The Structure, Stability, and Dynamics
of Self-Gravitating Systems

Fall Semester, 1997
Project #1

Eric Barnes

Rotating, Isothermal Equilibria

Assignment (by J.E. Tohline):

As I've explained in the introductory paragraphs of the section entitled, "Governing Equations for Axisymmetric Objects in Simple Rotation," as a rule the equilibrium properties of rotating, self-gravitating configurations are not describable in terms of analytical functions. One notable exception to this rule is models of (n = 0) Maclaurin Spheroids, which I have already discussed in some detail in the book. The other notable exception is an analytical solution for the equilibrium structure of rotating, (n = ) isothermal gas clouds derived by Hayashi, Narita and Miyama (1982; hereafter HNM). You should carefully review this work, then present a clear discussion of the equilibrium structure of rotating, isothermal spheres. The presentation should be in an HTML format, similar to the presentation that already has been developed in the context of Maclaurin Spheroids.

Ideally, you also should draw a connection between the structural properties of the HNM models and the known properties of equilibrium, isothermal spheres (being summarized by Lynne Valencic).

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