electron microscope (SEM). The apparatus and SEM comprise a system which provides the capability of performing dynamic friction and wear experiments in situ. When the system is used in conjunction with dispersive X-ray analysis, a wide range of information on the wearing process can be obtained. The type of wear and variation with speed, load, and time can be investigated. The source, size, and distribution of wear particles can be determined and metallic transferal observed. Some typical results obtained with aluminum, copper, and iron specimens are given.

Brainard, W. A.↗

Study of the effect of static/dynamic Coulomb friction variation at the tape-head interface of a spacecraft tape recorder by non-linear time response simulation

A description is presented of six simulation cases investigating the effect of the variation of static-dynamic Coulomb friction on servo system stability/performance. The upper and lower levels of dynamic Coulomb friction which allowed operation within requirements were determined roughly to be three times and 50% respectively of nominal values considered in a table. A useful application for the nonlinear time response simulation is the sensitivity analysis of final hardware design with respect to such system parameters as cannot be varied realistically or easily in the actual hardware. Parameters of the static/dynamic Coulomb friction fall in this category.

Mukhopadhyay, A. K.↗