User:Tohline/Apps/DysonWongTori
Self-Gravitating, Incompressible (Dyson-Wong) Tori
Much of the introductory material of this chapter has been drawn from the paper by Tohline & Hachisu (1990) titled, The Breakup of Self-Gravitating Rings, Tori, and Accretion Disks.
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Overview
In his pioneering work, Dyson (1893) used analytic techniques to determine the approximate equilibrium structure of axisymmetric, uniformly rotating, incompressible tori. Wong (1974) extended Dyson's work, using numerical techniques to obtain more accurate — but still approximate — equilibrium structures for incompressible tori having solid body rotation. Eriguchi & Sugimoto (1981) and Hachisu, Tohline & Eriguchi (1987) have mapped out the full sequence of Dyson-Wong tori, beginning from a bifurcation point on the Maclaurin spheroid sequence.
References
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- P. H. Chavanis (2006, International Journal of Modern Physics B, 20, 3113 - 3198) — Phase Transitions in Self-Gravitating Systems
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- Gunnar Randers (1942, ApJ, 95, 88) — The Equilibrium and Stability of Ring-Shaped 'barred SPIRALS'.
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