The virial theorem and the stability of clusters of galaxies '

1961 ◽  
Vol 66 ◽  
pp. 572 ◽  
Author(s):  
D. Nelson Limber
Keyword(s):  
Virial Theorem ◽  
Clusters Of Galaxies ◽  
The Stability

Resonance, Chaos and Stability in the General Three-Body Problem

2007 ◽  
Vol 3 (S246) ◽  
pp. 199-208 ◽  
Author(s):  
R. A. Mardling
Keyword(s):  
Chaos Theory ◽  
Clusters Of Galaxies ◽  
Three Body Problem ◽  
Orbital Elements ◽  
Resonance Overlap ◽  
Practical Algorithm ◽  
The Stability ◽  
Three Body ◽  
First Time ◽  
Analytical Expressions

AbstractThree-body stability is fundamental to astrophysical processes on all length and mass scales from planetary systems to clusters of galaxies, so it is vital we have a deep and thorough understanding of this centuries-old problem. Here we summarize an analytical method for determining the stability of arbitrary three-body hierarchies which makes use of the chaos theory concept of resonance overlap. For the first time the dependence on all orbital elements and masses can be given explicitly via simple analytical expressions which contain no empirical parameters. For clarity and brevity, analysis in this paper is restricted to coplanar systems including a description of a practical algorithm for use in N-body and other applications. A Fortran routine for arbitrarily inclined systems is available from the author, and animations of stable and unstable systems are available at www.maths.monash.edu.au/~ro/Capri.

Nonlocal Gravity and Dark Matter

2017 ◽  
Author(s):  
Bahram Mashhoon
Keyword(s):  
Dark Matter ◽  
Solar System ◽  
Observational Data ◽  
Virial Theorem ◽  
Spiral Galaxies ◽  
Clusters Of Galaxies ◽  
The Galaxy

The implications of linearized NLG for the gravitational physics of the Solar System, spiral galaxies and nearby clusters of galaxies are critically examined in this chapter. In the Newtonian regime, NLG involves a reciprocal kernel with three length parameters. We discuss the determination of these parameters by comparing the predictions of the theory with observational data. Furthermore, the virial theorem for the Newtonian regime of NLG is derived and its consequences for nearby “isolated” astronomical systems in virial equilibrium are investigated. For such a galaxy, in particular, the galaxy’s baryonic diameter namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time, is predicted to be larger than the basic nonlocality lengthscale, which is about 3 kpc, times the effective dark matter fraction of the galaxy.

The stability of clusters of galaxies

1961 ◽  
Vol 66 ◽  
pp. 566 ◽  
Author(s):  
Sidney van den Bergh
Keyword(s):  
Clusters Of Galaxies ◽  
The Stability

scholarly journals Dynamics and Clusters of Galaxies

1974 ◽  
Vol 62 ◽  
pp. 273-284
Author(s):  
D. G. Saari
Keyword(s):  
Virial Theorem ◽  
Gravitational Force ◽  
Clusters Of Galaxies ◽  
Expanding Universe ◽  
Evolution Of The Universe ◽  
Mathematical Probability ◽  
The Masses ◽  
The Universe

Under the assumption that the inverse square central force law is a good approximation to the gravitational force, at least for large distances, the different possibilities for the evolution of the Universe are sketched. Several of the possibilities lead naturally to a dynamical classification of clusters of galaxies in an expanding universe. In one of the classifications the galaxies must define configurations which are functions of the masses. The virial theorem approach of determining masses of galaxies in a cluster is briefly examined. Some tentative statements concerning a dynamical explanation of the local hypothesis for quasars are advanced. Finally, the role of mathematical probability in predicting the behavior of the Universe is discussed.

Open discussion

1982 ◽  
Vol 99 ◽  
pp. 605-613
Author(s):  
P. S. Conti
Keyword(s):  
Buenos Aires ◽  
Large Mass ◽  
List Type ◽  
Common Phenomenon ◽  
Open Discussion ◽  
The Stability ◽  
Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

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