Present a clear discussion of the equilibrium structure of nonrotating,
isothermal spheres. The presentation should be in an HTML format,
similar to the presentation that already has been developed
in the context of
Spherical Polytropes.
More specifically, in setting up the relevant governing equations
that must be solved in order to derive the structure of isothermal
spheres, you probably should adopt
"Solution Technique 2,"
but restructure the form of the
Lane-Emden equation so that it works for the case of n = ¥.
Then, the solution of this modified Lane-Emden equation should be presented
in a format similar to the presentation that already has been made for
"Spherical, n = 1 Polytropes."
Finally, discuss how the properties of this solution are modified if
the isothermal sphere is embedded in a diffuse, hot external medium.
This will lead to discussions of the structure of Bonner-Ebert Spheres.