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Isothermal spheres in the modified dynamics
Milgrom, M.
AA(Weizmann Institute of Science, Rehovot, Israel)
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 287, Dec. 15, 1984, p. 571-576. (ApJ Homepage)
Publication Date:
NASA/STI Keywords:
Celestial Sphere, Galactic Clusters, Globular Clusters, Gravitational Effects, Isotherms, Stellar Motions, Anisotropy, Asymptotic Methods, Integral Equations, Newton Theory
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Dynamics which differ from the Newtonian in the limit of small accelerations are used in the present consideration of self-gravitating isotropic and anisotropic isothermal spheres (IS), which serve as reference models for such astrophysical objects as globular and open clusters, galactic bulges, and clusters of galaxies. In these spheres, both the radial and the tangential velocity dispersions are independent of the radius. All ISs have finite mass, and their density decreases asymptotically according to a power law. There is an absolute maximum to the average surface density an IS can have, irrespective of the velocity dispersion, anisotropy ratio, or any other property of the IS. The mass of an IS is nearly proportional to the fourth power of the space velocity dispersion, sigma. Attention is given to a class of solutions for which acceleration is much smaller than the acceleration constant everywhere in the sphere, as is the case in clusters of galaxies, dwarf ellipticals, and some open clusters.

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