The N-body gravitational problem and the simulation of galactic clusters
Many-body gravitational problem and galactic star cluster simulation
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Computationally convenient forms for conic section equations
Three dimensional vector forms of selected section relationships applied to n-body trajectory simulation based on virtual mass concept
Novak, D. H.↗
Wing galaxies: A formation mechanism of the clumpy irregular galaxy Markarian 297
In order to contribute to an understanding of collision-induced starburst activities, the authors present a detailed case study on the starburst galaxy Markarian 297 (= NGC 6052 = Arp 209; hereafter Mrk 297). This galaxy is classified as a clumpy irregular galaxy (CIG) according to its morphological properties (cf. Heidmann, 1987). Two major clumps and many small clumps are observed in the entire region of Mrk 297 (Hecquet, Coupinot, and Maucherat 1987). The overall morphology of Mrk 297 is highly chaotic and thus it seems difficult to determine possible orbits of galaxy-galaxy collision. However, the authors have serendipitously found a possible orbit during a course of numerical simulations for a radial-penetration collision between galaxies. The radial-penetration collision means that an intruder penetrates a target galaxy radially passing by its nucleus. This kind of collision is known to explain a formation mechanism of ripples around disk galaxies (Wallin and Struck-Marcell 1988). Here, the authors show that the radial-penetration collision between galaxies successfully explains both overall morphological and kinematical properties of Mrk 297. The authors made two kinds of numerical simulations for Mrk 297. One is N-body (1x10(exp 4) particles) simulations in which effects of self gravity of the stellar disk are taken into account. These simulations are used to study detailed morphological feature of Mrk 297. The response of gas clouds are also investigated in order to estimate star formation rates in such collisions. The other is test-particle simulations, which are utilized to obtain a rough picture of Mrk 297 and to analyze the velocity field of Mrk 297. The techniques of the numerical simulations are the same as those in Noguchi (1988) and Noguchi and Ishibashi (1986). In the present model, an intruding galaxy with the same mass of a target galaxy moves on a rectilinear orbit which passes the center of the target.
Taniguchi, Yoshiaki↗
Rotation and flattening of globular clusters
Methods for measuring globular cluster ellipticities and the results of such measurements are reviewed, and the processes that determine the shapes of globular clusters and the ways in which they change with time are discussed. The use of the virial tensor theorem to study the connection between the global rotation, velocity anisotropy, and the shape of a self-gravitating system is addressed, and the employment of N-body models to simulate the evolution of globular clusters with initially anisotropic velocity distributions is examined. The application of a simple evaporation model and Fokker-Planck integrations to study the two-body diffusion in globular clusters is reviewed.
Fall, S. M.↗
How are quasars fueled? Simulating interstellar gas in tidally disturbed galaxies
Whether gravitational tides from companions trigger global instabilities in spiral galaxy disks and thus rapid flows of gas into the nucleus to fuel activity is investigated. An n-body computer program is used to simulate the disk of the spiral galaxy within a much more stable, high-velocity dispersion spherical halo. Under sufficient perturbation, the disk undergoes violent distortions due to the disturber and its self-gravitation. The tidal action of companions was simulated and the tidal strengths at which the instabilities appear to match those of the observed companions of Seyferts and quasars was shown. With the additional modifications planned, the gas flow will be more realistically simulated to compare with observations (e.g., colors, velocity fields) of active galaxies.
Byrd, Gene G.↗
Collapse and relaxation of rotating stellar systems
The evolution of initially spherical, uniform-density, and uniform-velocity-dispersion stellar systems is investigated by means of a three-dimensional N-body computer model. Some 100,000 simulation stars are used to follow the collapse and relaxation of the system for various amounts of angular momentum in solid-body rotation. For initially low values of the angular momentum satisfying the Ostriker-Pebbles stability criterion the systems quickly relax to an axisymmetric shape and resemble elliptical galaxies in appearance. The maximum flattening for these systems is equivalent only to an E2 system. For larger values of the initial angular momentum bars develop, and the systems undergo a much more drastic evolution. The apparent rotational and random velocities of the barred systems are very sensitive to the viewing direction. An additional complication is the frequent misalignment of the apparent major axis with the direction that reflects the maximum rotation.
Hohl, F.↗
Numerical simulations of the decay of satellite galaxy orbits
A multiple three-body technique is used to study the orbital evolution of satellite galaxies which is similar to the N-body method but neglects two-body forces between stars in the halo of the parent galaxy. It is found that, for satellites orbiting within the halo, Chandrasekhar's (1960) dynamical friction formula accurately describes the orbital decay rate, including its variation with satellite mass and size and with the number density and mass of halo stars. Significant frictional forces are present even outside the halo, and the orbital decay rate, instead of depending on the procedure used to place the satellite in its orbit, is determined only by the current orbital parameters. This semirestricted N-body method is sufficiently fast to have permitted the running of 200 simulations to date, many more than would have been possible by means of the conventional N-body technique.
Lin, D. N. C.↗
A simulation survey of galaxy interactions
Many carefully selected samples of interacting galaxies have been observed extensively in attempts to clarify whether interaction produces activity in galaxies. Because the sample members represent a wide range of encounter parameters and times, one can then study whether there are correlations between observable encounter features and, for example, Seyfert activity. On the other hand, in theoretical studies, simulations typically deal with either time-consuming detailed modelling of single galaxy pairs or tracing a few model encounters over time. The authors extend the observational survey approach by combining it with a simulation survey. The authors are conducting a survey of model encounters, covering the most important encounter parameters over a wide range. Some parameters, such as companion structure and initial velocity, are demonstratably less important and can be ignored in a first pass. The parameter range must be richly enough sampled so that the authors can evaluate the uniqueness of the observable morphology and velocity structure of the resulting simulated pairs to diagnose unobservable companion orbit parameters. They are using a self-gravitating polar n-body code run on the Cray X-MP at the Alabama Supercomputer Network. For each simulation, the authors have stellar and gas distributions predicted over, typically, a billion years, along with information on gas motions within the disk and any material captured by the companion or lost to the system. Features of disturbed spiral galaxies are sensitive enough to time and encounter parameters so that a match of the simulation survey results to observations can be applied as starting points to infer unobservable orbital or system parameters in actual sample members. This should enable them to examine whether interesting observed properties (Seyfert activity, nuclear star-formation rate) are functions of unobservable dynamical properties which characterize each encounter. Any correlations (or lack of some expected ones) will provide strong clues as to how or whether these phenomena are related to interactions. Aside from its use with such observed samples, this survey should greatly speed determination of initial orbital parameters for more detailed subsequent simulations of individual systems.
Byrd, Gene G.↗
Orbital decay in aspherical galaxies. II - Triaxial systems
A previous analysis of orbital decay of small satellite galaxies into moderately oblate, axisymmetrical cannibal galaxies with Staeckel potentials is generalized here to triaxial systems with arbitary anisotropy and internal streaming. The orbital evolution to be expected in systems with differing degrees of anisotropy or rotation is briefly discussed. The evolution of some representative orbits is presented in detail using the orbit-averaged anisotropic Chandrasekhar drag and the distribution functions for perfect ellipsoids. The validity of orbit averaging is assessed by comparing the results with ensembles of single-particle orbits integrated directly in the same potential and the same drag prescription. An attempt is made to gauge the validity of the Chandrasekhar formula by comparison with restricted N-body solutions. It is found that the orbit-averaged evolution is consistent with such simulations.
Statler, Thomas S.↗
Computer experiments on the effect of retrograde stars in disk galaxies
Using large-scale N-body calculations for flat disk galaxies, we examine the effect of reversing the angular momentum for various fractions of the stars upon the global bar-forming mode. The initial conditions for these simulations are based on stationary states of two classes of models: the isochrones studied recently by Kalnajs by means of linear theory, and a model resembling the Schmidt model of our own Galaxy. In both cases, as the fraction of retrograde stars is increased, the growth of the bar-forming mode is inhibited (although not eliminated). These N-body results for the isochrones agree with the predictions of linear theory, quantitatively as well as qualitatively.
Zang, T. A.↗
Navigation systems
The elements of the measurement and communications network comprising the global deep space navigation system (DSN) for NASA missions are described. Among the measurement systems discussed are: VLBI, two-way Doppler and range measurements, and optical measurements carried out on board the spacecraft. Processing of navigation measurement is carried out using two modules: an N-body numerical integration of the trajectory (and state transition partial derivatives) based on pre-guessed initial conditions; and partial derivatives of simulated observables corresponding to each actual observation. Calculations of velocity correction parameters is performed by precise modelling of all physical phenomena influencing the observational measurements, including: planetary motions; tracking station locations, gravity field structure, and transmission media effects. Some of the contributions to earth-relative orbit estimate errors for the Doppler/range system on board Voyager are discussed in detail. A line drawing of the DSN navigation system is provided.
Jordan, J. F.↗
The spiral-compact galaxy pair AM 2208-251: Computer simulations versus observations
The system AM2208-251 is a roughly edge-on spiral extending east-west with a smaller round compact E system about 60 arcsec east of the spiral nucleus along the major axis of the spiral. Bertola, Huchtmeier, and Zeilinger (1990) have presented optical spectroscopic as well as single dish 21 cm observations of this system. Their spectroscopic data show, via emission lines lambda lambda 3727-29A, a rising rotation curve near the nucleus. These spectroscopic observations may indicate a tidal interaction in the system. In order to learn more about such pairs, the authors simulated the interaction using the computer model developed by Miller (1976 a,b, 1978) and modified by the authors (Byrd 1986, 1987, 1988). To do the simulation they need an idea of the mutual orbits of the two galaxies. Their computer model is a two-dimensional polar N-body program. It consists of a self-gravitating disk of particles, within an inert axially symmetric stabilizing halo potential. The particles are distributed in a 24(radial) by 36(azimuthal) polar grid. Self consistent calculations can be done only within the grid area. The disk is modeled with a finite Mestel disk, where all the particles initially move in circular orbits with constant tangential velocities (Mestel 1963), resulting in a flat rotation curve. The gas particles in the spiral's disk, which make up 30 percent of its mass, collide in the following manner. The number of particles in each bin of the polar grid is counted every time step. If it is greater than a given critical density, all the particles in the bin collide, obtaining in the result the same velocities, equal to the average for the bin. This process produces clumps of gas particles-the star formation sites. The authors suppress the collision in the inner part of the disk (within the circle r = 6) to represent the hole seen in the gas in the nuclear bulge of spirals. They thus avoid spurious effects due to collisions in that region. They also varied the size of the collisional bins, which did not affect their conclusions.
Klaric, Mario↗
Space Trajectories Error Analysis (STEAP) Programs. Volume 1: Analytic manual, update
Manual revisions are presented for the modified and expanded STEAP series. The STEAP 2 is composed of three independent but related programs: NOMAL for the generation of n-body nominal trajectories performing a number of deterministic guidance events; ERRAN for the linear error analysis and generalized covariance analysis along specific targeted trajectories; and SIMUL for testing the mathematical models used in the navigation and guidance process. The analytic manual provides general problem description, formulation, and solution and the detailed analysis of subroutines. The programmers' manual gives descriptions of the overall structure of the programs as well as the computational flow and analysis of the individual subroutines. The user's manual provides information on the input and output quantities of the programs. These are updates to N69-36472 and N69-36473.
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Spiral structure produced by tidal interaction of galaxies
Simulation of a close passage of two galaxies where the self-gravity of the disk stars is taken into account was performed with the aid of a large-scale N-body model (Hohl and Hockney, 1969; Hohl, 1972). The calculation was performed by perturbing an initially stable axisymmetric disk consisting of 100,000 stars by the passage of a companion galaxy having one-fourth the mass of the primary galaxy. Parameters appropriate for M 51 and its companion NGC 5195 were used. The results show the evolution of a weak two arm spiral. The effect of large random velocities on the formation of spiral structure was studied by plotting the spatial distribution of stars for various velocity intervals. The spiral structure is quite pronounced for stars with the lower velocity dispersion, but it can hardly be detected for stars with higher velocities. The tidal interaction causes only slight changes in the azimuthally averaged density distribution.
Hohl, F.↗
Simulated trajectories error analysis program, version 2. Volume 2: Programmer's manual
A series of three computer programs for the mathematical analysis of navigation and guidance of lunar and interplanetary trajectories was developed. All three programs require the integration of n-body trajectories for both interplanetary and lunar missions. The virutal mass technique is used in all three programs. The user's manual contains the information necessary to operate the programs. The input and output quantities of the programs are described. Sample cases are given and discussed.
Vogt, E. D.↗
Cloud-particle galactic gas dynamics and star formation
Galactic gas dynamics, spiral structure, and star formation are discussed in relation to N-body computational studies based on a cloud-particle model of the interstellar medium. On the small scale, the interstellar medium is seen as cloud-dominated and supernova-perturbed. It is noted that the cloud-particle model simulates cloud-cloud collisions, the formation of stellar associations, and supernova explosions as dominant local processes. On the large scale, in response to a spiral galactic gravitational field, global density waves and galactic shocks develop having large-scale characteristics similar to those found in continuum gas dynamical studies. Both the system of gas clouds and the system of young stellar associations forming from the clouds figure in the global spiral structure. However, with the attributes of neither assuming a continuum of gas (as in continuum gas dynamical studies) or requiring a prescribed equation of state (such as the isothermal condition), the cloud-particle picture retains much of the detail lost in earlier work. By detail is meant the small-scale features and structures so important in understanding the local, turbulent state of the interstellar medium as well as the degree of raggedness often seen to be superposed on the global spiral structure.
Roberts, W. W., Jr.↗
Collisional dynamics of perturbed particle disks in the solar system
Theoretical and computational studies were carried out on galactic and planetary disks. With the goal of addressing important open questions centered on galactic structure, the cloudy interstellar medium, giant molecular clouds, and star formation in galactic disks and the collisional dynamics of perturbed particulate matter in planetary disks, focus was largely on the self-gravitational effects, dissipative effects, and collisional dynamics of cloud-particle disks. N-body, 'cloud-particle' computational algorithms were developed for the purpose of isolating the role of gaseous self gravity from the roles of other dominant physical mechanisms and dynamical processes, e.g. the collisional dynamics and dissipative processes. The efforts focused largely on galactic disks show that observational constraints provide stringent tests of the numerical simulation techniques developed. Self gravitational effects of the galactic interstellar medium's gas clouds are included by means of Fourier Transform technique.
Roberts, William W., Jr.↗
Relaxation time in disk galaxy simulations.
An initially stationary and stable axisymmetric disk of stars with a mass spectrum of stars is used to determine the collisional relaxation time. The relaxation time as determined from the rate of energy equipartition was found to be 560 rotation periods for stars with 10 times the mean star mass and was 1700 rotation periods for stars with 0.55 times the mean star mass. These times are in general agreement with theoretical predictions for the relaxation time of the two mass groups. The results show that the model used for the large-scale gravitational N-body calculations is indeed 'collisionless.'
Hohl, F.↗